Rank injustice?: How the scoring method for cross-country running competitions violates major social choice principles

The scoring method used by high schools and colleges in the U.S. to determine which team wins a cross-country meet can violate a major social choice principle, referred to here as Independence from Irrelevant Teams: whether team A is scored as defeating or losing to team B can depend on whether team C’s performance is included in the calculations. In addition, if a three-way meet is scored as three dual meets, the scoring method can produce a cycle, thereby violating the principle of Transitivity: team A beats team B, team B beats team C, but team C beats team A. Real-world violations of Independence and Transitivity are reported from a high school cross-country meet held in Michigan in the U.S. in 2003. Several results are presented about the conditions under which these two principles can be violated. An alternative scoring method that will violate neither Independence nor Transitivity is also discussed and evaluated.