Agreement Among Voting Rules Under Single-Peaked Preference Distributions

Overview & Synopsis

Many different voting rules have been proposed in the literature and they can select very different alternatives. This naturally raises the question of whether this diversity in outcomes often occurs. Previous works have shown that the probability that voting rules agree on the same outcome is generally quite low under impartial culture. In this article, we use a similar probabilistic approach on single-peaked cultures, which are more structured and typically more realistic than impartial culture. We provide conditions for voting rules to agree under standard single-peaked cultures, and show that the probability of agreement between rather large families of voting rules is much higher under such cultures, with fast convergence of this probability with respect to the number of voters. We finally provide some insights on other structured preference distributions, observing that many exhibit similar convergence in agreement, including the Mallows’ distribution. Our study reveals a tendency of several well-known voting cultures to bias the outcome of voting rules, which is worth knowing before conducting experiments on synthetic data.