Electoral competition in the presence of identity politics

Abstract

This paper studies the effects of cultural identity on electoral and policy outcomes when voters are “behavioral.” Building on the evidence that voters assess political or economic events through the lens of their partisan identifications, we analyze an election between two office-motivated candidates in which voters over-reward or under-punish the candidate that shares their cultural identity. Focusing on issues with cultural as well as distributional implications for voters such as immigration and the cultural divide based on nativism as the source of identity politics, we find that the candidates’ equilibrium policies are always preferred by the electorally dominant cultural group to the policy that would be optimal if policies only had distributional consequences. We also show that candidates do not necessarily target their own cultural bases in equilibrium. Furthermore, stronger identity politics increases policy polarization. Our findings contribute to the debates on the decoupling of voting behavior from economic interests, and the rise of immigration, trade protectionism, or engagement with global governing institutions as electoral issues that can shift historical voting patterns.

Keywords

Identity politics partisanship immigration protectionism nativism Downsian competition

1. Introduction

Partisanship and identity politics are playing increasingly important roles across the politics of Western democracies.¹ Moreover, cultural identity and values are increasingly replacing more traditional lines of division such as income as the bases on which partisanship and identity politics are defined. For instance, in a recent survey of political values among American voters, the Pew Research Center (2017) found record gaps between Democrats and Republicans in their attitudes toward the role of government in helping the poor, immigration, or the value of diplomacy in conducting foreign affairs, while demographic gaps have remained more or less constant.

Evidence suggests that voters assess political and economic events through the lens of their partisan identities.² In this paper, we study the effects of cultural identity politics on electoral and policy outcomes when voters judge candidates’ policy platforms subjectively. We demonstrate how candidates can take advantage of the cultural divisions in the electorate through strategic policy choices. As a theoretical contribution, we introduce such “behavioral” voters to an otherwise-standard Downsian model to generate equilibrium policy divergence and novel results on voter targeting.

In their seminal book, Campbell et al. (1960) state that “identification with a party raises a perpetual screen through which the individual tends to see what is favorable to his partisan orientation. The stronger the party bond, the more exaggerated the process of selection and perceptual distortion will be.” Experimental evidence such as in Chen and Li (2009) supports this view, indicating that individuals are more likely to reward and less likely to punish another individual they share a group identity with. However, even though growing identity politics is a widely documented phenomenon, the policy implications of voters’ identity-based assessments of candidates have received scant attention within a theoretical setting. Given the evolving nature of partisanship toward identity politics and its influence on voting behavior as summarized in Figure 1, this constitutes our focus in this paper.

Figure 1.

Identity politics and voting behavior.

We consider issues with cultural as well as distributional consequences in order to illustrate the role cultural identity plays in voting behavior and policy-making. Examples of such issues include immigration, trade protectionism, foreign aid, acceptance of refugees, or engagement with supranational institutions such as the United Nations. These issues increasingly define partisanship, as evidenced by, for instance, a Pew Research Center survey that had reported in 1994 that $30$ % of Republicans and $32$ % of Democrats expressed pro-immigration views while more recently finding that $84$ % of Democrats and only $42$ % of Republicans now think immigrants strengthen the country.³ A similar partisan gap exists on the question of whether steel and aluminum tariffs are good for the US, with $58$ % of Republicans and only $22$ % of Democrats supporting higher tariffs.⁴ It is possible to argue that attitudes toward these issues are related to identity politics. There also exists evidence that these attitudes have shaped voting outcomes in the recent past, in particular boosting the candidacies of some right-wing parties.⁵

The model features two office-motivated candidates who compete for the support of a culturally divided electorate. Each candidate has a fixed characteristic that represents her core ideology (reflecting her preference for, for instance, welfare programs or gun control), is defined by a cultural identity that is either open or nativist, and strategically chooses a policy to maximize her vote share. As explained previously, this policy can represent restrictions on immigration, trade protectionism, foreign aid, etc. Each voter is also described by his core ideology and his cultural identity as either open or nativist, where this identity drives preferences for the cultural implications of the policy. For instance, a nativist voter would be opposed to the cultural presence of immigrants in the society. Upon observing the candidates’ core ideologies, cultural identities and policy platforms, voters vote sincerely for their preferred candidate.

The voters’ core ideologies are uniformly distributed on some interval. On the other hand, although all voters agree on their assessments of the distributional consequences of the policy, their preferences regarding its cultural aspects depend on their cultural identity. Furthermore, based on the evidence that their cultural identity-based attachments guide voters’ judgments, we let the relative weight with which voters evaluate the cultural versus the distributional aspects of a given policy depend on the candidate. This dependence takes the form of amplifying voters’ cultural utility or disutility from a given policy when it is proposed by the candidate whose exogenous identity conforms with the policy’s cultural affiliation. We make the additional assumption that a policy’s cultural affiliation is determined relative to an exogenous reference point such as the status quo or a policy based on recent historical experience.

Our behavioral voting assumption implies that a policy deemed nativist based on the reference point yields greater (lower) cultural utility to the nativist voters and greater (lower) cultural disutility to the open voters if it is proposed by the nativist (open) candidate. Likewise, an open policy yields greater (lower) cultural utility to the open voters and greater (lower) cultural disutility to the nativist voters if it is proposed by the open (nativist) candidate. For example, voters may be divided based on their cultural attitudes toward immigrants, in which case nativist voters would reward a restrictionist immigration policy more when proposed by the nativist candidate. Likewise, if voters are divided based on their nationalist stands on trade, protectionist voters may be more receptive to trade agreements if a protectionist administration leads the negotiations.

In equilibrium, candidates target the swing voters from each cultural group to maximize their vote shares. A novel implication of our model is that it is possible in equilibrium to vote against a candidate despite preferring both her core ideology and policy to the other candidate’s. Such voting behavior may be observed if the candidates’ cultural identities are sufficiently strong that the behavioral implications of cultural identity politics dominate the fundamental issues of concern to the voters. In particular, a voter may over-reward or under-punish the policy of the candidate that shares his cultural identity to such an extent that his fundamental preference for the core ideology and policy of the other candidate may no longer matter. Accordingly, our model can account for recent cross-voting electoral phenomena such as working class Obama–Trump voters or previous Labour voters supporting Brexit.

In contrast to the symmetric equilibrium of the standard Downsian model, cultural identity politics leads to policy polarization when voters are behavioral. Moreover, the equilibrium of our model features the possibility of both cross-voting and targeting of the rival’s cultural base, phenomena that most standard models cannot simultaneously capture. By incorporating identity politics into a Downsian framework, we offer a model in which two important contemporary observations related to increasing policy polarization between candidates and the weakening of existing voter alignments can simultaneously arise in equilibrium.

We find that the candidates’ equilibrium policies are always preferred by the electorally dominant cultural group to the policy that would be optimal in the absence of a cultural component to voting.⁶ In other words, the electorally dominant group always succeeds in manipulating policies toward its preferred cultural direction in equilibrium, distorting them away from the unique optimum that maximizes all voters’ consumption utilities.

Our results indicate that a candidate does not necessarily target her own cultural base in equilibrium. Specifically, while it is possible that the open candidate proposes the more open and the nativist candidate proposes the more nativist policy in equilibrium, this ceases to be the case when a cultural group cuts sufficient slack to its own candidate in a way that allows her to target the opposite group. Overall, although candidates always take positions on the same side of the policy that would be optimal in the absence of a cultural component to voting, whether they lean deeper into their own base or target the opposite cultural group by exploiting their base’s partisan loyalty depends on the type of equilibrium. The relative strength of distributional versus cultural motives behind the candidates’ optimal policies guides their sorting on the policy spectrum.

We find that the candidates respond to greater cultural divisions (or more intense cultural preferences) in the electorate by increasing their targeting of the electorally dominant group. The same result is obtained if the cultural aspects of the policy gain prominence with regards to all other concerns in voting decisions.⁷ Moreover, equilibrium policies move in the preferred direction of the voter group whose cultural preferences intensify relative to the other group. For instance, our model predicts more open policies in response to media coverage on successful integration programs for immigrants if this leads to deeper cultural support from the open voters and milder opposition from the nativist voters. In addition, we find that policies become more polarized as identity politics strengthens (i.e., as voters over-reward or under-punish the candidate that shares their cultural identity to a greater extent), increasing the intensity of behavioral voting.

In response to growing identity politics, our model predicts the decoupling of the candidates’ vote shares to a greater extent from their core ideologies, a traditional basis of electoral division. We argue that the saliency of culturally tinted electoral issues can transform the nature of electoral competition by offering identity politics as a way for a candidate to overcome her disadvantage due to her core ideology. For instance, a traditionally right-wing candidate in terms of economic ideology can gain vote share among left-wing voters if her cultural identity allows her to capitalize on an electoral issue such as immigration. Accordingly, our results can shed light on how cultural identity politics and behavioral voting based on it can pave the way for shifts in traditional voting patterns.

The rest of the paper is organized as follows. Following a discussion of the related literature in the next section, Section 3 describes the model, Section 4 contains the main analysis and results of the paper, and Section 5 concludes.

2. Related literature

The contributions this paper aims to make are two-fold. First, we focus on cultural divisions among voters as an increasingly important source of identity politics and analyze the policy implications. Second, we introduce identity-based assessments of candidates’ policies as a novel basis for behavioral voting.

A recent and growing literature is focused on understanding the causes and effects of political extremism and populism. Among these studies, the most closely related are those by Eguia and Giovannoni (2019), who explain extremism as a tactical investment by a party into its future ability to offer an alternative to mainstream policies, and Diermeier and Li (2019), who explain polarization as an outcome of the voters’ tendencies to respond more to policy deviations by their own party. A model of populism that also considers voters’ reference-dependent preferences is provided by Panunzi et al. (2020), who study an election between an incumbent and a riskier opponent and obtain in equilibrium that the risky opponent can put together a coalition of rich and economically disadvantaged voters by proposing lower taxes. In addition, Karakas and Mitra (2020) offer a model of how income inequality can propel support for outsider candidates.⁸ In this paper, we offer an alternative take on extremism by focusing on culturally tinted electoral issues such as immigration to explain policy extremism as the strategic response of candidates to the existing cultural divisions in the electorate.

