Related papers: Matrix Rationalization via Partial Orders
In multiwinner approval elections with many candidates, voters may struggle to determine their preferences over the entire slate of candidates. It is therefore of interest to explore which (if any) fairness guarantees can be provided under…
We propose a theoretical framework under which preference profiles can be meaningfully compared. Specifically, given a finite set of feasible allocations and a preference profile, we first define a ranking vector of an allocation as the…
We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…
An interval matrix is a matrix whose entries are intervals in the set of real numbers. We generalize this concept, which has been broadly studied, to other fields. Precisely we define a rational interval matrix to be a matrix whose entries…
The goal of multi-winner elections is to choose a fixed-size committee based on voters' preferences. An important concern in this setting is representation: large groups of voters with cohesive preferences should be adequately represented…
The Possible Winner (PW) problem, a fundamental algorithmic problem in computational social choice, concerns elections where voters express only partial preferences between candidates. Via a sequence of investigations, a complete…
In the theory of voting, the Plurality rule for preferences that come in the form of linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the…
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
Multicriteria Decision Making problems are important both for individuals and groups. Pairwise comparisons have become popular in the theory and practice of preference modelling and quantification. We focus on decision problems where the…
Given a data-set of consumer behaviour, the Revealed Preference Graph succinctly encodes inferred relative preferences between observed outcomes as a directed graph. Not all graphs can be constructed as revealed preference graphs when the…
Our goal is to develop a partial ordering method for comparing stochastic choice functions on the basis of their individual rationality. To this end, we assign to any stochastic choice function a one-parameter class of deterministic choice…
I consider decision-making constrained by considerations of morality, rationality, or other virtues. The decision maker (DM) has a true preference over outcomes, but feels compelled to choose among outcomes that are top-ranked by some…
Preference orderings are orderings of a set of items according to the preferences (of judges). Such orderings arise in a variety of domains, including group decision making, consumer marketing, voting and machine learning. Measuring the…
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…
Polarization is a major concern for a well-functioning society. Often, mass polarization of a society is driven by polarizing political representation, even when the latter is easily preventable. The existing computational social choice…
We consider a two-round election model involving $m$ voters and $n$ candidates. Each voter is endowed with a strict preference list ranking the candidates. In the first round, the candidates are partitioned into two subsets, $A$ and $B$,…
Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…
Comparing the ranking of candidates by different voters is an important topic in social and information science with a high relevance from the point of view of practical applications. In general, ties and pairs of incomparable candidates…
In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that…
The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational…