Beyond Condorcet: Optimal Aggregation Rules Using Voting Records

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-maker's capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This paper presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters' past decisions is available, but the correct decisions are not known. We observe that any arbitrary evaluation of the decision-maker's capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers.

Voting Power Derives from the Poll Distribution. Shedding Light on Contentious Issues of Weighted Votes and the Constitutional Treaty

Analysis of the Constitutional Treaty of the European Union shows that there is a serious discrepancy between the voting power gradient of Member States computed by the Shapley-Shubik and Banzhaf indices. Given the lack of compelling arguments to choose between these indices on purely axiomatic grounds, we turn to a probabilistic approach as pioneered by Straffin (1977) focusing on the probability distribution of voting poll outcomes. We present a unifying model of power indices as expected decisiveness, which shows that the defining feature of each approach is a particular distribution of the voting poll. Empirical evidence drawn from voting situations, in addition to a consideration of first principles, leads us to reject one of these approaches. The unified formulation allows us to develop useful related concepts of efficiency and blocking leverage, previously used solely by a 'Banzhaf' approach, for the case of Shapley-Shubik, and a comparison of results is shown.Voting power indices, Power gradient, Coefficient of representation, Expected decisiveness, Efficiency, Blocking leverage, Constitution of the European Union

Does the Mobility of Football Players Influence the Success of the National Team?

This paper is motivated by the observation that there is a large discrepancy among football nations regarding the number of football players that play in the national team and also in their home league. Two extreme examples are Argentina and Italy : Almost all members of the national team of Argentina play in a foreign football league and all national team players of Italy play in their home league. We focus on the question whether a country's success in international competitions significantly depends on the mobility of its football players. More specifically, we analyze whether a country's success is influenced (i) by the number of national team players that do not play in the home league and (ii) by the number of national team players from other countries that play in the home league. Our study is based on data of all 32 national football teams qualified for the FIFA World Cup in Germany 2006 including more than 700 players with a total estimated market value of almost four billion Euros. The main finding is that a country's success crucially depends on both imports and exports. This suggests that all countries that qualified for the World Cup gain from trade.football, international trade, transfer market

Defining a geographically weighted regression model of urban evolution. Application to the city of Volos, Greece

The main objective of this paper is the multivariate analysis of urban space and specifically with the use of data that refer to the level of city block. Part of the analysis has been the comparative assessment of multiple linear regression and geographically weighted regression (GWR) analysis as well as the application of the aforementioned methods in the study of the central district of the Volos metropolitan area. The city of Volos is an urban conglomeration of approximately 110.000 inhabitants, located at the middle-east of Greece and is considered to be in the upper extreme in the cities’ urban hierarchy in Greece. The results provide a response to a question raised by spatial scientists during the last decades: is there a way that regression analysis can reveal spatial variations of results and with respect to scale fluctuation? The use of classical multiple regression analysis provides a single result – equation for the entire area. On the other hand, geographically weighted regression analysis stems from the fact that the above result is inadequate to reflect the different relational levels among selected variables characterizing the entire area. New estimations with the use of GWR declare the existence of various sub-areas – divisions of the initial territory – formulating a set of equations that reveal the spatial variations of variable relations. The results of the application have well proved the dominance of the analysis in the local level towards the analysis in the global level, highlighting the existence of intense spatial differentiations of variables that “interpret” the rate of land values in the city. Moreover, the distinct spatial patterns that emerge throughout the entire area, establish an alternative approach of urban spatial phenomena interpretation and a new explanatory basis for the clarification of obscure relations.

Individual Differences in EWA Learning with Partial Payoff Information

We extend experience-weighted attraction (EWA) learning to games in which only the set of possible foregone payoffs from unchosen strategies are known, and estimate parameters separately for each player to study heterogeneity. We assume players estimate unknown foregone payoffs from a strategy, by substituting the last payoff actually received from that strategy, by clairvoyantly guessing the actual foregone payoff, or by averaging the set of possible foregone payoffs conditional on the actual outcomes. All three assumptions improve predictive accuracy of EWA. Individual parameter estimates suggest that players cluster into two separate subgroups (which differ from traditional reinforcement and belief learning)

Power in the Design of Constitutional Rules

This paper examines different ways of measuring power and the use of these measures in the context of the European Union. The paper deals with classical power indices of co-operative games and more recent non-cooperative a priori measures. Special emphasis of the paper is in inter-institutional balance of power, Nice reforms and eastern enlargement.