Related papers: Single-Peaked Consistency for Weak Orders Is Easy
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…
In two-sided matching markets, ensuring both stability and strategy-proofness poses a significant challenge; it is impossible when agents' preferences are unrestricted. But what if agents' preferences have specific restricted structures?…
Single-peakedness is one of the most important and well-known domain restrictions on preferences. The computational study of single-peaked electorates has largely been restricted to elections with tie-free votes, and recent work that…
A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced…
We investigate preference profiles for a set $\mathcal{V}$ of voters, where each voter $i$ has a preference order $\succ_i$ on a finite set $A$ of alternatives (that is, a linear order on $A$) such that for each two alternatives $a,b\in A$,…
This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can…
We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality, that applies for many natural kinds of preference…
Many hard computational social choice problems are known to become tractable when voters' preferences belong to a restricted domain, such as those of single-peaked or single-crossing preferences. However, to date, all algorithmic results of…
This paper is devoted to a study of single-peakedness on arbitrary graphs. Given a collection of preferences (rankings of a set of alternatives), we aim at determining a connected graph G on which the preferences are single-peaked, in the…
We analyze the problem of locating a public facility in a domain of single-peaked and single-dipped preferences when the social planner knows the type of preference (single-peaked or single-dipped) of each agent. Our main result…
We study strategic candidate nomination by parties in elections decided by Plurality voting. Each party selects a nominee before the election, and the winner is chosen from the nominated candidates based on the voters' preferences. We…
This paper characterizes the single-peaked domain on a tree via the strategy-proofness of extreme rules defined on that tree. For any tree, these rules are unanimous and anonymous on any preference domain. In particular, we show that they…
Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced.…
Top monotonicity is a relaxation of various well-known domain restrictions such as single-peaked and single-crossing for which negative impossibility results are circumvented and for which the median-voter theorem still holds. We examine…
We provide novel simple representations of strategy-proof voting rules when voters have uni-dimensional single-peaked preferences (as well as multi-dimensional separable preferences). The analysis recovers, links and unifies existing…
We consider opinion diffusion for undirected networks with sequential updates when the opinions of the agents are single-peaked preference rankings. Our starting point is the study of preserving single-peakedness. We identify voting rules…
The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their…
We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- in which for each…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
Two distinct specifications of single peakedness as currently met in the relevant literature are singled out and discussed. Then, it is shown that, under both of those specifications, a voting rule as defined on a bounded distributive…