There exists a large body of literature on reconciling the convergence prediction of the classical Downsian model with the observed policy polarization in politics. In this vein, traditional models with valence in which all voters have the same preferences for the candidates’ qualitative characteristic, such as those from Ansolabehere and Snyder (2000), Groseclose (2001), Aragones and Palfrey (2002), and Schofield (2004), produce a mixed strategy equilibrium with expected policy divergence.⁹ This happens as the valence-advantaged and disadvantaged candidates possess different incentives on mimicking each other’s policies. Although the candidates’ fixed core ideologies in our model constitute a valence term, each voter also has a core ideology and, ceteris paribus, prefers the candidate with a core ideology closer to his.¹⁰ Based on our assumptions on the distribution of these core ideologies in the electorate and the candidates’ vote shares, we establish the existence of a divergent equilibrium, where this divergence ensues not in expectation owing to the candidates’ valence differences but owing to behavioral voting based on the candidates’ cultural identities in a pure strategy equilibrium.

More specifically, we build a voting model based on Lindbeck and Weibull (1987) with differentiated candidates as in Krasa and Polborn (2014) that can generate policy divergence. Krasa and Polborn (2014) study electoral competition between two office-motivated candidates that differ not only in their fixed characteristics but also in their abilities to provide a public good, while voters have both economic and social preferences. As is the case in this paper, they establish the dependence of equilibrium policies on the voters’ social as well as economic preferences. We build on this literature by introducing cultural identity as a novel source of candidate differentiation that constitutes the basis for the voters’ identity-based assessments of the candidates’ policies. Unlike valence, the candidates’ cultural identities are not additively separable from policies in the voters’ utilities in our model, affecting how voters evaluate policy platforms and consequently leading to policy divergence.¹¹

Dixit and Londregan (1996), who study pork-barrel spending when voters have partisan loyalties and the parties are differentiated in their targeting ability, provide a closely related model to ours. They find that each party targets the voter group it has a targeting advantage with, which we also show holds in equilibrium under certain conditions. If the parties also differ in their ability to levy taxes on different voter groups and this advantage dominates, each party taxes the voter group that they can tax more efficiently, to the benefit of other groups. In contrast, such an equilibrium in which each candidate targets the other’s core voter group (i.e., cross-targeting) does not require an additional source of candidate differentiation to obtain in our model. Specifically, we show that cultural identity politics and its behavioral voting implications are sufficient for obtaining in equilibrium observations such as cross-targeting by the candidates and cross-voting by the voters.¹²

An extensive literature documents the growth in identity politics. In this paper, we study the electoral and policy implications of this trend when cultural attachments guide voting behavior. In this regard, related studies that analyze the effects of social identities include Akerlof and Kranton (2000), who apply their seminal idea to various different strategic settings, Glaeser et al. (2005) on the parties’ incentives to energize their base through policies based on religious identities, and Dickson and Scheve (2006) on identity-based appeals by candidates during campaigns. Closely related papers include those by Grossman and Helpman (2020), who study electoral competition over trade policy in an environment in which social identity trends result in changes to trade policy, and Besley and Persson (2019), who model identity politics as instigating a feedback mechanism between policies and political preferences to find that immigration policies reflect the power of nationalism in the society.¹³

The behavioral focus of our model builds on a growing literature in behavioral political economy. For example, Levy and Razin (2015) analyze elections when voters fail to consider the correlation in their sources of political information and find that this cognitive bias may in fact improve information aggregation. Diermeier and Li (2017) ask whether accountability through elections is still viable when voters are forgetful and answer in the affirmative. Nunnari and Zapal (2020) provide a model in which voters focus disproportionately on policies over which the proposed options show more disagreement. To the best of the authors’ knowledge, ours is one of the first papers (along with Diermeier and Li, 2019) to study partisan evaluation of candidates’ policies as a behavioral problem.

3. The model

Two office-motivated candidates compete for the support of a continuum of voters. Each candidate has a fixed characteristic that represents her core ideology, is defined by a cultural identity, and announces a policy before the election. The candidates fully commit to implementing their policy announcements in case of their election. Based on the candidates’ core ideologies, cultural identities, and policy commitments, voters vote sincerely for their preferred candidate.

3.1. Basics

We denote the fixed core ideology of candidate $j$ as $σ_{j} \in R$ for $j \in {L, R}$ and let $σ_{L} < σ_{R}$ . For instance, $σ_{j}$ may represent candidate $j$ ’s stand on income inequality and redistribution, or any other characteristic that is not related to policy.

In addition, each candidate $j \in {L, R}$ has a cultural identity $c_{j} \in {n, o}$ such that $c_{L} \neq c_{R}$ , where $c_{j} = n$ indicates that candidate $j$ is a nativist and $c_{j} = o$ indicates that she is open. Without loss of generality, we fix $c_{L} = o$ and $c_{R} = n$ for clarity.¹⁴ Given the candidates’ history in politics, neither their core ideologies nor cultural identities can be credibly changed before voting takes place.

Before the election, each candidate $j$ announces a policy $p_{j} \in [0, 1]$ on an issue that has cultural as well as distributional consequences for the voters such as immigration or trade protections, where $p_{j} = 0$ indicates no restrictions and $p_{j} = 1$ indicates maximum restrictions. In general, whereas a high policy represents tight restrictions, such as through mass deportations or high tariffs, a low policy implies greater openness through, for instance, guest worker programs or free trade agreements.¹⁵

Similar to the candidates, each voter $i$ belongs to the cultural identity group $h \in {n, o}$ and has a core ideology denoted $σ_{ih} \in R$ . A fraction $α_{n} \in (0, 1)$ of voters are nativists and the remaining fraction $α_{o} = 1 - α_{n}$ are open. The core ideologies $σ_{ih}$ of voters $i$ in group $h$ are uniformly distributed with the continuous cumulative distribution function (CDF) $F_{h}$ and density $f_{h}$ for $h = n, o$ , which we accordingly denote by $f_{h} (σ_{h}) \equiv {\bar{f}}_{h}$ . The candidates can observe these distributions from which the voters’ core ideologies are drawn.

3.2. Payoffs

We focus on policies that have distributional as well as cultural consequences for the voters. For instance, although voters may perceive immigration to have an effect on their wages, it also adds new members to the society. Hence, we expect voters to evaluate an immigration policy based on both economic and cultural grounds.¹⁶

Although voters within each cultural group have the same preferences on the cultural consequences of a candidate’s policy, they differ in how they value her core ideology. We also simplify by assuming that all voters share the same preferences on the distributional effect of the policy.¹⁷

Accordingly, the utility that voter $i$ in cultural group $h$ receives from candidate $j$ , conditional on this candidate’s election, can be written as

u_{ih} (p_{j}; σ_{j}, c_{j}) = - η (σ_{j} - σ_{ih})^{2} + w (p_{j}) + λ_{j} (p_{j}) z_{h} (p_{j})

(1)

where $η > 0$ is a parameter common to all voters that represents the relative salience of the candidates’ core ideologies to policy. The policy components of equation (1) are described in the following.

The function $w (p_{j})$ in (1) represents the voters’ consumption preferences with regards to the policy. We assume it is a twice-differentiable and strictly concave function that satisfies $w' (0) > 0$ and $w' (1) < 0$ , exhibiting an inverted U-shape. For instance, in a competitive economy in which the only factors of production are capital and labor that earns its marginal product, fixing the amount of capital would imply that an influx of immigrants into the labor force unambiguously decreases the prevailing wage in the economy. Thus, voters would be hurt by immigration through a decrease in their wages. At the same time, they would benefit from a greater variety of consumption goods produced by an expanded work force due to immigration, thereby ensuring, under standard assumptions, that some immigration is preferred to none even for purely consumption-related reasons. Likewise, in a factor-proportions model of international trade, a more protectionist trade policy in a capital-abundant economy will increase workers’ wages while restricting the variety of consumption goods, leading to a similar $w (p_{j})$ function.

The function $λ_{j} (p_{j}) z_{h} (p_{j})$ captures the voters’ cultural preferences toward the policy. The main contribution of our model, behavioral voting based on cultural identity politics, manifests itself in this term. Whereas the function $z_{h} (p_{j})$ represents a group- $h$ voter’s cultural like or dislike of the policy, the function $λ_{j} (p_{j})$ yields the relative weight with which voters evaluate the cultural versus the distributional aspects of any given policy proposed by candidate $j$ .

We assume that voters evaluate the cultural consequences of a policy relative to a common reference point $\bar{p} \in (0, 1)$ , which may be the status quo or a centrist policy such as $p_{j} = \frac{1}{2}$ . We assume that voters perceive any policy $p_{j} > \bar{p}$ as nativist and any $p_{j} < \bar{p}$ as open.¹⁸ For tractability, we let $z_{n} (p_{j}) = β_{n} (p_{j} - \bar{p})$ and $z_{o} (p_{j}) = β_{o} (\bar{p} - p_{j})$ for $j \in {L, R}$ , where $β_{h} > 0$ for both $h$ so that $z_{h} (p_{j})$ is strictly increasing for $h = n$ and strictly decreasing for $h = o$ . We refer to the fact that nativist and open voters have opposite cultural preferences as the “cultural divide” in the electorate.

Identity politics, which we interpret as the voters’ attachment to the candidate that shares their cultural identity, forms the basis of our behavioral assumption: the cultural utility (or disutility) $z_{h} (p_{j})$ that a given policy $p_{j}$ yields for a group- $h$ voter is amplified when it is proposed by the candidate $j$ whose cultural identity $c_{j}$ conforms with her policy’s cultural affiliation. Specifically, a nativist policy $p_{j} > \bar{p}$ yields greater (lower) cultural utility to the nativist voters and greater (lower) cultural disutility to the open voters if $j$ is the nativist (open) candidate (compared with their utilities or disutilities if the same policy was proposed by the other candidate). Similarly, an open policy $p_{j} < \bar{p}$ yields greater (lower) cultural utility to the open voters and greater (lower) cultural disutility to the nativist voters if $j$ is the open (nativist) candidate.

Formally, because $c_{L} = o$ and $c_{R} = n$ , we let $λ_{L} (p) > λ_{R} (p)$ for any given $p_{L} = p_{R} \equiv p < \bar{p}$ , and $λ_{L} (p) < λ_{R} (p)$ for any given $p_{L} = p_{R} \equiv p > \bar{p}$ . In our analysis, we use the simplest functional form for $λ_{j} (p_{j})$ that still allows us to capture the model’s essence by letting

λ_{L} (p_{L}) = {\begin{matrix} \bar{λ} & if p_{L} \leq \bar{p} \\ \underline{λ} & otherwise \end{matrix}

(2)

and

λ_{R} (p_{R}) = {\begin{matrix} \underline{λ} & if p_{R} \leq \bar{p} \\ \bar{λ} & otherwise \end{matrix}

(3)

where $\bar{λ} > \underline{λ} > 0$ .

