Research note Partial single-peakedness: An extension and clarification
✍ Scribed by Scott L. Feld; Bernard Grofman
- Publisher
- Springer US
- Year
- 1986
- Tongue
- English
- Weight
- 545 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0048-5829
No coin nor oath required. For personal study only.
✦ Synopsis
, 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 was there to be a transitive group ordering. Niemi also found that the likelihood of transitivity increased with n, group size -approaching one as n grew large. Niemi's simulation was restricted to the case of three alternatives. Also, he provided no theoretical explanation for the results of his simulation. Here we provide a theoretical explanation for Niemi's results in terms of a model based on the idea of net preferences, and we extend his results for the general case of any finite number of alternatives, m, for electorates that are large relative to the number of alternatives being considered. In addition to providing a rationale for Niemi's (1969) simulation results, the ideas of net preferences and opposite preference we make use of have a wide range of potential applications. * We are indebted to Jonathan Riley for helpful bibliographic assistance, and to Sue Pursche and the staff of the Word Processing Center, School of Social Sciences, U.C.I. for typing several earlier drafts of this manuscript.