Showing papers in "Mathematical Social Sciences in 2012"

TL;DR: A comparison of several methods for Kemeny rank aggregation originating in social choice theory, machine learning, and theoretical computer science finds that, for this theoretically NP-hard task, in practice the problems span three regimes: strong consensus, weak consensus, and no consensus.

TL;DR: In this article, the authors give a computational study of the problem of determining which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added.

TL;DR: In this paper, the authors analyze mathematical properties of apportionment functions in the context of allocating seats in the European Parliament and present the corresponding allocations of seats among the Member States of the European Union.

TL;DR: Analysis of how the presence of other risks modifies the optimal level of prevention to protect against one risk shows that results differ depending on both the nature of the other risks and the properties of the utility function.

TL;DR: In 2011, seven mathematicians and one political scientist met at the Cambridge Apportionment Meeting and agreed a unanimous recommendation to the European Parliament for its future apportionments between the EU Member States as discussed by the authors.

TL;DR: In this paper, the authors analyze and evaluate the different decision rules describing the Council of Ministers of the EU starting from 1958 up to now, and propose a methodology for the design of the optimal (fair) decision rules, and conclude that Germany should receive more than the other three large countries under the optimal voting rule.

TL;DR: Insight is given into the complex balance between coalition structures, resource states or dynamics and the agent heterogeneity necessary to avoid bio-economic collapses and it is suggested that the stability of the grand coalition occurs for large enough stocks.

TL;DR: Eight power indices that admit a probabilistic interpretation for voting rules with abstention or with three levels of approval in the input, briefly (3, 2) games are introduced and procedures based on generating functions for weighted games, and extensible to (j,k) games, are provided.

TL;DR: In this article, the problem of assigning seats to the European Parliament within the special requirements imposed by the rules of the EU is dealt with by using integer linear programming (ILP) to provide at the same time rounding and satisfaction of the requirements.

TL;DR: A coalitional value is described from a non-cooperative point of view, assuming coalitions are formed for the purpose of bargaining and all the players have the same chances to make proposals.

TL;DR: It is shown that a ranking rule of the following type axiomatically is characterized by a monotonicity condition and a multi-stage cancellation property.

TL;DR: It is found that the Lisbon rules hurt medium sized countries, especially Central Eastern European countries with declining populations, most, while the United Kingdom is the clear winner.

TL;DR: This analysis is based on computational experiments and extends manipulability indices defined for single-valued social choice rules to the multi-valued case.

TL;DR: This brief article argues, via the maximum likelihood approach to voting, that it is optimal to ignore the social network structure altogether—one person, one vote.

TL;DR: The Cambridge Compromise composition of the European Parliament allocates five base seats to each Member State’s citizenry, and apportions the remaining seats proportionately to population figures using the divisor method with rounding upwards and observing a 96 seat capping as mentioned in this paper.

TL;DR: The von Neumann–Morgenstern expected utility model with incomplete preferences is revisited using a “constructive” approach, as opposed to earlier treatments that use convex analysis.

TL;DR: The position value for network situations is characterized along the lines of the characterization of the Shapley value by Shapley (1953) in contrast to previous attempts to provide such an axiomatization.

TL;DR: It is shown that in a direct revelation claim game, if the underlying division rule satisfies efficiency, equal treatment of equals, and weak order preservation, then all (pure strategy) Nash equilibria induce equal division.

TL;DR: This paper contains a proposal to determine the distribution of seats of the European Parliament among the member states by using linear spline functions.

TL;DR: It is deduced that the computation of a median complete preorder or of a Median weak order of a profile Π of m linear orders is NP-hard for any even m greater than or equal to 4 or for odd m large enough with respect to |X| (about |X |2).

TL;DR: This paper reviews the arguments that justify the principles of proportional and degressively proportional representation and concludes that proportional representation should be considered as a categorical category.

TL;DR: A model-theoretic framework is proposed for the analysis of judgement aggregation and it is shown that the conditions typically imposed on aggregators induce an ultrafilter on the set of individuals, thus establishing a generalised version of the Kirman–Sondermann correspondence.

TL;DR: A numerical method which determines uniquely a distribution of seats in the European Parliament which fulfil the requirements of degressive proportionality is proposed.

TL;DR: “consensus’ rules and “constant” rules are characterized as the only strongly group strategy-proof rules when there are more than two people.

TL;DR: It is found that the longer that players have gone without cooperating, the lower is the probability that they will cooperate in the next period, and there is a positive probability that cooperation never occurs.

TL;DR: In this article, a large population of voters with single-peaked preferences are partitioned into disjoint constituency, and collective decisions are taken by their representatives, one from each constituency, according to a weighted voting rule.

TL;DR: This work introduces some new voting rules based on a spatial version of the median known as the mediancentre, or Fermat-Weber point, which suggests that a voter who is further from consensus exerts a stronger tug on the election outcome, because her rubber band is more stretched.

TL;DR: This paper evaluates the Cambridge Compromise’s formula in relation to compromises between big and small states that have characterised the EU since its foundation and evaluates the formula by the degree to which the Compromises departs from normative standards of equality among citizens.

TL;DR: In this article, the authors study the set of allocation rules generated by component efficiency and weighted component fairness, a generalization of component fairness introduced by Herings et al. (2008).

TL;DR: An iterative algorithm for the numerical optimization of the utilitarian social welfare function is suggested and applied to the case of the European Parliament, confirming that the optimal system of weights exhibits a form of degressive proportionality.