Partial Single-Peakedness: An Extension and Clarification

In: Public choice, Band 51, Heft 1, S. 71-80

Abstract

R. G. Niemi ("Majority Decision Making with Partial Unidimensionality," American Political Science Review, 1969, 63, 488-497), in an important but neglected paper, found that when orderings were drawn from a simulation based on the impartial culture, the greater the proportion of voter orderings that were single-peaked (a condition he called partial single-peakedness), the more likely there was to be a transitive group ordering. In addition, the likelihood of transitivity increased with group size. However, Niemi's simulation was restricted to the case of three alternatives, & he provided no theoretical explanation for the results of his simulation. This is provided here in terms of a model based on the idea of net preferences, & Niemi's results are extended for the general case of any finite number of alternatives, for electorates that are large relative to the number of alternatives being considered. In addition to providing a rationale for Niemi's simulation results, the ideas of net preferences & opposite preferences have a wide range of potential applications. 23 References. HA