3.3. Discussion of the main assumptions

To reiterate, each candidate $j$ is described by the triplet $(σ_{j}, c_{j}, p_{j})$ before voting takes place. Of these three dimensions, only the policy $p_{j}$ is strategic, and only the core ideology $σ_{j}$ and policy $p_{j}$ enter the voters’ utilities directly. The fixed cultural identity $c_{j}$ affects the utility that voters would receive from the election of candidate $j$ only indirectly by affecting the weight with which the cultural versus the distributional consequences of a given policy $p_{j}$ are evaluated. In particular, although the core ideology $σ_{j}$ is additively separable from the policy $p_{j}$ in the voters’ utility functions, this is not the case for cultural identity $c_{j}$ .

Voters are divided based on their like or dislike of the cultural consequences of the policy, which captures their nativism or openness. The behavioral aspect of our model is due to identity politics, which implies that voters have a partisan attachment to the candidate that shares their cultural identity, and either over-reward or under-punish this candidate’s policy depending on its affiliation.

We motivate the assumption that voters assess the cultural consequences of a given policy differently depending on the candidate proposing it in two different ways. First, there exists widespread evidence that partisanship and identity influence voters’ assessments of various political and economic outcomes. For instance, Bartels (2002) and Gerber and Huber (2009) document and analyze the phenomenon that voters positively judge the state of the economy based on whether their party holds the executive branch.¹⁹ More generally, Chen and Li (2009) demonstrate using an experiment that participants are more likely to reward and less likely to punish a member of their group respectively for good and bad behavior. In this paper, we build on the evidence that partisanship influences voting behavior and that voters’ cultural identities constitute an important source of their partisan affiliations to motivate the candidate-specific policy assessments that we assume voters perform.²⁰

Our second motivation is based on theories of intent. It has long been recognized that people evaluate actions by taking into account the intent and motives they perceive behind them.²¹ Accordingly, we argue here that voters might consider the candidates’ perceived intentions when evaluating policies. For instance, upon observing a nativist policy proposed by an open candidate, voters may deduce that the candidate’s “heart is not in it” and not be as energized, positively or negatively, by the policy’s nativism.

Our model implies that the nativist (open) candidate has an unambiguous policy advantage with the nativist (open) voters whenever the two candidates propose the same policy, regardless of where this policy lies relative to the reference point. At the same time, even while her cultural identity shapes the relative weight with which the cultural versus the distributional aspects of her policy are evaluated, our model allows a candidate the ability to influence this weight through her policy choice.

4. Equilibrium

Equation (1) suggests that voters’ policy utility is candidate-specific. Thus, in our set-up, a voter does not necessarily vote solely based on his core ideology and therefore always for the same candidate when the two candidates propose the same policy. This is because the different degrees to which the candidates emphasize the distributional versus the cultural aspects of the same policy may result in voters switching their votes depending on the policy proposed.²² The following remark illustrates this property that voter preferences have in our model.

Remark 1. Consider a nativist voter $i$ and let $| σ_{in} - σ_{R} | > | σ_{in} - σ_{L} |$ . Suppose $p_{L} = p_{R} \equiv p < \bar{p}$ is such that $u_{in} (p; σ_{L}, c_{L}) \geq u_{in} (p; σ_{R}, c_{R})$ , i.e.,

η [(σ_{R} - σ_{in})^{2} - (σ_{L} - σ_{in})^{2}] \geq [λ_{R} (p) - λ_{L} (p)] z_{n} (p)

(4)

As this policy becomes more open, the nativist voter’s cultural utility $z_{n} (p) < 0$ decreases. As $λ_{L} (p) > λ_{R} (p)$ for any given $p < \bar{p}$ , it is possible to observe $u_{in} (p'; σ_{L}, c_{L}) < u_{in} (p'; σ_{R}, c_{R})$ for sufficiently small $p' < p$ . Then, the nativist voter would choose candidate $L$ when the common policy is $p$ and candidate $R$ when it is $p'$ .

In this case, what makes the nativist voter switch his vote from the open candidate $L$ , whose core ideology is closer to his, to the nativist candidate $R$ as the common policy becomes more open is the greater policy disutility from candidate $L$ owing to her increasing focus on the cultural implications of a more open policy (such as greater diversity). Although candidate $R$ ’s cultural focus also increases with the openness of the policy, her nativism serves as an effective check on how much nativist voters blame her compared with the open candidate.

Based on this preliminary, the following section characterizes equilibrium voting behavior.

4.1. The swing voters

A swing voter of group $h \in {n, o}$ is defined as a voter $i$ with core ideology $σ_{ih}$ who becomes indifferent between the two candidates upon observing their policies. These are the voters from each group that the candidates target as they are most susceptible to switching their votes in response to a policy change.

Given $σ_{j}$ , $c_{j}$ , and $p_{j}$ for $j \in {L, R}$ , a voter $i$ in group $h \in {n, o}$ votes for candidate $L$ over candidate $R$ if and only if

η (σ_{R} - σ_{ih})^{2} - η (σ_{L} - σ_{ih})^{2} \geq [w (p_{R}) - w (p_{L})] + [λ_{R} (p_{R}) z_{h} (p_{R}) - λ_{L} (p_{L}) z_{h} (p_{L})]

(5)

Based on (5), we can define the function ${\bar{σ}}_{h} : [0, 1]^{2} \to R$ for $h \in {n, o}$ such that the core ideology

{\bar{σ}}_{h} (p_{L}, p_{R}) = \frac{[w (p_{R}) - w (p_{L})] + [λ_{R} (p_{R}) z_{h} (p_{R}) - λ_{L} (p_{L}) z_{h} (p_{L})] - η (σ_{R}^{2} - σ_{L}^{2})}{2 η (σ_{L} - σ_{R})}

(6)

uniquely defines the group- $h$ swing voter for any given policy pair $(p_{L}, p_{R})$ . Accordingly, letting ${\bar{σ}}_{h} \equiv {\bar{σ}}_{h} (p_{L}, p_{R})$ , all voters $i$ in group $h \in {n, o}$ such that $σ_{ih} \leq {\bar{σ}}_{h}$ vote for $L$ and all voters $i$ in group $h \in {n, o}$ such that $σ_{ih} > {\bar{σ}}_{h}$ vote for $R$ .

To see how the nativist and open swing voters are influenced by the candidates’ different cultural identities, first suppose $p_{L} = p_{R}$ . If we had $c_{L} = c_{R}$ so that only the candidates’ core ideologies would matter to the voters, then (6) would imply ${\bar{σ}}_{h} = \frac{σ_{L} + σ_{R}}{2}$ for $h = n, o$ . On the other hand, when $c_{L} \neq c_{R}$ , we have

{\bar{σ}}_{h} \equiv {\bar{σ}}_{h} (p_{L}, p_{R}) = \frac{(λ_{R} (p) - λ_{L} (p)) z_{h} (p)}{2 η (σ_{L} - σ_{R})} + \frac{σ_{L} + σ_{R}}{2}

(7)

for $h \in {n, o}$ , where $p \equiv p_{L} = p_{R}$ . Equation (7) indicates that a swing voter is unbiased toward either candidate if and only if $p = \bar{p}$ . For example, consider the nativist voters and let $p > \bar{p}$ so that $z_{n} (p) > 0$ . As we fixed $c_{R} = n$ and $c_{L} = o$ so that $λ_{L} (p) < λ_{R} (p)$ , Equation (7) implies ${\bar{σ}}_{n} < \frac{σ_{L} + σ_{R}}{2}$ , i.e., the nativist swing voter has a left-wing bias in terms of core ideology. This is because the nativist candidate has a policy advantage with the nativist voters and their indifference between the candidates therefore requires an ideological bias for the open candidate $L$ .

When the candidates adopt different policies, our behavioral assumptions yield novel implications of voter behavior that are difficult to obtain using traditional models. For instance, suppose $p_{R} < p_{L} < \bar{p}$ is such that $w (p_{L}) > w (p_{R})$ . Consider a nativist voter with core ideology $σ_{in}$ that is closer to $σ_{L}$ than to $σ_{R}$ so that this nativist voter prefers both the core ideology and the policy of candidate $L$ . Nonetheless, this voter can still vote for $R$ : If $λ_{R} (p_{R}) = \underline{λ}$ is sufficiently smaller than $λ_{L} (p_{L}) = \bar{λ}$ that the condition $| w (p_{R}) - w (p_{L}) | < \underline{λ} z_{n} (p_{R}) - \bar{λ} z_{n} (p_{L})$ holds despite the fact that $z_{n} (p_{R}) < z_{n} (p_{L})$ , then ${\bar{σ}}_{n} < \frac{σ_{L} + σ_{R}}{2}$ . This implies that there exist nativist voters with $σ_{in} \in ({\bar{σ}}_{n}, \frac{σ_{L} + σ_{R}}{2})$ so that they vote for $R$ . This phenomenon would be observed if $L$ is perceived as a very open candidate that even relatively restrictive policies she proposes would be greatly discounted by the nativist voters. Likewise, candidate $R$ ’s nativism must be sufficiently strong that the nativist voters receive disproportionately less cultural disutility from her relatively open policies.

Although each group’s swing voter is still determined by the voters’ core ideologies and policy utilities as in the standard models, the cultural components of the policy utilities here are weighted according to the candidates’ cultural identities. As described previously, this gives rise to voting behavior that might seem detached from the candidates’ core ideologies or strategic platforms, and instead driven by identity politics. This insight is the primary motivation for modeling a candidate’s non-policy characteristic (or valence) $σ_{j}$ as core ideology over which voters have different preferences (and not as, say, competence or charisma that all voters presumably would enjoy). Preference heterogeneity in the electorate for the candidates’ non-policy-related fixed characteristics implies that identity politics-driven behavioral voting generates the phenomenon we refer to as cross-voting. In particular, as explained previously, such heterogeneity yields the existence of nativist voters who vote for the nativist right-wing candidate despite having relatively left-wing core ideologies and a preference for the policy of the left-wing candidate. Similarly, there may exist open voters who vote for the open left-wing candidate despite having relatively right-wing core ideologies and a preference for the policy of the right-wing candidate. This is a dynamic we cannot capture with a valence term or shock in its simplest form that all voters would enjoy equally.

