Distortion Under Public-Spirited Voting

Bailey Flanigan, Ariel D. Procaccia, Sven Wang

Abstract:

A key promise of democratic voting is that, by accounting for all constituents’ preferences,
it produces decisions that benefit the constituency overall. It is alarming, then, that all
deterministic voting rules have unbounded distortion: all such rules — even under reasonable
conditions — will sometimes select outcomes that yield essentially no value for constituents.
In this paper, we show that this problem is mitigated by voters being public-spirited: that is,
when deciding how to rank alternatives, voters weigh the common good in addition to their
own interests. We first generalize the standard voting model to capture this public-spirited
voting behavior. In this model, we show that public-spirited voting can substantially — and
in some senses, monotonically— reduce the distortion of several voting rules. Notably,
these results include the finding that if voters are at all public-spirited, some voting rules
have constant distortion in the number of alternatives. Further, we demonstrate that these
benefits are robust to adversarial conditions likely to exist in practice. Taken together, our
results suggest an implementable approach to improving the welfare outcomes of elections:
democratic deliberation, an already-mainstream practice that is believed to increase voters’
public spirit.