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Consider a committee election consisting of (i) a set of candidates who are divided into arbitrary groups each of size ${at~most}$ two and a diversity constraint that stipulates the selection of ${at~least}$ one candidate from each group…
We consider the participatory budgeting problem where each of $n$ voters specifies additive utilities over $m$ candidate projects with given sizes, and the goal is to choose a subset of projects (i.e., a committee) with total size at most…
Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such…
Approval-based committee selection is a model of significant interest in social choice theory. In this model, we have a set of voters $\mathcal{V}$, a set of candidates $\mathcal{C}$, and each voter has a set $A_v \subset \mathcal{C}$ of…
We consider a committee voting on whether to adopt a reform under a quota rule, where members differ in how much they value the reform some supporting it, others opposing it. We examine how members can influence each other's votes through…
We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice…
Multi-winner approval voting selects a size-$k$ committee that aggregates voters' approval preferences over a set of alternatives. A central question is coalitional stability: No coalition should be able to pick a committee -- of size at…
Some argue that political stability is best served through a two-party system. This study refutes this. The author mathematically defines the stability and rigidity of electoral systems comprised of any quantity of electors and parties. In…
The classic Gibbard-Satterthwaite theorem says that every strategy-proof voting rule with at least three possible candidates must be dictatorial. Similar impossibility results hold even if we consider a weaker notion of strategy-proofness…
In rank aggregation, the task is to aggregate multiple weighted input rankings into a single output ranking. While numerous methods, so-called social welfare functions (SWFs), have been suggested for this problem, all of the classical SWFs…
Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice. In our work, we propose a concept called Strong Proportionality,…
Committee selection with diversity or distributional constraints is a ubiquitous problem. However, many of the formal approaches proposed so far have certain drawbacks including (1) computationally intractability in general, and (2)…
When selecting multiple candidates based on approval preferences of agents, the proportional representation of agents' opinions is an important and well-studied desideratum. Existing criteria for evaluating the representativeness of…
We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely…
We study popularity for matchings under preferences. This solution concept captures matchings that do not lose against any other matching in a majority vote by the agents. A popular matching is said to be robust if it is popular among…
We identify a whole family of approval-based multi-winner voting rules that satisfy PJR. Moreover, we identify a subfamily of voting rules within this family that satisfy EJR. All these voting rules can be computed in polynomial time as…
Perpetual voting was recently introduced as a framework for long-term collective decision making. In this framework, we consider a sequence of subsequent approval-based elections and try to achieve a fair overall outcome. To achieve…
We study a budget aggregation setting where voters express their preferred allocation of a fixed budget over a set of alternatives, and a mechanism aggregates these preferences into a single output allocation. Motivated by scenarios in…
We propose a new single-winner election method ("Schulze method") and prove that it satisfies many academic criteria (e.g. monotonicity, reversal symmetry, resolvability, independence of clones, Condorcet criterion, k-consistency,…
Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every quasi-order must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of…