Building on this analysis, the following section characterizes the candidates’ equilibrium policy choices.

4.2. Optimal policy platforms

We assume that the office-motivated candidates are vote share maximizers. Given the voters’ optimal voting behavior as described in the previous section, candidate $L$ chooses her policy $p_{L} \in [0, 1]$ in order to maximize

V_{L} (p_{L}, p_{R}) = α_{n} F_{n} ({\bar{σ}}_{n}) + α_{o} F_{o} ({\bar{σ}}_{o})

(8)

and candidate $R$ chooses $p_{R} \in [0, 1]$ in order to maximize

V_{R} (p_{L}, p_{R}) = α_{n} (1 - F_{n} ({\bar{σ}}_{n})) + α_{o} (1 - F_{o} ({\bar{σ}}_{o}))

(9)

The vote shares in (8) and (9) that the candidates maximize in equilibrium are weighted sums of support from the nativist and open voters, where a group’s weight is determined by its size ( $α_{h}$ for $h = n, o$ ) in the electorate. As we show in the subsequent analysis, identity politics that leads to behavioral voting in the form of candidate-specificity of the voters’ policy utilities implies an asymmetric equilibrium. This is in contrast to standard Downsian models in which equilibrium is always symmetric: as a policy change affects the voters of a given group identically on the margin regardless of the candidate’s identity, the candidates always face the same necessary and sufficient condition for optimality, leading to identical policy choices. In contrast, the form of behavioral voting we model will imply that the candidates have different marginal effects on the voters’ policy utilities and hence will find different policies optimal.

In the following analysis, we let $β_{n} = β_{o} \equiv β$ in order to characterize the equilibrium under a baseline scenario in which neither group has more intense cultural preferences than the other.²³ In addition, we make the following assumption on the candidates’ vote shares that allows us to obtain the existence of a unique pure strategy equilibrium.

Assumption 1. If $(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \min {\bar{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}), \underline{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o})} < 0$ , then

(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \max {\bar{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}), \underline{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o})} < 0

(10)

so that candidate $j$ ’s vote share $V_{j} (p_{j}, p_{- j})$ is strictly quasiconcave in her own policy $p_{j}$ for $j \in {L, R}$ .

Note that the candidates’ vote share functions as given in (8) and (9) are continuous. However, they are not differentiable at the reference point $\bar{p}$ , where the marginal vote shares have a jump discontinuity. Given that these marginal vote shares are strictly decreasing in $p_{j}$ for all $p_{j} \neq \bar{p}$ , Assumption 1 ensures the strict quasiconcavity of the candidates’ vote share functions in their own policies by restricting the magnitude of the jumps at $\bar{p}$ .

Our first main result asserts the existence of a unique pure strategy equilibrium and provides a general description of the candidates’ equilibrium policies.²⁴

Proposition 1. There exists a unique pure strategy equilibrium in which candidate $j$ ’s policy $p_{j}^{*}$ is such that $p_{j}^{*} < \tilde{p}$ if and only if $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ for $j \in {L, R}$ , where $\tilde{p}$ is implicitly defined by $w' (\tilde{p}) = 0$ . Moreover, in an interior equilibrium, $p_{L}^{*} \neq p_{R}^{*}$ .

Proposition 1 states that a candidate’s optimal policy is more open than the policy $\tilde{p}$ that uniquely maximizes the consumption component of both groups’ policy utilities if and only if open voters are the electorally dominant group.²⁵ As the two groups agree on their evaluations of the distributional consequences of the policy, this result demonstrates the power of cultural identities: the electorally dominant voter group always succeeds in manipulating policy toward its preferred cultural direction in equilibrium. Moreover, as long as both candidates’ optimal policies are not at the same corner, the equilibrium is asymmetric.

There are two separate forces acting on the results in Proposition 1: the first is a dominant group effect, as a result of which the equilibrium policies are biased in favor of the dominant electoral group. This is a well-known effect and is a consequence of the Lindbeck and Weibull (1987) structure of the model. More specifically, whenever the open voters dominate the nativists in terms of size and ideological density, both candidates’ optimal policies will be skewed in the open voters’ preferred cultural direction. Fundamentally, it is the presence of a cultural divide in the electorate as manifested by different cultural utility functions for open and nativist voters that gives rise to this effect.

The second force is a polarization effect, which is novel and is a consequence of identity politics. As voters perform candidate-specific policy assessments by over-rewarding or under-punishing the candidate they share a cultural identity with, candidates affect voters’ policy utilities differently on the margin, leading to an asymmetric equilibrium. This polarization effect does not exist in the basic Lindbeck–Weibull framework, where candidates face the same optimality conditions and equilibrium is symmetric. While the dominant group effect shifts both candidates’ policies in favor of the electorally dominant group, the polarization effect ensures that they choose different policies while remaining in the preferred policy side of the dominant group. To reiterate, the Lindbeck–Weibull structure is solely responsible for the dominant group effect while identity politics produces the polarization effect.

Note that the strategy profile $(\tilde{p}, \tilde{p})$ would be the unique pure strategy equilibrium either in the absence of a cultural component to voting ( $z_{h} (p_{j}) = 0$ for both $h$ ) or if the two voter groups had equal electoral importance for the candidates ( $α_{o} {\bar{f}}_{o} = α_{n} {\bar{f}}_{n}$ ). In the former scenario, all voters would have the same policy preferences and the absence of a cultural payoff would abolish the voter groups altogether. In contrast, although the Lindbeck–Weibull structure would remain intact in the latter scenario, the two voter groups’ electoral clout would cancel each other out as they exert equal “pull” on the candidates’ policies, resulting in a symmetric equilibrium at the maximizer of all voters’ consumption utilities.²⁶

On the other hand, equilibrium would be symmetric (but not necessarily at the strategy profile $(\tilde{p}, \tilde{p})$ as long as $α_{o} {\bar{f}}_{o} \neq α_{n} {\bar{f}}_{n}$ ) if there did not exist identity politics and hence behavioral voting in our model. More specifically, if $λ_{L} (\cdot) = λ_{R} (\cdot)$ but $z_{o} (\cdot) \neq z_{n} (\cdot)$ , then the polarization effect would be muted, leaving only the dominant group effect to pull both policies in the preferred cultural direction of the electorally dominant group. If, in addition, there existed a cultural component to policies but not a cultural divide (i.e., if we had $z_{o} (p_{j}) = z_{n} (p_{j}) \neq 0)$ , then the equilibrium would again be symmetric owing to the absence of identity politics, but now be determined at the policy that maximizes the sum of all voters’ (identical) consumption and cultural utilities. In either case, it would be the addition of identity politics to our model by letting $λ_{L} (\cdot) \neq λ_{R} (\cdot)$ that would re-introduce the polarization effect.

4.3 Targeting

The relative position of the consumption utility maximizer $\tilde{p}$ with respect to the reference point $\bar{p}$ has implications for equilibrium targeting, i.e., the equilibrium alignments between the candidates and the groups of voters.

The unique pure strategy equilibrium may belong to one of two classes of equilibria based on the relative positions of the policies $\bar{p}$ and $\tilde{p}$ : First, $\tilde{p}$ and $\bar{p}$ may be positioned such that the equilibrium policies are unambiguously below or above $\bar{p}$ , depending on the ranking between the electoral importance of the open and nativist voters. Alternatively, the relative positions of $\bar{p}$ and $\tilde{p}$ may in principle allow equilibrium policies to be on opposite sides of $\bar{p}$ .²⁷ Figure 2 illustrates this point that various equilibrium cases may arise based on the relative positions of the policies $\tilde{p}$ and $\bar{p}$ , and depicts these cases for when $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ so that $p_{j}^{*} < \tilde{p}$ for both $j$ according to Proposition 1.²⁸

Figure 2.

Possible equilibria when $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ . (a) Policies are unambiguously open. (b) Policies are both nativist. (c) Policies are both open. (d) Policies cannot diverge in cultural affiliation.

We begin our characterization of equilibrium targeting by focusing on the first of these two classes of equilibria, which we denote a Type 1 equilibrium and illustrate in Figure 2(a) (for the case in which open voters dominate nativists). In a Type 1 equilibrium, candidates’ policies unambiguously carry the same cultural affiliation. Specifically, assuming $α_{o} {\bar{f}}_{o} \neq α_{n} {\bar{f}}_{n}$ , a Type 1 equilibrium is defined such that either $p_{j}^{*} < \tilde{p} \leq \bar{p}$ (so the policies are not only open but are also more open than $\tilde{p}$ ) or $\bar{p} \leq \tilde{p} < p_{j}^{*}$ (so the policies are not only nativist but are also more nativist than $\tilde{p}$ ) for $j = L, R$ , where Proposition 1 indicates that the former is observed only if $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ and the latter is observed only if $α_{o} {\bar{f}}_{o} < α_{n} {\bar{f}}_{n}$ . We focus on interior solutions in the following results for clarity.

Proposition 2. Let $(p_{L}^{*}, p_{R}^{*})$ be a Type 1 equilibrium, i.e., $p_{j}^{*} < \tilde{p} \leq \bar{p}$ or $\bar{p} \leq \tilde{p} < p_{j}^{*}$ for $j = L, R$ . Then, $p_{L}^{*} < p_{R}^{*}$ so that the open candidate $L$ offers the more open policy.

Proposition 2 states that the open candidate always adopts the more open policy in a Type 1 equilibrium, regardless of the ranking between the electoral importance of the two voter groups. The open candidate elevates her partisan advantage with the open voters by targeting them to a greater extent than the nativist candidate finds optimal, whereas the nativist candidate plays to her advantage with the nativist voters by proposing a less open policy.

For instance, in Figure 2(a), we have $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ so that the open voters dominate the nativists, and $\bar{p} > \tilde{p}$ so that the policy that maximizes the consumption utility of all voters is more open than the reference point. This implies that the equilibrium policies are unambiguously open by Proposition 1, and are determined where each candidate’s marginal vote share intersects the horizontal axis. When open voters dominate the nativists, the open candidate $L$ ’s marginal vote share lies below that of the nativist candidate $R$ in the range of open policies. Thus, one can observe that the open candidate always proposes the more open policy in this equilibrium so that each candidate targets relatively more her own cultural base. Intuitively, given that an open policy is unambiguously optimal for both, the open candidate exploits the open voters’ deeper appreciation of her whereas the nativist candidate capitalizes on the nativist voters’ milder dissatisfaction compared to their disdain of her opponent.

