Searching for a Compromise in Multiple Referendum

Abstract

We consider a multiple referendum setting where voters cast approval ballots, in which they either approve or disapprove of each of finitely many dichotomous issues. A program is a set of socially approved issues. Assuming that individual preferences over programs are derived from ballots by means of the Hamming distance criterion, we consider two alternative notions of compromise. The majoritarian compromise is the set of all programs supported by the largest majority of voters at the minimum utility loss. A program is an approval compromise if it is supported by the highest number of voters at a utility loss at most half of the maximal achievable one. We investigate the conditions under which issue-wise majority voting allows for reaching each type of compromise. Finally, we argue that our results hold for many other preferences that are consistent with the observed ballots.