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It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
The Aldous-Hoover Theorem concerns an infinite matrix of random variables whose distribution is invariant under finite permutations of rows and columns. It states that, up to equality in distribution, each random variable in the matrix can…
We consider different choice procedures such as scoring rules, rules, using majority relation, value function and tournament matrix, which are used in social and multi-criteria choice problems. We focus on the study of the properties that…
In modern democracies, the outcome of elections and referendums is often remarkably tight. The repetition of these divisive events are the hallmark of a split society; to the physicist, however, it is an astonishing feat for such large…
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…
In any physical theory that admits true indeterminism, the thermodynamic arrow of time can arise regardless of the system's initial conditions. Hence on such theories time's arrow emerges out of the basic physical interactions. The example…
Politics around the world exhibits increasing polarization, demonstrated in part by rigid voting configurations in institutions like legislatures or courts. A crux of polarization is separation along a unidimensional ideological axis, but…
Understanding how biological organisms make decisions is of fundamental importance in understanding behavior. Such an understanding within evolutionary game theory so far has been sought by appealing to bounded rationality. Here, we present…
A primary challenge in collective decision-making is that achieving unanimous agreement is difficult, even at the level of criteria. The history of social choice theory illustrates this: numerous normative criteria on voting rules have been…
Recent research on the thermodynamic arrow of time, at the microscopic scale, has questioned the universality of its direction. Theoretical studies showed that quantum correlations can be used to revert the natural heat flow (from the hot…
The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by…
Classical results in voting theory show that strategic manipulation by voters is inevitable if a voting rule simultaneously satisfy certain desirable properties. Motivated by this, we study the relevant question of how often a voting rule…
We study the mutual influence of authority and persuasion in the flow of opinion. Many social organizations are characterized by a hierarchical structure where the propagation of opinion is asymmetric. In the normal flow of opinion…
We consider a coupled system mimicking opinion formation under the influence of a group of $q$ neighbors ($q$-lobby) that consists of an Ising part governed by temperature-like parameter $T$ and a voter dynamics parameterized by noise…
We compare two versions of the nonlinear $q$-voter model: the original one, with annealed randomness, and the modified one, with quenched randomness. In the original model, each voter changes its opinion with a certain probability…
The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the…
Despite the prevalence of voting systems in the real world there is no consensus among researchers of how people vote strategically, even in simple voting settings. This paper addresses this gap by comparing different approaches that have…
The proportional veto principle, which captures the idea that a candidate vetoed by a large group of voters should not be chosen, has been studied for ranked ballots in single-winner voting. We introduce a version of this principle for…
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…
Consider an undirected graph G, representing a social network, where each node is blue or red, corresponding to positive or negative opinion on a topic. In the voter model, in discrete time rounds, each node picks a neighbour uniformly at…