In a Type 1 equilibrium, the divergence between the marginal cultural utilities that voters receive from candidates $L$ and $R$ results in greater targeting by the candidate whose cultural base is electorally dominant. However, an alternative relative positioning between the policies $\tilde{p}$ and $\bar{p}$ introduces important nuances to this conclusion. More specifically, in contrast to Figure 2(a), whether the candidates’ optimal policies are nativist or open is ambiguous and depends on the candidates’ exact marginal vote share functions when $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ and $\bar{p} < \tilde{p}$ as in the remaining figures.

We denote this second class of equilibria as Type 2 and, again assuming $α_{o} {\bar{f}}_{o} \neq α_{n} {\bar{f}}_{n}$ , define it such that either $p_{j}^{*} < \tilde{p}$ when $\bar{p} \leq \tilde{p}$ (so that the policies, although more open than $\tilde{p}$ , may be open or nativist), or $p_{j}^{*} > \tilde{p}$ when $\bar{p} \geq \tilde{p}$ (so that the policies, although more nativist than $\tilde{p}$ , may be nativist or open) for $j = L, R$ . There are three cases that may potentially describe a Type 2 equilibrium. First, $p_{j}^{*}$ for $j = L, R$ may be such that $\bar{p} \leq p_{j}^{*} < \tilde{p}$ or $\bar{p} \geq p_{j}^{*} > \tilde{p}$ . In the former possibility, the policies are both nativist despite being more open than the consumption utility maximizer $\tilde{p}$ , whereas in the latter, the policies are both open despite being more nativist than $\tilde{p}$ . Second, $p_{j}^{*}$ for $j = L, R$ may be such that $p_{j}^{*} \leq \bar{p} \leq \tilde{p}$ or $p_{j}^{*} \geq \bar{p} \geq \tilde{p}$ , which implies that the policies’ cultural affiliations and their positions relative to $\tilde{p}$ are congruent. Third, we may, in principle, have $p_{j}^{*} < \bar{p} < p_{- j}^{*} < \tilde{p}$ or $p_{j}^{*} > \bar{p} > p_{- j}^{*} > \tilde{p}$ for $j \in {L, R}$ , indicating an equilibrium that is divergent in the policies’ cultural affiliation. Momentarily leaving aside the question of when the unique pure strategy equilibrium would be described by either of these cases, the following proposition describes their properties.

Proposition 3. Let $(p_{L}^{*}, p_{R}^{*})$ be a Type 2 equilibrium, i.e., $p_{j}^{*} < \tilde{p}$ when $\bar{p} \leq \tilde{p}$ , or $p_{j}^{*} > \tilde{p}$ when $\bar{p} \geq \tilde{p}$ for $j = L, R$ .

If $\bar{p} \leq p_{j}^{*} < \tilde{p}$ or $\bar{p} \geq p_{j}^{*} > \tilde{p}$ for $j = L, R$ , then $p_{R}^{*} < p_{L}^{*}$ so that the nativist candidate $R$ proposes the more open policy.

If $p_{j}^{*} \leq \bar{p} \leq \tilde{p}$ or $p_{j}^{*} \geq \bar{p} \geq \tilde{p}$ for $j = L, R$ , then $p_{L}^{*} < p_{R}^{*}$ so that the open candidate $L$ proposes the more open policy.

Equilibrium policies $p_{L}^{*}$ and $p_{R}^{*}$ cannot be on opposite sides of the reference point $\bar{p}$ .

We denote the equilibrium described in part (a) of Proposition 3 in which there exists discrepancy between the electorally dominant voter group and the one that is targeted by the candidates a Type 2A equilibrium. For instance, in Figure 2(b), the equilibrium policies are between $\bar{p}$ and $\tilde{p}$ so that they are both considered nativist despite the greater electoral importance of the open voters. Here, the nativist candidate $R$ proposes the more open policy as her marginal vote share jumps down and that of the open candidate $L$ jumps up at the reference point $\bar{p}$ . In this policy range, the open candidate is penalized less by the open voters but also rewarded less by the nativist voters relative to the nativist candidate. Given the aforementioned discrepancy, the voters’ punishment incentives take center stage in the candidates’ policy calculus, leading the nativist candidate $R$ to adopt the more open policy.

In contrast, if $\tilde{p} < \bar{p}$ and the nativist voters are assumed to dominate electorally, the marginal disutility to the nativist voters of a more open policy is greater from the open candidate than from the nativist candidate. Selective punishment by the electorally dominant voter group is elevated to the forefront of the candidates’ policy calculus again, resulting in the open candidate $L$ choosing the more nativist policy relative to the nativist candidate $R$ in this equilibrium. Overall, the candidates’ policies downplay their cultural identities in a Type 2A equilibrium.

Similar to Proposition 2, part (b) of Proposition 3 indicates that the open candidate proposes the more open policy in a Type 2 equilibrium in which equilibrium policies that are more open (nativist) than $\tilde{p}$ are also considered open (nativist) based on the reference point. In this case, which we denote a Type 2B equilibrium and illustrate in Figure 2(c) for when open voters dominate, the candidate whose cultural identity conforms with the target voter group’s leans deeper into her base than her opponent as she capitalizes on her reward advantage with them. Finally, as part (c) of Proposition 3 indicates, the case depicted in Figure 2(d) cannot be observed in equilibrium.²⁹

To summarize, the analysis has established that each candidate’s optimal policy lies below the policy $\tilde{p}$ that maximizes the value of $w (p_{j})$ if and only if the open voters are electorally more important than the nativist voters, and that the equilibrium will belong to one of two classes of equilibria based on the relative positions of $\tilde{p}$ and the reference point $\bar{p}$ . Having described these possible equilibrium types, we briefly discuss the conditions under which each of these types would describe the model’s unique pure strategy equilibrium.

Note that if $\bar{p} \geq \tilde{p}$ and $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ , we have an open Type 1 equilibrium (i.e., $p_{j}^{*} < \tilde{p} \leq \bar{p}$ for $j = L, R$ ), and if $\bar{p} \leq \tilde{p}$ and $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ , we have a nativist Type 1 equilibrium (i.e., $\bar{p} \leq \tilde{p} < p_{j}^{*}$ for $j = L, R$ ). Given relative positions between $\tilde{p}$ and $\bar{p}$ that produce a Type 2 equilibrium, a Type 2B equilibrium, defined by congruence between the electorally dominant voter group and the group that is being targeted, ensues if and only if marginal cultural concerns outweigh distributional ones at the reference point for both candidates. The reverse is true for a Type 2A equilibrium so that rather than reinforcing the distributional imperative that positions both policies on the same side of $\tilde{p}$ , candidates go against it in a Type 2A equilibrium by targeting the group that shares the cultural affiliation of $\tilde{p}$ . Overall, the relative strength of distributional versus cultural motives in the determination of a candidate’s optimal policy guides the behavioral sorting of the candidates on the policy spectrum.

4.4 Comparative statics

In this section, we explore the effects of changes to the depth of the cultural division in the electorate and the strength of identity politics on equilibrium policies and the candidates’ vote shares. Then, we relax the assumption that open and nativist voters have equally intense cultural preferences. We focus for clarity on optimal policies not at the reference point.

The following proposition focuses on the implications of a deeper cultural divide in the electorate as manifested in greater values of $β$ .

Proposition 4. As the cultural divide deepens (i.e., as $β$ increases), equilibrium policies become more open and the vote share of the open candidate in a Type 1 or Type 2B equilibrium increases if and only if $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ .

Proposition 4 indicates that equilibrium policies become more open as the cultural divide in the electorate deepens whenever the open voters are electorally dominant. In the opposite scenario, candidates respond by increasing their targeting of the nativist voters through more restrictive policies. This arises as the vote share effect of the greater disutility nativist voters receive from a given policy due to more intense cultural preferences exceeds the corresponding effect of the open voters’ greater cultural utility.

Moreover, greater values of $β$ help the open candidate’s vote share whenever the open voters are electorally dominant if the open candidate is the one proposing the more open policy, which happens in a Type 1 or Type 2B equilibrium. As before, this result is due to open voters having an outsize effect on vote shares in this case due to the combination of their size and ideological density. The intuition for why the nativist candidate benefits from a deeper cultural divide in the same types of equilibria when nativist voters are electorally dominant is equivalent.

The parameter $β$ can also be interpreted as the relative importance of the cultural aspects of the policy for voters to other concerns. This suggests that more restrictive policies would follow a shock such as the refugee crisis in Europe that intensifies all voters’ cultural attitudes toward immigrants whenever the combination of the nativist voters’ size and ideological homogeneity elevates them to dominance. Furthermore, when cultural concerns outweigh distributional ones in the candidates’ policy choices so that each candidate targets relatively more her own base, such a shock is expected to benefit the nativist candidate at the expense of the open candidate.

Next, we investigate how equilibrium policies would be affected by stronger identity politics. In our model, stronger identity politics implies voters over-rewarding or under-punishing the candidate that shares their cultural identity to an even greater extent. Technically, this trend can be captured by an increase in $\bar{λ}$ and a decrease in $\underline{λ}$ . The following proposition summarizes the implications.

Proposition 5. Equilibrium policy polarization always increases in response to stronger identity politics (i.e., an increase in $\bar{λ}$ and a decrease in $\underline{λ}$ ).

Proposition 5 indicates that regardless of the ranking between the electoral importance of the two voter groups and the type of equilibrium, the distance between the equilibrium policies $p_{L}^{*}$ and $p_{R}^{*}$ always increases as behavioral voting intensifies due to stronger identity politics.

More specifically, in a Type 1 or Type 2B equilibrium in which $p_{L}^{*} < p_{R}^{*}$ is always true so that each candidate targets relatively more her own cultural base, stronger identity politics leads to more open policies from the open candidate and more nativist policies from the nativist candidate. This happens as stronger identity politics reinforces the same cultural forces that, by dominating distributional concerns, induced a Type 1 or Type 2B equilibrium. On the other hand, in a Type 2A equilibrium in which $p_{R}^{*} < p_{L}^{*}$ , stronger identity politics increases the nativism of the open candidate’s policy and the openness of the nativist candidate’s policy as it similarly fortifies the cultural motivations behind the candidates’ choices.

