Related papers: Consistent Probabilistic Social Choice
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
This paper studies a general class of social choice problems in which agents' payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions…
Consider a sequence of $n$ independent random variables with a common continuous distribution $F$, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must be…
We have found that known community identification algorithms produce inconsistent communities when the node ordering changes at input. We propose two metrics to quantify the level of consistency across multiple runs of an algorithm:…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an…
Desirability can be understood as an extension of Anscombe and Aumann's Bayesian decision theory to sets of expected utilities. At the core of desirability lies an assumption of linearity of the scale in which rewards are measured. It is a…
A central theme in social choice theory is that of impossibility theorems, such as Arrow's theorem and the Gibbard-Satterthwaite theorem, which state that under certain natural constraints, social choice mechanisms are impossible to…
We consider how an agent should update her beliefs when her beliefs are represented by a set P of probability distributions, given that the agent makes decisions using the minimax criterion, perhaps the best-studied and most commonly-used…
This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of…
We provide the first social choice theory approach to the question of what constitutes a community in a social network. Inspired by the classic preferences models in social choice theory, we start from an abstract social network framework,…
I provide simplified proofs for each of the following fundamental theorems regarding selection principles: 1. The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of…
The persistence probability is a statistical index that has been proposed to detect one or more communities embedded in a network. Even though its definition is straightforward, e.g, the probability that a random walker remains in a group…
An assembly of $n$ voters needs to decide on $t$ independent binary issues. Each voter has opinions about the issues, given by a $t$-bit vector. Anscombe's paradox shows that a policy following the majority opinion in each issue may not…
We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…
Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of…
Voting rules allow multiple agents to aggregate their preferences in order to reach joint decisions. Perhaps one of the most important desirable properties in this context is Condorcet-consistency, which requires that a voting rule should…
Stability Selection was recently introduced by Meinshausen and Buhlmann (2010) as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection…
The von Neumann and Morgenstern theory postulates that rational choice under uncertainty is equivalent to maximization of expected utility (EU). This view is mathematically appealing and natural because of the affine structure of the space…
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,…