Related papers: Complete Characterization of Functions Satisfying …
Revised proofs of Kenneth Arrow's impossibility theorem have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters. This study develops another approach to proving the theorem. Using a proof…
We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between…
We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the…
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…
In the field of Judgment Aggrgation, a domain, that is a subset of a Cartesian power of $\{0,1\}$, is considered to reflect abstract rationality restrictions on vectors of two-valued judgments on a number of issues. We are interested in the…
The First Fundamental Theorem of Welfare Economics assumes that welfare-bearing agents are autonomous and implicitly relies on a binary distinction between autonomy and instrumentality. Welfare subjects are those who have autonomy and…
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…
Social choice theory is a theoretical framework for analysis of combining individual preferences, interests, or welfare to reach a collective decision or social welfare in some sense. We introduce a new criterion for social choice protocols…
We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…
We present some conditions for social preference transitivity under the majority rule when the individual preferences include cycles. First, our concern is with the restriction on the preference orderings of individuals except those (called…
Consider a social-choice function (SCF) is chosen to decide votes in a formal system, including votes to replace the voting method itself. Agents vote according to their ex-ante belief over what decisions are considered, and whether they…
We study the assignment problem of objects to agents with heterogeneous preferences under distributional constraints. Each agent is associated with a publicly known type and has a private ordinal ranking over objects. We are interested in…
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…
Without monetary payments, the Gibbard-Satterthwaite theorem proves that under mild requirements all truthful social choice mechanisms must be dictatorships. When payments are allowed, the Vickrey-Clarke-Groves (VCG) mechanism implements…
A Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is called a dictator if it depends on exactly one variable i.e $f(x_1, x_2, \ldots, x_n) = x_i$ for some $i\in [n]$. In this work, we study a $k$-query dictatorship test. Dictatorship…
A word-to-word function is rational if it can be realized by a non-deterministic one-way transducer. Over finite words, it is a classical result that any rational function is regular, i.e. it can be computed by a deterministic two-way…
By endowing the class of tops-only and efficient social choice rules with a dual order structure that exploits the trade-off between different degrees of manipulability and dictatorial power rules allow agents to have, we provide a proof of…
May's classical theorem states that in a single-winner choose-one voting system with just two candidates, majority rule is the only social choice function satisfying anonimity, neutrality and positive responsiveness axiom. Anonimity and…
Arrow proved that for three or more candidates, the IIA condition is enough to forbid all non-dictatorial election rules (or Social Welfare Functions). Maskin introduced the weaker MIIA condition, which permits the ``Borda'' election rules…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…