Finally, we relax the simplifying assumption that $β_{n} = β_{o} \equiv β$ , i.e., that the open and nativist voters must have equally intense cultural preferences. This allows us to consider shocks that may impact open and nativist voters differently. Once the value of $β_{h}$ is allowed to differ between the voter groups, it is straightforward to observe the following modification to Proposition 1: candidate $j$ ’s equilibrium policy $p_{j}^{*}$ is such that $p_{j}^{*} < \tilde{p}$ for $j \in {L, R}$ if and only if $β_{o} α_{o} {\bar{f}}_{o} > β_{n} α_{n} {\bar{f}}_{n}$ . Intuitively, the parameter $β_{h}$ also becomes a determinant of the electoral importance of group $h \in {n, o}$ , which, in turn, determines whether the equilibrium policies will be more or less restrictive than the policy $\tilde{p}$ . Together with its size and the density of its swing voters, more intense cultural preferences help a voter group pull the candidates’ equilibrium policies toward the side of $\tilde{p}$ that they culturally prefer.³⁰

The shock to the parameter $β$ considered in Proposition 4 implied an intensification of all voters’ innate cultural attitudes. In other words, an increase in $β$ meant greater positive feelings by the open voters and greater negative feelings by the nativist voters simultaneously. However, it is also conceivable that certain shocks might change all voters’ views on the cultural consequences of the policy in the same direction. For instance, greater media coverage on the plight of the refugees or the success of integration efforts may intensify the open voters’ positive attitudes while diminishing the nativist voters’ negative feelings. Alternatively, a period of high unemployment after an economic crisis might make all voters partially blame immigrants for their hardships, which in turn may manifest itself in a greater electorate-wide dislike of immigrants.

Whereas the former example would be captured in our model by an increase in $β_{o}$ and a decrease in $β_{n}$ , the latter example would be captured by the opposite movements. The following corollary to Proposition 4 focuses on such asymmetric shocks to the voter groups’ intensity of cultural preferences.

Corollary 1. Equilibrium policies become more open and the open candidate’s vote share in a Type 1 or 2B equilibrium increases in response to a shock that increases $β_{o}$ and decreases $β_{n}$ .

Corollary 1 indicates that equilibrium policies become more open as all voters increase their appreciation of the cultural aspects of the policy, whereas they get more restrictive in response to an opposite shock. Furthermore, it states that in an equilibrium in which candidates target their own bases, the open candidate’s vote share increases as a result because she is the candidate proposing the more open policy. Intuitively, what benefits the open candidate in such an equilibrium is the elevation of her more open policy in the eyes of the voters.

Proposition 4 and Corollary 1 both summarize the conditions under which the open candidate’s vote share increases (and, consequently, the nativist candidate’s vote share decreases) in response to shocks to the cultural divide in the electorate. However, note that a candidate’s vote share is determined jointly by her core ideology and policy choice, and therefore the winning candidate depends not only on the voters’ policy evaluations but also on the distribution of core ideologies among both open and nativist voters.

5 Conclusion

This paper has studied the effects of cultural identities on candidates’ policy proposals and vote shares when voters are behavioral. Although voters care about the candidates’ core ideologies and policies, they evaluate these attributes through the lens of identity politics. Specifically, voters either over-reward or under-punish the candidate that shares their cultural identity. Focusing on policies with cultural as well as distributional consequences for the voters, and the cultural divide based on nativism as the source of identity politics, the model allowed for voting behavior ostensibly detached from the candidates’ core ideologies and policy platforms.

Our main results indicate that behavioral voting based on identity politics creates policy polarization, and stronger identity politics that translates into more intense behavioral voting exacerbates this outcome. We find that equilibrium policies are always biased in the cultural direction that the electorally dominant voter group prefers. However, we also find that candidates do not necessarily target their own cultural bases in equilibrium and that the cultural affiliation of equilibrium policies need not agree with the cultural identity of the electorally dominant group.

With a focus on demonstrating the powerful pull of identity politics, this paper provides a theoretical foundation for understanding the observed decoupling of voting behavior from traditional lines of division such as economic ideology. The results further suggest that culture-based alignments between a voter group and a candidate that propels that candidate to office may lead to the adoption of economic policies that oppose the interests of even a majority of the members of that voter group. Thus, we aim to highlight a channel through which identity politics can create an alliance between voter groups and candidates that is grounded not in economic ideology or policy interests but in behavioral traits.

Our analysis can be extended in various directions with potentially interesting results. First, although we take as given the saliency of culturally tinted policies as an election issue, it is reasonable that a candidate who would benefit from exploiting cultural divisions could take actions to influence the saliency of an issue. In other words, saliency of a policy such as immigration or protectionism as an election issue might itself be endogenous. Second, although we characterize how the saliency of issues such as immigration creates policy effects based on the existing cultural divide in the electorate, it is also possible that feedback effects may exist from policies to the voters’ cultural identities, core ideologies, or to other policy areas. Finally, we believe that adding a campaigning stage to our model during which the candidates may choose the focus of their rhetoric on the policy between its distributional and cultural aspects in order to influence the behavioral weights with which their policy proposals are evaluated would be a valuable extension.

Footnotes

Appendix

Proof of Proposition 1. Note that the candidates’ vote share functions as given in (8) and (9) are continuous. Given the strategy set $[0, 1]$ for each candidate and the uniform distribution assumption on the voters’ core ideologies, the strict quasiconcavity of $V_{j} (p_{j}, p_{- j})$ in $p_{j}$ for $j \in {L, R}$ is sufficient for the existence of a unique pure strategy equilibrium. Therefore, we first show the sufficiency of Assumption 1 for the strict quasiconcavity of $V_{j} (p_{j}, p_{- j})$ in $p_{j}$ .

Given that $V_{j} (p_{j}, p_{- j})$ is differentiable everywhere except at $p_{j} = \bar{p}$ , candidate $j$ ’s marginal vote share for a given $p_{- j}$ is defined by $V'_{j} (p_{j}, p_{- j})$ for all $p_{j} \neq \bar{p}$ by

(11)

α_{n} {\bar{f}}_{n} \frac{\partial {\bar{σ}}_{n} (p_{j}, p_{- j})}{\partial p_{j}} + α_{o} {\bar{f}}_{o} \frac{\partial {\bar{σ}}_{o} (p_{j}, p_{- j})}{\partial p_{j}}

which can be written as

(12)

\frac{(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (p_{j}) + β λ_{j} (p_{j}) (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o})}{2 η (σ_{R} - σ_{L})}

First, suppose $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ . Then, given $λ_{L} (p_{L}) = \bar{λ}$ for all $p_{L} \leq \bar{p}$ and $λ_{L} (p_{L}) = \underline{λ}$ for all $p_{L} > \bar{p}$ , candidate $L$ ’s marginal vote share jumps down at $\bar{p}$ . Since $V'_{j} (p_{j}, p_{- j})$ as defined in (12) for all $p_{j} \neq \bar{p}$ is strictly decreasing in $p_{j}$ by the strict concavity of $w (p_{j})$ , it follows that $V_{L} (p_{L}, p_{R})$ is strictly quasiconcave in $p_{L}$ when $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ . On the other hand, because $λ_{R} (p_{R}) = \underline{λ}$ for all $p_{R} \leq \bar{p}$ and $λ_{R} (p_{R}) = \bar{λ}$ for all $p_{R} > \bar{p}$ , candidate $R$ ’s marginal vote share jumps up at $\bar{p}$ . If, based on (12), $(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \underline{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) \geq 0$ , then we can claim the strict quasiconcavity of $V_{R} (p_{R}, p_{L})$ in $p_{R}$ . However, in the opposite scenario in which $(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \underline{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) < 0$ , candidate $R$ ’s vote share $V_{R} (p_{R}, p_{L})$ is strictly quasiconcave in $p_{R}$ if and only if $(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \bar{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) < 0$ .

Second, suppose $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ . This time, candidate $R$ ’s marginal vote share jumps down at $\bar{p}$ , and therefore $V_{R} (p_{R}, p_{L})$ is strictly quasiconcave in $p_{R}$ . On the other hand, given that candidate $L$ ’s marginal vote share jumps up at $\bar{p}$ , the conditions for strict quasiconcavity again depend on the sign of (12). If $(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \bar{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) \geq 0$ , the strict quasiconcavity of $V_{L} (p_{L}, p_{R})$ is readily obtained. However, in the opposite scenario, candidate $L$ ’s vote share $V_{L} (p_{L}, p_{R})$ is strictly quasiconcave in $p_{L}$ if and only if $(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \underline{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) < 0$ .

Finally, if $α_{n} {\bar{f}}_{n} = α_{o} {\bar{f}}_{o}$ , then each $V_{j} (p_{j}, p_{- j})$ is strictly concave and therefore strictly quasiconcave in $p_{j}$ .

In sum, $V_{L} (p_{L}, p_{R})$ is strictly quasiconcave in $p_{L}$ whenever $α_{n} {\bar{f}}_{n} \geq α_{o} {\bar{f}}_{o}$ , and $V_{R} (p_{R}, p_{L})$ is strictly quasiconcave in $p_{R}$ whenever $α_{o} {\bar{f}}_{o} \geq α_{n} {\bar{f}}_{n}$ . In addition, under Assumption 1, the strict quasiconcavity of $V_{L} (p_{L}, p_{R})$ in $p_{L}$ whenever $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ and the strict quasiconcavity of $V_{R} (p_{R}, p_{L})$ in $p_{R}$ whenever $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ are also ensured. Therefore, a pure strategy equilibrium exists and is unique.

To see that $p_{j}^{*} < \tilde{p}$ in equilibrium if and only if $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ , first note that there exists a unique $\tilde{p} \in (0, 1)$ such that $w' (\tilde{p}) = 0$ , $w' (p_{j}) > 0$ for all $p_{j} < \tilde{p}$ and $w' (p_{j}) < 0$ for all $p_{j} > \tilde{p}$ for $j \in {L, R}$ .

