The Cutoff Paradox in the Kansas Presidential Caucuses

Abstract

The Kansas Republican Party uses an apportionment method of its own invention to apportion delegates to candidates in its presidential caucus. This method includes a threshold that eliminates candidates (and their votes) who receive less than 10% of the vote. Eliminating candidates can lead to a Cutoff Paradox, a paradox in which a surviving candidate receives fewer delegates as a result of the elimination of the candidates that fall beneath the threshold. We calculate the proportion of elections that are susceptible to this paradox for three candidate elections using the method of the Kansas Republican Party. For comparative purposes, we calculate the same proportions for Hamilton's method, the method used by the Democratic Party in all of its presidential primaries and caucuses.