Related papers: A tight quantitative version of Arrow's impossibil…
The Gibbard-Satterthwaite theorem states that every non-dictatorial election rule among at least three alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random…
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…
Suppose that G is a finite group and A is a subset of G such that 1_A has algebra norm at most M. Then 1_A is a plus/minus sum of at most L cosets of subgroups of G, and L can be taken to be triply tower in O(M). This is a quantitative…
In Terao [24], Hiroaki Terao defined and studied "admissible map", which is a generalization of "social welfare function" in the context of hyperplane arrangements. Using this, he proved a generalized Arrow's Impossibility Theorem using…
We generalize the Arrow's impossibility theorem--a key result in social choice theory--to the setting where the arity $k$ of the relation under consideration is greater than $2$. Some special but natural properties of $k$-ary relations are…
In this paper we study Arrow's Impossibility Theorem in the quantum setting. Our work is based on the work of Bao and Halpern, in which it is proved that the quantum analogue of Arrow's Impossibility Theorem is not valid. However, we feel…
In this paper we develop a novel approach to relaxing Arrow's axioms for voting rules, addressing a long-standing critique in social choice theory. Classical axioms (often styled as fairness axioms or fairness criteria) are assessed in a…
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…
To the best of our knowledge, a complete characterization of the domains that escape the famous Arrow's impossibility theorem remains an open question. We believe that different ways of proving Arrovian theorems illuminate this problem.…
The classical hypercontractive inequality for the noise operator on the discrete cube plays a crucial role in many of the fundamental results in the Analysis of Boolean functions, such as the KKL (Kahn-Kalai-Linial) theorem, Friedgut's…
We conjecture that in a consistent supergravity theory with non-vanishing gravitino mass, the limit $m_{3/2}\rightarrow 0$ is at infinite distance. In particular one can write $M_{\mathrm{tower}} \sim m_{3/2}^\delta$ so that as the…
It is shown that, since an ultrafilter over an operator-algebraically finite (i.e. isomorphic to the lattice of projectors of a finite Von Neumann algebra) quantum logic is not necessarily principal, Arrow's Impossibility Theorem doesn't…
The Majority is Stablest Theorem has numerous applications in hardness of approximation and social choice theory. We give a new proof of the Majority is Stablest Theorem by induction on the dimension of the discrete cube. Unlike the…
A Condorcet cycle election is an election (often called a Social Welfare Function, or SWF) between three candidates, where each voter ranks the three candidates according to a fixed cyclic order. Maskin showed that if such a SWF obeys the…
In rank aggregation, the goal is to combine multiple input rankings into a single output ranking. In this paper, we analyze rank aggregation methods, so-called social welfare functions (SWFs), with respect to strategyproofness, which…
By relaxing the dominating set in three ways (e.g., from "each member beats every non-member" to "each member beats or ties every non-member, with an additional requirement that at least one member beat every non-member"), we propose a new…
A group of individuals wishes to classify $m$ objects into $n$ categories in such a way that no class is left empty, a condition known as surjectivity. The opinions of the individuals are aggregated separately for each object using an…
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…
We study the probability of Boolean functions with small max influence to become constant under random restrictions. Let $f$ be a Boolean function such that the variance of $f$ is $\Omega(1)$ and all its individual influences are bounded by…
The Gibbard-Satterthwaite Impossibility Theorem holds that dictatorship is the only Pareto optimal and strategyproof social choice function on the full domain of preferences. Much of the work in mechanism design aims at getting around this…