Based on (12), the necessary and sufficient condition for the optimality of an interior $p_{j}^{*} \neq \bar{p}$ for $j \in {L, R}$ is given by

(13)

(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (p_{j}^{*}) + β λ_{j} (p_{j}^{*}) (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) = 0

As $λ_{j} (p_{j}) > 0$ for all $p_{j}$ and $β > 0$ , Equation (13) implies that $w' (p_{j}^{*}) > 0$ if and only if $α_{n} {\bar{f}}_{n} < α_{o} {\bar{f}}_{o}$ . This implies $p_{j}^{*} < \tilde{p}$ if and only if $α_{n} {\bar{f}}_{n} < α_{o} {\bar{f}}_{o}$ . The analysis for possible corner solutions is similar and requires recognizing that $w' (1) < 0$ implies $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ , while $w' (0) > 0$ implies the opposite. Finally, if $p_{j}^{*} = \bar{p}$ , then candidate $j$ ’s marginal vote share must jump down at $\bar{p}$ such that $V'_{j} (p_{j}, p_{- j}) < 0$ for all $p_{j} > \bar{p}$ . For candidate $L$ , $p_{L}^{*} = \bar{p}$ implies $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ for $j = L$ , which further implies $w' (\bar{p}) < 0$ and therefore $\bar{p} > \tilde{p}$ . For candidate $R$ , $p_{R}^{*} = \bar{p}$ implies $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ , which further implies $w' (\bar{p}) > 0$ and therefore $\bar{p} < \tilde{p}$ . Thus, $p_{j}^{*} = \bar{p} < \tilde{p}$ if and only if $α_{n} {\bar{f}}_{n} < α_{o} {\bar{f}}_{o}$ as well. □

Proof of Proposition 2. The necessary and sufficient condition (13) for the optimality of $p_{j}^{*} \in (0, 1)$ , where $p_{j}^{*} \neq \bar{p}$ , can be written as

(14)

- \frac{α_{n} {\bar{f}}_{n}}{α_{o} {\bar{f}}_{o}} = \frac{w' (p_{j}^{*}) - β λ_{j} (p_{j}^{*})}{w' (p_{j}^{*}) + β λ_{j} (p_{j}^{*})}

for $j \in {L, R}$ , and the fact that the right-hand sides of (14) are equalized for candidates $L$ and $R$ in equilibrium yields

(15)

\frac{w' (p_{L}^{*})}{w' (p_{R}^{*})} = \frac{λ_{L} (p_{L}^{*})}{λ_{R} (p_{R}^{*})}

First, consider a Type 1 equilibrium such that $p_{j}^{*} < \tilde{p} \leq \bar{p}$ for both $j$ . Then, $λ_{L} (p_{L}^{*}) > λ_{R} (p_{R}^{*})$ . Given $λ_{j} (p_{j}) > 0$ for all $p_{j}$ and $j$ , and the fact that $w' (p_{j}) > 0$ for all $p_{j} < \tilde{p}$ , Equation (15) implies $w' (p_{L}^{*}) > w' (p_{R}^{*})$ . As $w' (p_{j})$ is decreasing in $p_{j}$ by the strict concavity of $w (p_{j})$ , we have $p_{L}^{*} < p_{R}^{*}$ in an open Type 1 equilibrium. Second, consider a Type 1 equilibrium such that $p_{j}^{*} > \tilde{p} \geq \bar{p}$ for both $j$ . As $λ_{R} (p_{R}^{*}) > λ_{L} (p_{L}^{*})$ , we obtain $w' (p_{L}^{*}) > w' (p_{R}^{*})$ owing to the fact that $w' (p_{j}) < 0$ for all $p_{j} > \tilde{p}$ . The strict concavity of $w (p_{j})$ then implies $p_{L}^{*} < p_{R}^{*}$ in a nativist Type 1 equilibrium as well. □

Proof of Proposition 3. For part (a), first consider a Type 2 equilibrium such that $\bar{p} < p_{j}^{*} < \tilde{p}$ for both $j$ . Then, $λ_{R} (p_{R}^{*}) > λ_{L} (p_{L}^{*})$ . By (15) and the fact that we must have $w' (p_{R}^{*}) > w' (p_{L}^{*}) > 0$ , it follows that $p_{R}^{*} < p_{L}^{*}$ in this Type 2 equilibrium. Note that there exists no equilibrium in which $\bar{p} \leq p_{j}^{*} < \tilde{p}$ for both $j$ and $p_{j}^{*} = \bar{p}$ for at least one $j \in {L, R}$ . This is because if $p_{R}^{*} = \bar{p} < \tilde{p}$ , then $(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \bar{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) < 0$ , which implies $p_{L}^{*} < \bar{p}$ . Moreover, $p_{L}^{*} = \bar{p} < \tilde{p}$ is not possible in equilibrium, because $p_{L}^{*} < \tilde{p}$ implies $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ by Proposition 1, which further implies that candidate $L$ ’s marginal vote share jumps up at $\bar{p}$ , contradicting the optimality of $\bar{p}$ .

Second, consider a Type 2 equilibrium such that $\tilde{p} < p_{j}^{*} < \bar{p}$ for both $j$ . As $λ_{L} (p_{L}^{*}) > λ_{R} (p_{R}^{*})$ here, Equation (15) and the fact that $0 > w' (p_{R}^{*}) > w' (p_{L}^{*})$ together imply $p_{R}^{*} < p_{L}^{*}$ in this Type 2 equilibrium. Similar to the analysis as shown previously, there exists no equilibrium in which $\tilde{p} < p_{R}^{*} = \bar{p}$ . However, if $\tilde{p} < p_{L}^{*} = \bar{p}$ , then $(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (\bar{p}) + β \underline{λ} (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) < 0$ , which implies $p_{R}^{*} < \bar{p}$ . Given $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ by Proposition 1, this implies there exists a Type 2 equilibrium in which $\tilde{p} < p_{R}^{*} < \bar{p} = p_{L}^{*}$ .

The proof of part (b) is identical to the proof of Proposition 2 if $p_{j}^{*} \neq \bar{p}$ for $j \in {L, R}$ . Suppose $p_{R}^{*} = \bar{p} < \tilde{p}$ . Then, as noted in the proof of part (a) above, $p_{L}^{*} < p_{R}^{*}$ . As also noted previously, $p_{L}^{*} = \bar{p} < \tilde{p}$ is not possible in equilibrium. Likewise, there exists no equilibrium in which $\tilde{p} < p_{R}^{*} = \bar{p}$ , and if $\tilde{p} < p_{L}^{*} = \bar{p}$ , then $p_{R}^{*} < \bar{p}$ as shown previously, which is the type of equilibrium analyzed in part (a).

For part (c), first note that equilibrium divergence in cultural affiliation is impossible by Proposition 1 when $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ and $\bar{p} > \tilde{p}$ , or when $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ and $\bar{p} < \tilde{p}$ , i.e., in a Type 1 equilibrium. As a Type 2 equilibrium in which policies diverge in cultural affiliation implies that $λ_{L} (p_{L}^{*}) = λ_{R} (p_{R}^{*})$ , we obtain $p_{L}^{*} = p_{R}^{*}$ by (15), a contradiction. □

Proof of Proposition 4. Implicitly differentiating (13) with respect to $β$ for $p_{j} \neq \bar{p}$ yields

(16)

\frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial β \partial p_{j}} + \frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}^{2}} \frac{\partial p_{j}^{*}}{\partial β} = 0

for $j \in {L, R}$ . Note that $\frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}^{2}} < 0$ and $\frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial β \partial p_{j}} = (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o}) λ_{j} (p_{j}^{*})$ , which is negative if and only if $α_{n} {\bar{f}}_{n} < α_{o} {\bar{f}}_{o}$ . It follows that $\frac{\partial p_{j}^{*}}{\partial β} < 0$ for $j \in {L, R}$ if and only if $α_{n} {\bar{f}}_{n} < α_{o} {\bar{f}}_{o}$ .

As $\frac{d V_{j} (p_{j}, p_{- j})}{d β}$ evaluated at the optimal policies equals $\frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial β} + \frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}} \frac{\partial p_{j}^{*}}{\partial β} + \frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{- j}} \frac{\partial p_{- j}^{*}}{\partial β}$ and $\frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}} = \frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{- j}} = 0$ by optimality for $j \in {L, R}$ , it follows that

(17)

\frac{d V_{L} (p_{L}^{*}, p_{R}^{*})}{d β} = \frac{(α_{o} {\bar{f}}_{o} - α_{n} {\bar{f}}_{n}) [λ_{R} (p_{R}^{*}) (\bar{p} - p_{R}^{*}) - λ_{L} (p_{L}^{*}) (\bar{p} - p_{L}^{*})]}{2 η (σ_{L} - σ_{R})}

In a Type 1 or Type 2B equilibrium, the inequality $λ_{R} (p_{R}^{*}) (\bar{p} - p_{R}^{*}) < λ_{L} (p_{L}^{*}) (\bar{p} - p_{L}^{*})$ is always true. Thus, in a Type 1 or Type 2B equilibrium, Equation (17) is positive for the open candidate $L$ if and only if $α_{o} {\bar{f}}_{o} > α_{n} {\bar{f}}_{n}$ . □

Proof of Proposition 5. Note that $\frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}^{2}} < 0$ for $p_{j} \neq \bar{p}$ , and implicitly differentiating (13) with respect to $λ_{j} (p_{j}^{*})$ by holding policy constant yields $β (α_{n} {\bar{f}}_{n} - α_{o} {\bar{f}}_{o})$ for $j \in {L, R}$ . As a result, we obtain $\frac{\partial p_{j}^{*}}{\partial \bar{λ}} > 0$ and $\frac{\partial p_{- j}^{*}}{\partial \underline{λ}} > 0$ if and only if $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ , where $j \in {L, R}$ is the candidate whose cultural identity conforms with the (same) cultural affiliation of policies $p_{j}^{*}$ and $p_{- j}^{*}$ .

In a Type 1 equilibrium, $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ if and only if $p_{j}^{*} > \bar{p}$ for $j = L, R$ . This implies that a simultaneous increase in $\bar{λ}$ and a decrease in $\underline{λ}$ unambiguously result in an increase in $p_{R}^{*}$ and a decrease in $p_{L}^{*}$ so that, given $p_{L}^{*} < p_{R}^{*}$ in a Type 1 equilibrium, policy polarization $p_{R}^{*} - p_{L}^{*}$ increases. The same is true for a Type 2B equilibrium.

