相关论文: A quantitative Gibbard-Satterthwaite theorem witho…
Three arguments based on the Greenberger-Horne-Zeilinger (GHZ) proof of the nonexistence of local hidden variables are presented. The first is a description of a simple game which a team that uses the GHZ method will always win. The second…
Mechanism design is concerned with settings where a policymaker (or social planner) faces the problem of aggregating the announced preferences of multiple agents into a collective (or social), system-wide decision. One of the most important…
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…
In the early 2000's the first and second named authors worked for a period of six years in an attempt of proving the Compositional Shuffle Conjecture [1]. Their approach was based on the discovery that all the Combinatorial properties…
A voting rule decides on a probability distribution over a set of m alternatives, based on rankings of those alternatives provided by agents. We assume that agents have cardinal utility functions over the alternatives, but voting rules have…
In this paper we obtain new quantitative forms of Hilbert's Irreducibility Theorem. In particular, we show that if $f(X, T_1, \ldots, T_s)$ is an irreducible polynomial with integer coefficients, having Galois group $G$ over the function…
Divided Government is nowadays a common feature of the U.S. political system. The voters can cast partisan ballots for two political powers the executive (Presidential elections) and the legislative (the Congress election). Some recent…
The problem of finding good approximations of arbitrary 1-qubit gates is identical to that of finding a dense group generated by a universal subset of $SU(2)$ to approximate an arbitrary element of $SU(2)$. The Solovay-Kitaev Theorem is a…
Measuring social influence is difficult due to the lack of counter-factuals and comparisons. By combining machine learning-based modeling and network science, we present general properties of social value, a recent measure for social…
Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose…
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a…
Different voters behave differently, different governments make different decisions, or different organizations are ruled differently. Many research questions important to political scientists concern choice behavior, which involves dealing…
In the context of single-winner ranked-choice elections between $m$ candidates, we explore the tradeoff between two competing goals in every democratic system: the majority principle (maximizing the social welfare) and the minority…
We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…
The median voter theorem has long been the default model of voter behavior and candidate choice. While contemporary work on the distribution of political opinion has emphasized polarization and an increasing gap between the "left" and the…
We study online temporal voting, where a group of voters submit 0/1 approvals on sets of alternatives that arrive online over multiple rounds and a single alternative is chosen in each round. We introduce online variants of two well-known…
Given a set of conflicting arguments, there can exist multiple plausible opinions about which arguments should be accepted, rejected, or deemed undecided. We study the problem of how multiple such judgments can be aggregated. We define the…
We consider a social choice problem where only a small number of people out of a large population are sufficiently available or motivated to vote. A common solution to increase participation is to allow voters use a proxy, that is, transfer…
Social choice is replete with various settings including single-winner voting, multi-winner voting, probabilistic voting, multiple referenda, and public decision making. We study a general model of social choice called Sub-Committee Voting…
An alternative form of Fermats equation[1] is proposed. It represents a portion of the identity that includes three terms of Fermats original equation. This alternative form permits an elementary and compact proof of the first case of…