Related papers: What majority decisions are possible with possible…
This is a survey paper on rainbow sets (another name for ``choice functions''). The main theme is the distinction between two types of choice functions: those having a large (in the sense of belonging to some specified filter, namely closed…
The voter model consists of a set of agents whose opinion is a binary variable. At each time step, an agent along with a social neighbor is selected and the agent imitates the social neighbor at the next time step. In this paper, we study a…
We analyze Assessment Voting, a new two-round voting procedure that can be applied to binary decisions in democratic societies. In the first round, a randomly-selected number of citizens cast their vote on one of the two alternatives at…
We prove that the following problem is decidable: given a finite set of relations, decide whether this set admits a near-unanimity function.
Let m>2 be an integer. We show that ZF + "For every integer n, Every countable family of non-empty sets of cardinality at most n has an infinite partial choice function" is not strong enough to prove that every countable set of m-element…
We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings…
Voting rules may implement the will of the society when all eligible voters vote, and only them. However, they may fail to do so when sybil (fake or duplicate) votes are present and when only some honest (non sybil) voters actively…
We study approval-based committee voting in which a target number of candidates are selected based on voters' approval preferences over candidates. In contrast to most of the work, we consider the setting where voters express uncertain…
In approval-based committee (ABC) voting, the goal is to choose a subset of predefined size of the candidates based on the voters' approval preferences over the candidates. While this problem has attracted significant attention in recent…
This paper addresses decision-aiding problems that involve multiple objectives and uncertain states of the world. Inspired by the capability approach, we focus on cases where a policy maker chooses an act that, combined with a state of the…
We present an alternative voting system that aims at bridging the gap between proportional representative systems and majoritarian, single winner election systems. The system lets people vote for multiple parties, but then assigns each…
For a voting ensemble that selects an odd-sized subset of the ensemble classifiers at random for each example, applies them to the example, and returns the majority vote, we show that any number of voters may minimize the error rate over an…
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 analyze properties of apportionment functions in context of the problem of allocating seats in the European Parliament. Necessary and sufficient conditions for apportionment functions are investigated. Some exemplary families of…
We derive a simple mathematical "theory" to show that two decision-making entities can work better together only if at least one of them is occasionally willing to stay neutral. This provides a mathematical "justification" for an age-old…
We describe a model that explains possibly indecisive choice behavior, that is, quasi-choices (choice correspondences that may be empty on some menus). The justification is here provided by a proportion of ballots, which are quasi-choices…
Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting…
We provide a necessary and sufficient condition for rationalizable implementation of social choice functions, i.e., we offer a complete answer regarding what social choice functions can be rationalizably implemented.
The well-known Condorcet's Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study this result under an asymmetric…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…