Related papers: A Phase Transition in Arrow's Theorem

A modified version of a finite random field Ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making. Fields may have a non-zero average. A postulate of minimum…

Our preferences depend on the circumstances in which we reveal them. We will introduce a dependency which allows us to illustrate the relation between the possibility of winning of particular candidates in a quantum election and the type of…

Judgment aggregation studies how to combine individual judgments on logically related propositions into a collective judgment. Classical impossibility results show that sufficiently strong logical interconnections force dictatorship under…

We consider voting on multiple independent binary issues. In addition, a weighting vector for each voter defines how important they consider each issue. The most natural way to aggregate the votes into a single unified proposal is…

A two state model for opinion forming, which has proven heuristic power, is reviewed with a novel emphasis on the existence or absence of a threshold for the dynamics. Monitored by repeated small groups discussions floater agents update…

This paper looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter",…

There is a common belief that humans and many animals follow transitive inference (choosing A over C on the basis of knowing that A is better than B and B is better than C). Transitivity seems to be the essence of rational choice. We…

Consider the decision-making setting where agents elect a panel by expressing both positive and negative preferences. Prominently, in constitutional AI, citizens democratically select a slate of ethical preferences on which a foundation…

In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins…

Aging is considered as the property of the elements of a system to be less prone to change states as they get older. We incorporate aging into the noisy voter model, a stochastic model in which the agents modify their binary state by means…

We study systems with two symmetric absorbing states, such as the voter model and variations of it, which have been broadly used as minimal neutral models in genetics, population ecology, sociology, etc. We analyze the effects of a key…

There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we…

Observational learning is an important information aggregation mechanism. However, it occasionally leads to a state in which an entire population chooses a sub-optimal option. When it occurs and whether it is a phase transition remain…

We study the noisy voter model using a specific non-linear dependence of the rates that takes into account collective interaction between individuals. The resulting model is solved exactly under the all-to-all coupling configuration and…

By the Gibbard--Satterthwaite theorem, every reasonable voting rule for three or more alternatives is susceptible to manipulation: there exist elections where one or more voters can change the election outcome in their favour by…

We examine critically the issue of phase transitions in one-dimensional systems with short range interactions. We begin by reviewing in detail the most famous non-existence result, namely van Hove's theorem, emphasizing its hypothesis and…

The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study…

We discuss voting scenarios in which the set of voters (agents) and the set of alternatives are the same; that is, voters select a single representative from among themselves. Such a scenario happens, for instance, when a committee selects…

The mathematical study of voting, social choice theory, has traditionally only been applicable to choices among a few predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We…

In 1950 Arrow famously showed that there is no social welfare function satisfying four basic conditions. In 1976, on the other hand, Gibbard and Sonnenschein showed that there does exist a unique probabilistic social welfare method that…