ISSN:
1436-4646
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract This paper considers an election between candidatesA andB in which (1) voters may be uncertain about which candidate they will vote for, and (2) the winner is to be determined by a lottery betweenA andB that is based on their vote totals. This lottery is required to treat voters equally, to treat candidates equally, and to respond nonnegatively to increased support for a candidate. The setΛ n of all such lottery rules based on a total ofn voters is the convex hull of aboutn/2 ‘basic’ lottery rules which include the simple majority rule. For odd values ofn ≥ 3 let $$\mu (n) = \tfrac{1}{2} + (n - 1)/[2n(n + 3)]$$ , and for even values ofn ≥ 4 let $$\mu (n) = \tfrac{1}{2} + [(n + 2)(2n(n + 2))^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - n(n + 6)]/[n(n - 2)(n + 4)]$$ . With $$\bar p$$ the average of then voters probabilities of voting forA, it is shown that withinΛ n the simple majority rule maximizes candidateA's overall win probability whenever $$\bar p \geqslant \mu (n)$$ , and thatμ(n) is the smallest number for which this is true. Similarly, the simple majority rule maximizesB's overall win probability whenever $$1 - \bar p$$ (the average of the voters probabilities of voting forB) is as large asμ(n).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01580368
