Social Choice Theory in 10,000 Meters: Examining Independence and Transitivity in the Ncaa Cross-Country Championships

Abstract

A recent study by Hammond (2007) delves into scoring methods in athletic events as a way of illuminating social choice problems. Hammond's study indicates, using data from a girls' high school cross-country meet in Michigan, that the current scoring method for high school cross-country is plagued by two problems related to inconsistency and ambiguity in the results – problems that can be characterized as violations of the principles of independence from irrelevant teams (IIT) and transitivity. Our note supports and extends Hammond's study by examining the results from both the 2008 and 2009 NCAA Division I men's cross-country championships, wherein the types of scoring problems found by Hammond are present. Unlike high school-level cross-country, however, we show that salaries, bonuses, and budgets at the collegiate level can be substantial, so that any inconsistencies and ambiguities in the scoring mechanism can be quite costly for individuals and institutions.

Keywords

social choice independence of irrelevant alternatives transitivity sports economics

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