Narrowing the field in elections: The Next-Two rule

We suggest a new approach to narrowing the field in elections, based on the 'deservingness' of candidates to be contenders in a runoff, or to be declared one of several winners. Instead of specifying some minimum percentage (e.g., 50) that the leading candidate must surpass to avoid a runoff (usually between the top two candidates), we propose that the number of contenders depends on the distribution of votes among all candidates. Divisor methods of apportionment proposed by Jefferson and Webster, among others, provide measures of deservingness, but they can prescribe a runoff even when one candidate receives more than 50 percent of the vote. We propose a new measure of derservingness, called the Next-Two rule, which compares the performance of candidates to the two that immediately follow them. It identifies as contenders candidates who are bunched together near the top. We apply the Next-Two rule to several empirical examples.