Related papers: Representation-Compatible Power Indices
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
We consider the problem of manipulation of elections using positional voting rules under Impartial Culture voter behaviour. We consider both the logical possibility of coalitional manipulation, and the number of voters that must be…
We exhibit the hidden beauty of weighted voting and voting power by applying a generalization of the Penrose-Banzhaf index to social choice rules. Three players who have multiple votes in a committee decide between three options by…
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…
Electing a committee of size k from m alternatives (k < m) is an interesting problem under the multi-winner voting rules. However, very few committee selection rules found in the literature consider the coalitional possibilities among the…
We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interval, whose admissible length depends on whether or not we…
Aggregating preferences under incomplete or constrained feedback is a fundamental problem in social choice and related domains. While prior work has established strong impossibility results for pairwise comparisons, this paper extends the…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
Given a set of agents with approval preferences over each other, we study the task of finding $k$ matchings fairly representing everyone's preferences. We model the problem as an approval-based multiwinner election where the set of…
The rankability of data is a recently proposed problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have…
In reinforcement learning, state representations are used to tractably deal with large problem spaces. State representations serve both to approximate the value function with few parameters, but also to generalize to newly encountered…
Within the domain of game theory, power indexes are defined as functions that quantify the influence of individual participants in collective decision-making processes. Felsenthal [D. Felsenthal. A Well-Behaved Index of a Priori P-Power for…
AI agents are commonly trained with large datasets of demonstrations of human behavior. However, not all behaviors are equally safe or desirable. Desired characteristics for an AI agent can be expressed by assigning desirability scores,…
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…
Coalitional manipulation in voting is considered to be any scenario in which a group of voters decide to misrepresent their vote in order to secure an outcome they all prefer to the first outcome of the election when they vote honestly. The…
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…
A new game-theoretic approach for combining multiple classifiers is proposed. A short introduction in Game Theory and coalitions illustrate the way any collective decision scheme can be viewed as a competitive game of coalitions that are…
Consider an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is $p>1/2$. Condorcet's Jury Theorem which he derived from the weak law of large…
Following Zhang and Grossi~(AAAI 2021), we study in more depth a variant of weighted voting games in which agents' weights are induced by a transitive support structure. This class of simple games is notably well suited to study the…
Participatory budgeting (PB) is a democratic paradigm whereby voters decide on a set of projects to fund with a limited budget. We consider PB in a setting where voters report ordinal preferences over projects and have (possibly) asymmetric…