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Are there voting methods which (i) give everyone, including minorities, an equal share of effective power even if voters act strategically, (ii) promote consensus rather than polarization and inequality, and (iii) do not favour the status…
Coordination games admit two types of equilibria: pure equilibria, where all players successfully coordinate their actions, and mixed equilibria, where players frequently experience miscoordination. The existing literature shows that under…
Voting is the aggregation of individual preferences in order to select a winning alternative. Selection of a winner is accomplished via a voting rule, e.g., rank-order voting, majority rule, plurality rule, approval voting. Which voting…
We analyze the winning coalitions that arise under Bloc voting when voters preferences are single-peaked. For small numbers of candidates and numbers of winners, we determine conditions under which candidates in winning coalitions are…
The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An example is constructed to show that the averaged coefficients may become…
Many applications, such as content moderation and recommendation, require reviewing and scoring a large number of alternatives. Doing so robustly is however very challenging. Indeed, voters' inputs are inevitably sparse: most alternatives…
The constrained voter model describes the dynamics of opinions in a population of individuals located on a connected graph. Each agent is characterized by her opinion, where the set of opinions is represented by a finite sequence of…
We introduce a class of facilitated asymmetric exclusion processes in which particles are pushed by neighbors from behind. For the simplest version in which a particle can hop to its vacant right neighbor only if its left neighbor is…
Inspired by the spread of discontent as in the 2016 presidential election, we consider a voter model in which 0's are ordinary voters and 1's are zealots. Thinking of a social network, but desiring the simplicity of an infinite object that…
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 $B$,…
A voting center is in charge of collecting and aggregating voter preferences. In an iterative process, the center sends comparison queries to voters, requesting them to submit their preference between two items. Voters might discuss the…
We consider the simple exclusion process in the integer segment $ [1, N]$ with $k\le N/2$ particles and spatially inhomogenous jumping rates. A particle at site $x\in [ 1, N]$ jumps to site $x-1$ (if $x\ge 2$) at rate $1-\omega_x$ and to…
In many collective decision making situations, agents vote to choose an alternative that best represents the preferences of the group. Agents may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their…
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,…
Electing a single committee of a small size is a classical and well-understood voting situation. Being interested in a sequence of committees, we introduce and study two time-dependent multistage models based on simple Plurality voting.…
The classic Gibbard-Satterthwaite theorem says that every strategy-proof voting rule with at least three possible candidates must be dictatorial. In \cite{McL11}, McLennan showed that a similar impossibility result holds even if we consider…
How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is…
We give conditions for equilibria in the following Voronoi game on the discrete hypercube. Two players position themselves in $\{0,1\}^d$ and each receives payoff equal to the measure (under some probability distribution) of their Voronoi…
What is the emergent long-run equilibrium of a society where many interacting agents bet on the optimal energy to put in place in order to climb on the Bandwagon? In this paper we study the collective behavior of a large population of…
The best-response dynamics is an example of an evolutionary game where players update their strategy in order to maximize their payoff. The main objective of this paper is to study a stochastic spatial version of this game based on the…