Stemmingen zonder winnaar

W. R. van Zwet

Statistica Neerlandica, 1969, vol. 23, issue 4, 269-276

Abstract: Summary A group of n persons has to decide on one out of k alternatives. To achieve this end each pair of alternatives is put to a vote. It is assumed that each person ranks the k alternatives according to an individual preference scale and that on every vote between two alternatives he will vote for the alternative that occurs higher on his scale. If n is odd and an alternative obtains a majority on each of the (k ‐ 1) occasions on which it is put to a vote, the group will decide on that alternative. If no such winning alternative exists, a paradox of voting is said to occur. For even values of n the definition of a paradox is slightly more complicated. On the assumption that the preference scales of the n persons are obtained by n independent random drawings from the k! permutations of the numbers 1, 2,…,k, we discuss the computation of the probability of a paradox of voting Pk,n. Values of P3,n and Pk= lim Pk,n are given.

Date: 1969
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