Preferential Polarization Measures

Given opinions of members of a society on a set of policies, as ordinal preferences; an approach to polarization is introduced. The concept here is considering polarization in a society as an aggregation of pairwise antagonisms, which depend on identi fication within groups as well as alienation among groups. Among measures which comply to this sort of conceptualization, a class of functions which satisfi es certain plausible properties is introduced for the case of three alternatives. This class coincides with the class characterized for unidimensional spaces in Esteban and Ray (1994)

Measuring Polarization in Preferences

In this paper, we study the measurement of polarization in collective decision making problems with ordinal preferences over alternatives. We argue that polarization can be measured as an aggregation of antagonisms over pairs of alternatives in the society. We propose a measure of this sort and show that it is the only measure satisfying some normatively appealing conditions

Polarisation Measurement on Three Alternatives

This bachelor thesis adresses the principle of polarisation on three different alternatives. It finds three different functions that find a measure for polarisation, that satisfy certain constraints. Then it argues about the usefulness of these function

Measuring polarization of preferences

In this paper, we study the measurement of polarization in collective decision making problems with ordinal preferences over alternatives. We argue that polarization can be measured as an aggregation of antagonisms over pairs of alternatives in the society. We propose a measure of this sort and show that it is the only measure satisfying some normatively appealing conditions

Representative democracy and the implementation of majority-preferred alternatives

In this paper, we contrast direct and representative democracy. In a direct democracy, individuals have the opportunity to vote over the alternatives in every choice problem the population faces. In a representative democracy, the population commits to a candidate ex ante who will then make choices on its behalf. While direct democracy is normatively appealing, representative democracy is the far more common institution because of its practical advantages. The key question, then, is whether representative democracy succeeds in implementing the choices that the group would make under direct democracy. We find that, in general, it does not. We analyze the theoretical setting in which the two methods are most likely to lead to the same choices, minimizing potential sources of distortion. We model a population as a distribution of voters with strict preferences over a finite set of alternatives and a candidate as an ordering of those alternatives that serves as a binding, contingent plan of action. We focus on the case where the direct democracy choices of the population are consistent with an ordering of the alternatives. We show that even in this case, where the normative recommendation of direct democracy is clear, representative democracy may not elect the candidate with this ordering

Measuring the cohesiveness of preferences: an axiomatic analysis

The final publication is available at Springer via http://dx.doi.org/10.1007/s00355-012-0716-9In this paper, we axiomatically study how to measure the similarity of preferences in a group of individuals. For simplicity, we refer to this as the cohesiveness. First, we provide axioms that characterize a family of linear and additive measures whose intersection is a partial ordinal criterion similar to first order stochastic dominance. The introduction of some additional properties isolates a one-parameter subfamily. This parameter evaluates the effect on the cohesiveness if one individual changes his ranking on a single pair of objects, as a function of how many of the remaining individuals in the group rank the first object over the second and vice versa. Finally, we characterize the focal measures of this subfamily separately showing that they coincide with measures constructed using two, at first sight, totally different approaches suggested in the literature.The author Jorge Alcalde-Unzu gratefully acknowledges financial support from the Spanish Ministry of Education and Science, through the projects ECO2009-11213 and ECO2009-12836. The author Marc Vorsatz gratefully acknowledges financial support from the Spanish Ministry of Education and Science (through the project ECO2009-07530) and from the Spanish Ministry of Economy and Competitiveness (through the project ECO2012-31985)

Medidas de consenso en contextos preferenciales generadas por distancias

En esta tesis se ha analizado cómo medir el consenso entre agentes que muestran sus preferencias sobre alternativas en diversos escenarios. El concepto de medida de consenso, introducido por Bosch para órdenes lineales, se ha extendido a órdenes débiles, órdenes dicotómicos y preferencias aprobatorias. Se han propuesto varias clases de medidas de consenso que tienen en cuenta las distancias entre las preferencias individuales; además, se ha desarrollado un procedimiento para que las distancias entre preferencias sean generadas por distancias entre vectores. Se han introducido distancias ponderadas sobre órdenes débiles, órdenes dicotómicos y preferencias aprobatorias que son sensibles a dónde se producen desacuerdos en la ordenación de las alternativas. Se ha llevado a cabo un estudio de las propiedades de las correspondientes medidas de consenso en los escenarios mencionados. Por otra parte se han utilizado medidas de consenso para la creación de conglomerados mediante un nuevo criterio, denominado método del consensoDepartamento de Economía Aplicad

Assent-maximizing social choice

We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population’s preferences and on the probability distribution over the sets of feasible alternatives that the society will face. Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule, it is known a priori that the subset of feasible alternatives will be a pair. We define a distinct social choice function for each distribution over the feasible subsets. Our rules can be interpreted as distance minimization—selecting the order closest to the population’s preferences, using a metric on the orders that reflects the distribution over the possible feasible sets. The distance is the probability that two orders will disagree about the optimal choice from a randomly selected available set. We provide an algorithmic method to compute these metrics in the case where the probability of a given feasible set is a function only of its cardinality.Economic