Deliberation, Single-Peakedness, and Coherent Aggregation

Rational deliberation helps to avoid cyclic or intransitive group preferences by fostering meta-agreements, which in turn ensures single-peaked profiles. This is the received view, but this paper argues that it should be qualified. On one hand we provide evidence from computational simulations that rational deliberation tends to increase proximity to so-called single-plateaued preferences. This evidence is important to the extent that, as we argue, the idea that rational deliberation fosters the creation of meta-agreement and, in turn, single-peaked profiles does not carry over to single-plateaued ones, and the latter but not the former makes coherent aggregation possible when the participants are allowed to express indifference between options. On the other hand, however, our computational results show, against the received view, that when the participants are strongly biased towards their own opinions, rational deliberation tends to create irrational group preferences, instead of eliminating them. These results are independent of whether the participants reach meta-agreements in the process, and as such they highlight the importance of rational preference change and biases towards one’s own opinion in understanding the effects of rational deliberation.

On strategy-proofness and single-peakedness: median-voting over intervals

We study correspondences that choose an interval of alternatives when agents have single-peaked preferences over locations and ordinally extend their preferences over intervals. We extend the main results of Moulin (Public Choice 35:437–455, 1980) to our setting and show that the results of Ching (Soc Choice Welf 26:473–490, 1997) cannot always be similarly extended. First, strategy-proofness and peaks-onliness characterize the class of generalized median correspondences (Theorem 1). Second, this result neither holds on the domain of symmetric and single-peaked preferences, nor can in this result min/max continuity substitute peaks-onliness (see counter-Example 3). Third, strategy-proofness and voter-sovereignty characterize the class of efficient generalized median correspondences (Theorem 2).

Incomplete Preferences in Single-Peaked Electorates

Incomplete preferences are likely to arise in real-world preference aggregation scenarios. This paper deals with determining whether an incomplete preference profile is single-peaked. This is valuable information since many intractable voting problems become tractable given singlepeaked preferences. We prove that the problem of recognizing single-peakedness is NP-complete for incomplete profiles consisting of partial orders. Despite this intractability result, we find several polynomial-time algorithms for reasonably restricted settings. In particular, we give polynomial-time recognition algorithms for weak orders, which can be viewed as preferences with indifference.