Related papers: Symmetric majority rules
Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamiltonian cycle. For these and several other common…
We introduce three different qualifications of the reversal bias in the framework of social choice correspondences. For each of them, we prove that the Minimax social choice correspondence is immune to it if and only if the number of voters…
Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to single transferable vote (STV) as the…
I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must…
Traditionally, the problem of apportioning the seats of a legislative body has been viewed as a one-shot process with no dynamic considerations. While this approach is reasonable for some settings, dynamic aspects play an important role in…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…
We study the committee selection problem in the canonical impartial culture model with a large number of voters and an even larger candidate set. Here, each voter independently reports a uniformly random preference order over the…
Approval-based committee (ABC) voting rules elect a fixed size subset of the candidates, a so-called committee, based on the voters' approval ballots over the candidates. While these rules have recently attracted significant attention,…
Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X…
Consider an election where N seats are distributed among parties with proportions p_1,...,p_m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a…
We study a \emph{Plurality-Consensus} process in which each of $n$ anonymous agents of a communication network initially supports an opinion (a color chosen from a finite set $[k]$). Then, in every (synchronous) round, each agent can revise…
In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal…
During deliberation processes, mediators and facilitators typically need to select a small and representative set of opinions later used to produce digestible reports for stakeholders. In online deliberation platforms, algorithmic selection…
We consider a social choice setting with agents that are partitioned into disjoint groups, and have metric preferences over a set of alternatives. Our goal is to choose a single alternative aiming to optimize various objectives that are…
In multiwinner approval voting, the goal is to select $k$-member committees based on voters' approval ballots. A well-studied concept of proportionality in this context is the justified representation (JR) axiom, which demands that no large…
We study the complexity of (approximate) winner determination under the Monroe and Chamberlin--Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their…
We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…
A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…