Related papers: Self-Equivalent Voting Rules
In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…
We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model,…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
We consider the following well-studied problem of metric distortion in social choice. Suppose we have an election with $n$ voters and $m$ candidates located in a shared metric space. We would like to design a voting rule that chooses a…
A method is given for quantitatively rating the social acceptance of different options which are the matter of a complete preferential vote. Completeness means that every voter expresses a comparison (a preference or a tie) about each pair…
Many democratic societies use district-based elections, where the region under consideration is geographically divided into districts and a representative is chosen for each district based on the preferences of the electors who reside…
We consider the multi-unit random assignment problem in which agents express preferences over objects and objects are allocated to agents randomly based on the preferences. The most well-established preference relation to compare random…
In distortion-based analysis of social choice rules over metric spaces, one assumes that all voters and candidates are jointly embedded in a common metric space. Voters rank candidates by non-decreasing distance. The mechanism, receiving…
We study the efficiency (in terms of social welfare) of truthful and symmetric mechanisms in one-sided matching problems with {\em dichotomous preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are particularly…
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…
Consider Plurality with random tie-breaking. This paper uses standard axiomatic extensions of preferences over elements to preferences over sets (Kelly, Gardenfors, Responsiveness) to characterize all better-replies of a voter under…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
In the face of adverse motives, it is indispensable to achieve a consensus. Elections have been the canonical way by which modern democracy has operated since the 17th century. Nowadays, they regulate markets, provide an engine for modern…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
We address the self-stabilizing exact majority problem in the population protocol model, introduced by Angluin, Aspnes, Diamadi, Fischer, and Peralta (2004). In this model, there are $n$ state machines, called agents, which form a network.…
We investigate the phenomena of political bi-polarization in a population of interacting agents by means of a generalized version of the model introduced in PRE E 101, 012101 (2020) for the dynamics of voting intention. Each agent has a…