In a Type 2A equilibrium, in contrast, we have $α_{n} {\bar{f}}_{n} > α_{o} {\bar{f}}_{o}$ if and only if $p_{j}^{*} < \bar{p}$ for $j = L, R$ . In this case, an increase in $\bar{λ}$ and a decrease in $\underline{λ}$ unambiguously imply an increase in $p_{L}^{*}$ and a decrease in $p_{R}^{*}$ . As $p_{R}^{*} < p_{L}^{*}$ in a Type 2A equilibrium, policy polarization $p_{L}^{*} - p_{R}^{*}$ again increases. □

Proof of Corollary 1. In the absence of imposing $β_{n} = β_{o}$ , the necessary and sufficient condition (13) for the optimality of an interior $p_{j}^{*} \neq \bar{p}$ becomes

(18)

(α_{n} {\bar{f}}_{n} + α_{o} {\bar{f}}_{o}) w' (p_{j}^{*}) + (β_{n} α_{n} {\bar{f}}_{n} - β_{o} α_{o} {\bar{f}}_{o}) λ_{j} (p_{j}^{*}) = 0

Implicitly differentiating equation (18) with respect to $β_{n}$ yields

(19)

\frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial β_{n} \partial p_{j}} + \frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}^{2}} \frac{\partial p_{j}^{*}}{\partial β_{n}} = 0

for $j \in {L, R}$ , where $\frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}^{2}} < 0$ . Given $\frac{\partial^{2} V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial β_{n} \partial p_{j}} = α_{n} {\bar{f}}_{n} λ_{j} (p_{j}^{*}) > 0$ , it follows that $\frac{\partial p_{j}^{*}}{\partial β_{n}} > 0$ for $j \in {L, R}$ . We similarly obtain $\frac{\partial p_{j}^{*}}{\partial β_{o}} < 0$ for $j \in {L, R}$ .

As $\frac{d V_{j} (p_{j}, p_{- j})}{d β_{h}}$ evaluated at the optimal policies equals $\frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial β_{h}} + \frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}} \frac{\partial p_{j}^{*}}{\partial β_{h}} + \frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{- j}} \frac{\partial p_{- j}^{*}}{\partial β_{h}}$ for both $h$ and $j$ , and $\frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{j}} = \frac{\partial V_{j} (p_{j}^{*}, p_{- j}^{*})}{\partial p_{- j}} = 0$ by optimality for $j \in {L, R}$ , we have

(20)

\frac{d V_{L} (p_{L}^{*}, p_{R}^{*})}{d β_{o}} = \frac{α_{o} {\bar{f}}_{o} [λ_{R} (p_{R}^{*}) (\bar{p} - p_{R}^{*}) - λ_{L} (p_{L}^{*}) (\bar{p} - p_{L}^{*})]}{2 η (σ_{L} - σ_{R})}

and

(21)

\frac{d V_{L} (p_{L}^{*}, p_{R}^{*})}{d β_{n}} = - \frac{α_{n} {\bar{f}}_{n} [λ_{R} (p_{R}^{*}) (\bar{p} - p_{R}^{*}) - λ_{L} (p_{L}^{*}) (\bar{p} - p_{L}^{*})]}{2 η (σ_{L} - σ_{R})}

Given $σ_{L} < σ_{R}$ , it follows that $\frac{d V_{L} (p_{L}^{*}, p_{R}^{*})}{d β_{o}} > 0$ and $\frac{d V_{L} (p_{L}^{*}, p_{R}^{*})}{d β_{n}} < 0$ if and only if $λ_{R} (p_{R}^{*}) (\bar{p} - p_{R}^{*}) - λ_{L} (p_{L}^{*}) (\bar{p} - p_{L}^{*}) < 0$ , which is always satisfied in a Type 1 or Type 2B equilibrium as established in Proposition 4. Then, in response to a shock that increases $β_{o}$ and decreases $β_{n}$ , the open candidate $L$ ’s vote share increases in a Type 1 or Type 2B equilibrium. □

Acknowledgements

We thank the seminar participants at SUNY Binghamton, the 2018 Great Lakes Political Economy Theory Conference, the 2018 Canadian Public Economics Group Meeting, the 2019 DC Political Economy Center Research Workshop, Chinese University of Hong Kong, and the 2019 Barcelona GSE Summer Forum. In particular, we are grateful to Kristy Buzard, Wiola Dziuda, Hugo Jales, Abdul Shifa, Al Slivinski, Konstantin Sonin, and Richard Van Weelden for their detailed comments. We are also indebted to two anonymous referees and the editor John Patty for very useful suggestions.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

ORCID iDs

Leyla D. Karakas

Devashish Mitra

References

Abrajano

Hajnal

(2015) White Backlash: Immigration, Race, and American Politics. Princeton, NJ: Princeton University Press.

Akerlof

Kranton

(2000) Economics and identity. Quarterly Journal of Economics 115(3): 715–753.

Ansolabehere

Puy

(2016) Identity voting. Public Choice 169: 77–95.

Ansolabehere

Snyder

(2000) Valence politics and equilibrium in spatial election models. Public Choice 103: 327–336.

Aragones

Palfrey

(2002) Mixed strategy equilibrium in a Downsian model with a favored candidate. Journal of Economic Theory 103: 131–161.

Aragones

Xefteris

(2017) Voters’ private valuation of candidates’ quality. Journal of Public Economics 156: 121–130.

Barone

D’Ignazio

de Blasio

Naticchioni

(2016) Mr. Rossi, Mr. Hu and politics: The role of immigration in shaping natives’ voting behavior. Journal of Public Economics 136: 1–13.

Bartels

(2002) Beyond the running tally: Partisan bias in political perceptions. Political Behavior 24(2): 117–150.

Besley

Persson

(2019) The Rise of Identity Politics. Working Paper.

10.

Bisgaard

(2015) Bias will find a way: Economic perceptions, attributions of blame, and partisan-motivated reasoning during crisis. Journal of Politics 77(3): 849–860.

11.

Buisseret

Van Weelden

(2020) Crashing the party? Elites, outsiders, and elections. American Journal of Political Science 64(2): 356–370.

12.

Campbell

Converse

Miller

Stokes

(1960) The American Voter. Chicago, IL: University of Chicago Press.

13.

Chen

(2009) Group identity and social preferences. American Economic Review 99(1): 431–457.

14.

Dickson

Scheve

(2006) Social identity, political speech, and electoral competition. Journal of Theoretical Politics 18(1): 5–39.

15.

Diermeier

(2017) Electoral control with behavioral voters. Journal of Politics 79(3): 890–902.

16.

Diermeier

(2019) Partisan affect and elite polarization. American Political Science Review 113(1): 277–281.

17.

Dixit

Londregan

(1996) The determinants of success of special interests in redistributive politics. Journal of Politics 58(4): 1132–1155.

18.

Eguia

Giovannoni

(2019) Tactical extremism. American Political Science Review 113(1): 282–286.

19.

Evans

Andersen

(2006) The political conditioning of economic perceptions. Journal of Politics 68(1): 194–207.

20.

Fischbacher

Utikal

(2013) On the acceptance of apologies. Games and Economic Behavior 82: 592–608.

21.

Gerber

Huber

(2009) Partisanship and economic behavior: Do partisan differences in economic forecasts predict real economic behavior? American Political Science Review 103(3): 407–426.

22.

Glaeser

Ponzetto

GAM

Shapiro

(2005) Strategic extremism: Why Republicans and Democrats divide on religious values. Quarterly Journal of Economics 120(4): 1283–1330.

23.

Groseclose

(2001) A model of candidate location when one candidate has a valence advantage. American Journal of Political Science 45(4): 862–886.

24.

Grossman

Helpman

(2020) Identity politics and trade policy. Review of Economic Studies, forthcoming.

25.

Guiso

Herrera

Morelli

Sonno

(2018) Populism: Demand and supply. Working Paper.

26.

Hajnal

Rivera

(2014) Immigration, Latinos, and White partisan politics: The new Democratic defection. American Journal of Political Science 58(4): 773–789.

27.

Halla

Wagner

Zweimuller

(2017) Immigration and voting for the far right. Journal of the European Economic Association 15(6): 1341–1385.

28.

Huddy

Mason

Aaroe

(2015) Excessive partisanship: Campaign involvement, political emotion, and partisan identity. American Political Science Review 109(1): 1–17.

29.

Kahneman

Tversky

(1979) Prospect theory: An analysis of decision under risk. Econometrica 47(2): 263–291.

30.

Karakas

Mitra

(2020) Inequality, Redistribution and the Rise of Outsider Candidates. Games and Economic Behavior 124: 1–16

31.

Krasa

Polborn

(2012) Political competition between differentiated candidates. Games and Economic Behavior 76(1): 249–271.

32.

Krasa

Polborn

(2014) Social ideology and taxes in a differentiated candidates framework. American Economic Review 104(1): 308–322.

33.

Levy

Razin

(2015) Correlation neglect, voting behavior, and information aggregation. American Economic Review 105(4): 1634–1645.

34.

Lindbeck

Weibull

(1987) Balanced-budget redistribution as the outcome of political competition. Public Choice 52(3): 273–297.

35.

Matakos

Xefteris

(2017) Divide and rule: Redistribution in a model with differentiated candidates. Economic Theory 63(4): 867–902.

36.

Mayda

(2006) Who is against immigration? A cross-country investigation of individual attitudes toward immigrants. Review of Economics and Statistics 88(3): 510–530.

37.

McCabe

Rigdon

Smith

(2003) Positive reciprocity and intentions in trust games. Journal of Economic Behavior and Organization 52(2): 267–275.

38.

Miller

Schofield

(2003) Activists and partisan realignments in the United States. American Political Science Review 97(2): 245–260.

39.

Nunnari

Zapal

(2020) A Model of Focusing in Political Choice. Working Paper.

40.

Panunzi

Pavoni

Tabellini

(2020) Economic Shocks and Populism: The Political Implications of Reference-Dependent Preferences. Working Paper.

41.

Pew Research Center (2017) The Partisan Divide on Political Values Grows Even Wider. Pew Research Center.

42.

Pew Research Center (2018) Americans are Generally Positive about Free Trade Agreements, More Critical of Tariff Increases. Pew Research Center.

43.

Prato

Wolton

(2018) Rational ignorance, populism, and reform. European Journal of Political Economy 55: 119–135.

44.

Schofield

(2004) Equilibrium in the spatial valence model of politics. Journal of Theoretical Politics 16(4): 447–481.

45.

Stokes

(2017) As Republicans’ Views Improve, Americans Give the Economy Its Highest Marks since Financial Crisis. Pew Research Center.