SOCIAL CHOICE THEORY IN 10,000 METERS: EXAMINING INDEPENDENCE AND TRANSITIVITY IN THE NCAA CROSS-COUNTRY CHAMPIONSHIPS by Franklin G. Mixon, Jr.* and Ernest W. King** 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 transitiv- ity. 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 JEL Classifications: D70; D71; L83 I. Introduction and Background A recent study by Hammond (2007) – one that is built on the “long . . . recognized [result] that our methods for making social and political choices may violate desirable principles such as transitivity and the Pareto principle . . . (see Arrow, 1963; Sen, 1970; Schwartz, 1986; Brams and Fishburn, 2002) . . .” – delves into scoring methods in athletic events as a way of illuminating social choice prob- lems. In that regard, Hammond’s study follows a decades old tradition (see McKay, 1980; Saari, 2001) that examines scoring in popular Olympic competitions, such as decathlon, track, and figure skating. Hammond follows and extends Saari (2001) by showing that in a multi-team high school girls’ cross-country (track) meet, which is a long- distance race that does not take place on a standard oval track, violations of long-established social choice principles can and do occur. As Hammond (2007: 360) explains, a team’s score in a cross-country meet is “based on the sum of the positions in which some k of the team’s runners finished the race.” For example, in the NCAA Division I men’s cross-country champion- ships, participating teams bring seven runners, though k equals the top five finishers for scoring purposes. Hammond also points out that on occa- sion three or more teams will participate in a cross- country meet, yet officials may score the event as (1) a single three-way meet (i.e., A versus B versus C), or (2) three separate dual meets (i.e., A versus B, A versus C, and B versus C). 1 These two choices have profound implications for determin- ing the order of finish in cross-country meets, and thus have similarly profound implications regard- ing the three different general purposes of scoring methods used for cross-country meets. According to Hammond: “First, we usually want to find an overall winner of the meet: of all the teams running, which is the ‘best’? Second, we may also want a ranking of how the teams finished: we are often interested in the top-3 finishers, for example, not just the first; it is most desirable, of course, to finish first, but it is often considered noteworthy to have finished * Corresponding author: D. Abbott Turner College of Business, Columbus State University, 4225 University Avenue, Columbus, GA 31907, USA, 706-568-5368, mixon_franklin@columbusstate.edu ** Department of Legal Studies, University of Southern Mississippi, Hattiesburg, MS 39407 32 THE AMERICAN ECONOMIST