Related papers: Outer Diversity of Structured Domains
We study the setting of committee elections, where a group of individuals needs to collectively select a given size subset of available objects. This model is relevant for a number of real-life scenarios including political elections,…
We characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. In particular, we show the following. 1. Every preference profile with up to two voters is one-dimensional Euclidean if and only…
Condorcet domains are subsets of permutations arising in voting theory: regarding their permutations as preference orders on a list of candidates, one avoids Condorcet's paradox when aggregating the preferences via a simple majority…
Population domain means are frequently expected to respect shape or order constraints that arise naturally with survey data. For example, given a job category, mean salaries in big cities might be expected to be higher than those in small…
Definable continuous injective maps defined on definable open sets into the Euclidean spaces of the same dimension are open maps in definably complete locally o-minimal expansions of ordered groups.
We exploit the standard inner product of Euclidean space to provide a new direction from which one can understand and analyze certain voting methods. Using this perspective along with the action of the symmetric and special orthogonal…
This paper formalizes the lattice structure of the ballot voters cast in a ranked-choice election and the preferences that this structure induces. These preferences are shown to be counter to previous assumptions about the preferences of…
The notion of preferences plays an important role in many disciplines including service robotics which is concerned with scenarios in which robots interact with humans. These interactions can be favored by robots taking human preferences…
The Pareto dominance relation of a preference profile is (the asymmetric part of) a partial order. For any integer n, the problem of the existence of an n-agent preference profile that generates the given Pareto dominance relation is to…
We show how hidden interesting subelections can be discovered in ordinal elections. An interesting subelection consists of a reasonably large set of voters and a reasonably large set of candidates such that the former have a consistent…
Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `$<$', `$=$', `$>$' between pairs of points are known. We do an attempt of formalizing structures behind…
Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected…
A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…
A definition of structural diversity, adapted from the biodiversity literature, is introduced to provide a general characterization of structures of condensed matter. Using the Favored Local Structure (FLS) lattice model as a testbed, the…
We study a public decision problem in which a finite society selects a public-good level from a closed interval. Agents either have single-peaked preferences or are completely indifferent over the interval; the latter capture abstention or…
This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can…
In order to represent the preferences of a group of individuals, we introduce Probabilistic CP-nets (PCP-nets). PCP-nets provide a compact language for representing probability distributions over preference orderings. We argue that they are…
A preference profile with m alternatives and n voters is 2-dimensional Euclidean if both the alternatives and the voters can be placed into a 2-dimensional space such that for each pair of alternatives, every voter prefers the one which has…
When composing multiple preferences characterizing the most suitable results for a user, several issues may arise. Indeed, preferences can be partially contradictory, suffer from a mismatch with the level of detail of the actual data, and…
We analyse strategic, complete information, sequential voting with ordinal preferences over the alternatives. We consider several voting mechanisms: plurality voting and approval voting with deterministic or uniform tie-breaking rules. We…