Notes on Ostrogorski's paradox (Q760324)

When voters must choose between two parties holding contrasting positions on a series of issues, one party can win an election by majority rule even if its opponents' positions on every issue are preferred by a majority of the voters. This possibility has been termed Ostrogorski's Paradox. An example, borrowed from \textit{D. W. Rae} and \textit{H. Daudt} [Eur. J. Political Res. 4, 391-398 (1976)], illustrates the paradox. In the example, four groups of voters have different sets of positions on three salient issues. Two parties, X and Y, are competing for votes; party X favors position P on each issue, while party Y favors position Q in each case. It is evident that although a majority of the voters prefer position Q in each case, those in groups 1,2, and 3 will support Party X, which will consequently command a majority of the votes. In their investigations, Rae and Daudt have examined some characteristics of Ostrogorski's paradox when partisan positions are fixed. This paper extends the analysis of Ostrogorski's Paradox by analyzing the necessary conditions for its occurrence and by considering the case of variable party positions.