相关论文: What majority decisions are possible

We pursue the study of families of functions on the natural numbers, with emphasis here on the bounded families. The situation being more complicated than the unbounded case, we attack the problem by classifying the families according to…

A Condorcet winning set addresses the Condorcet paradox by selecting a few candidates--rather than a single winner--such that no unselected alternative is preferred to all of them by a majority of voters. This idea extends to…

Let V be a finite society whose members express weak orderings (hence also indifference, possibly) about two alternatives. We show a simple representation formula that is valid for all, and only, anonymous, non-manipulable, binary social…

We show that almost all permutations have some power that is a cycle of prime length. The proof includes a theorem giving a strong upper bound on the proportion of elements of the symmetric group having no cycles with length in a given set.

The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…

As the world's democratic institutions are challenged by dissatisfied citizens, political scientists and also computer scientists have proposed and analyzed various (innovative) methods to select representative bodies, a crucial task in…

Suppose a committee consisting of three members has to match $n$ candidates to $n$ different positions. Each member of the committee proposes a matching, however the proposed matchings totally disagree, i.e., every candidate is matched to…

Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…

Impartial selection is the selection of an individual from a group based on nominations by other members of the group, in such a way that individuals cannot influence their own chance of selection. For this problem, we give a deterministic…

We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains…

Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via…

The voting process is formalized as a multistage voting model with successive alternative elimination. A finite number of agents vote for one of the alternatives each round subject to their preferences. If the number of votes given to the…

More and more processes governing our lives use in some part an automatic decision step, where -- based on a feature vector derived from an applicant -- an algorithm has the decision power over the final outcome. Here we present a simple…

In the marriage problem, a variant of the bi-parted matching problem, each member has a `wish-list' expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain…

For probability vectors x and y, the catalytic majorization relation x prec_T y is defined to hold when there exists a probability vector z such that x otimes z is majorized by y otimes z. In this paper, an infinite family of functions is…

Classical results in voting theory show that strategic manipulation by voters is inevitable if a voting rule simultaneously satisfy certain desirable properties. Motivated by this, we study the relevant question of how often a voting rule…

The goal of this paper is twofold. First and foremost, we aim to experimentally and quantitatively show that the choice of a multiwinner voting rule can play a crucial role on the way minorities are represented. We also test the possibility…

A cornerstone of social choice theory is Condorcet's paradox which says that in an election where $n$ voters rank $m$ candidates it is possible that, no matter which candidate is declared the winner, a majority of voters would have…

Complexity theory is a useful tool to study computational issues surrounding the elicitation of preferences, as well as the strategic manipulation of elections aggregating together preferences of multiple agents. We study here the…

This paper discusses the question of how many non-empty subsets of the set $[n] = \{ 1, 2, ..., n\}$ we can choose so that no chosen subset is the union of some other chosen subsets. Let $M(n)$ be the maximum number of subsets we can…