Mathematics and Democracy [book]

Bruno Simeone, Friedrich Pukelsheim
2006 Studies in Choice and Welfare  
What is democracy? Democracy is a mechanism of creating the collective wisdom of a society from individual wisdoms of members of that society. However, starting from the famous Arrow's impossibility theorem that there are no reasonably good voting systems, some recent results shows that there are severe theoretical limitations for such a collective wisdom and even the mere possibility of it is somewhat doubtful. In this paper we illustrate these difficulties on a simple model of some
more » ... l parliament of some hypothetical country. Let us outline the basic assumptions of this model. The main object of consideration will be political programs which are viewed as packages of bills related to at least two independent issues; it could be, for example, internal and external policy. To measure them we need at least one separate dimension for each issue. Therefore we suggest that:
doi:10.1007/3-540-35605-3 fatcat:wghbztpunja3fhy2lzkaxhyhmi