Voters from m disjoint constituencies (regions, federal states, etc.) are represented in an assembly which contains one delegate from each constituency and applies a weighted voting rule. All agents are assumed to have single-peaked preferences over an interval; each delegate's preferences match his constituency's median voter; and the collective decision equals the assembly's Condorcet winner. We characterize the asymptotic behavior of the probability of a given delegate determining the outcome (i.e., being the weighted median of medians) in order to address a contentious practical question: which voting weights w 1 , . . . , w m ought to be selected if constituency sizes differ and all voters are to have a priori equal influence on collective decisions? It is shown that if ideal point distributions have identical median M and are suitably continuous, the probability for a given delegate i's ideal point λ i being the Condorcet winner becomes asymptotically proportional to i's voting weight w i times λ i 's density at M as m → ∞. Indirect representation of citizens is approximately egalitarian for weights proportional to the square root of constituency sizes if all individual ideal points are i.i.d. In contrast, weights that are linear in -or, better, induce a Shapley value linear in -size are egalitarian when preferences are sufficiently strongly affiliated within constituencies.
Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may ABSTRACTWe investigate the geographical concentration of representatives and the distribution of fiscal transfers both theoretically and empirically. We develop a model which predicts that funds to an area are positively correlated with the number of representatives residing in that area. Our empirical analysis uses the fact that due to the electoral rules for German state elections the number of representatives varies quasi-randomly across electoral districts. Controlling for various socio-economic and demographic variables and using a variety of estimation techniques, we find that areas with greater number of representatives receive more government funds.
Abstract:The paper investigates how voting weights should be assigned to differently sized constituencies of an assembly. The one-person, one-vote principle is interpreted as calling for a priori equal indirect influence on decisions. The latter are elements of a one-dimen sional convex policy space and may result from strategic behavior consistent with the median voter theorem. Numerous artificial constituency configurations, the EU and the US are investigated by Monte-Carlo simulations. Penrose's square root rule, which originally applies to preferencefree dichotomous decision environments and holds only under very specific conditions, comes close to ensuring equal representation. It is thus more robust than previously su ggested.
Power index research has been a very active field in the last decades. Will this continue or are all the important questions solved? We argue that there are still many opportunities to conduct useful research with and on power indices. Positive and normative questions keep calling for theoretical and empirical attention. Technical and technological improvements are likely to boost applicability.
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