Related papers: Two statements of the Duggan-Schwartz theorem
The Gibbard-Satterthwaite theorem is a cornerstone of social choice theory, stating that an onto social choice function cannot be both strategy-proof and non-dictatorial if the number of alternatives is at least three. The Duggan-Schwartz…
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…
An important -- but very demanding -- property in collective decision-making is strategyproofness, which requires that voters cannot benefit from submitting insincere preferences. Gibbard (1977) has shown that only rather unattractive rules…
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…
Social decision schemes (SDSs) map the voters' preferences over multiple alternatives to a probability distribution over these alternatives. In a seminal result, Gibbard (1977) has characterized the set of SDSs that are strategyproof with…
The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by…
We study the efficiency (in terms of social welfare) of truthful and symmetric mechanisms in one-sided matching problems with {\em dichotomous preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are particularly…
The purpose of this note is to prove the existence of a randomized mechanism, a social decision scheme (SDS), with desirable fairness, efficiency, and strategyproofness properties unmatched by all known SDSs. In particular, we disprove a…
In this paper, the social impact theory introduced by Latan\'e is reconsidered. A fully differentiated society is considered; that is, initially every actor has their own opinion. The equivalent of Muller's ratchet guards that -- even for…
The Friendship Theorem states that if in a party any pair of persons has precisely one common friend, then there is always a person who is everybody's friend and the theorem has been proved by Paul Erd\H{o}s, Alfr\'{e}d R\'{e}nyi, and Vera…
Student's theorem is an important result in statistics which states that for normal population, the sample variance is independent from the sample mean and has a chi-square distribution. The existing proofs of this theorem either overly…
One of the central economic paradigms in multi-agent systems is that agents should not be better off by acting dishonestly. In the context of collective decision-making, this axiom is known as strategyproofness and turns out to be rather…
Humans have been arguing about the benefits of dictatorial versus democratic regimes for millennia. Despite drastic differences between the dictatorships in the world, one of the key common features is the \emph{Dictator's Dilemma} as…
Schulze's rule is used in the elections of a large number of organizations including Wikimedia and Debian. Part of the reason for its popularity is the large number of axiomatic properties, like monotonicity and Condorcet consistency, which…
This paper studies the evolution of social power in influence networks with stubborn individuals. Based on the Friedkin-Johnsen opinion dynamics and the reflected appraisal mechanism, two models are proposed over issue sequences and over a…
We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a determinant conjecture of R. Stanley (2017). This conjecture…
Voting is the aggregation of individual preferences in order to select a winning alternative. Selection of a winner is accomplished via a voting rule, e.g., rank-order voting, majority rule, plurality rule, approval voting. Which voting…
In the Sznajd model of 2000, a pair of neighbouring agents on a square lattice convinces its six neighbours of the pair opinion if and only if the two agents of the pair share the same opinion. It differs from other consensus models of…
Gibbard and Satterthwaite have shown that the only single-valued social choice functions (SCFs) that satisfy non-imposition (i.e., the function's range coincides with its codomain) and strategyproofness (i.e., voters are never better off by…
Shininess and strong politeness are properties related to theory combination procedures. In a paper titled "Many-sorted equivalence of shiny and strongly polite theories", Casal and Rasga proved that for decidable theories, these properties…