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Papers by William Zwicker

Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on ... more Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on a referendum. If the winning combination is NYY on the ®rst, second, and third propositions, respectively, the paradox of multiple elections is that NYY can receive the fewest votes of the 2 3 = 8 combinations. Several variants of this paradox are illustrated, and necessary and sucient conditions for its occurrence, related to the``incoherence'' of support, are given.

Journal of Symbolic Logic, 1982

We present a moving-knife procedure, requiring only 11 cuts, that produces an envy-free allocatio... more We present a moving-knife procedure, requiring only 11 cuts, that produces an envy-free allocation of a cake among four players and discuss possible extensions to ve players.

Social Choice and Welfare, 2015

Page 1. Alan D.Iaylor AND William S.Iwicker i Pseudoweightings Page 2. Page 3. SIMPLE S Desirabil... more Page 1. Alan D.Iaylor AND William S.Iwicker i Pseudoweightings Page 2. Page 3. SIMPLE S Desirability Relations, Trading;, */ Pseudoweightings Alan D. laylor AND William S. /wicker Simple games are mathematical struc ...

... The authors would like to thank Larry Becker, Clifford Brown, Vin Moscardelli, and FredJonas ... more ... The authors would like to thank Larry Becker, Clifford Brown, Vin Moscardelli, and FredJonas for their assistance. Extensive remarks by Moshe“ Machover as well as comments by an anonymous referee greatly improved the manuscript. ...

Acta científica venezolana

The notion of iterated ultrapowers is adapted to the framework of filter spaces, introduced by th... more The notion of iterated ultrapowers is adapted to the framework of filter spaces, introduced by the authors in Part I [Ann. Pure Appl. Logic 41, No.2, 93-106 (1989; Zbl 0668.03025)]. A condition is given which guarantees that all ultrapowers be well-founded.

The Mathematical Intelligencer, 1995

In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes so... more In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes some convex combination of the measures used by those who receive the resulting pieces of cake. Also, given any sequence of positive real numbers that sum to one (which may be thought of as representing the players' relative entitlements), we

ABSTRACT If K is an index of relative voting power for simple voting games, the bicameral postula... more ABSTRACT If K is an index of relative voting power for simple voting games, the bicameral postulate requires that the distribution of K -power within a voting assembly, as measured by the ratios of the powers of the voters, be independent of whether the assembly is viewed as a separate legislature or as one chamber of a bicameral system, provided that there are no voters common to both chambers. We argue that a reasonable index – if it is to be used as a tool for analysing abstract, ‘uninhabited’ decision rules – should satisfy this postulate. We show that, among known indices, only the Banzhaf measure does so. Moreover, the Shapley–Shubik, Deegan–Packel and Johnston indices sometimes witness a reversal under these circumstances, with voter x ‘less powerful’ than y when measured in the simple voting game G1 , but ‘more powerful’ than y when G1 is ‘bicamerally joined’ with a second chamber G2 . Thus these three indices violate a weaker, and correspondingly more compelling, form of the bicameral postulate. It is also shown that these indices are not always co-monotonic with the Banzhaf index and that as a result they infringe another intuitively plausible condition – the price monotonicity condition. We discuss implications of these findings, in light of recent work showing that only the Shapley–Shubik index, among known measures, satisfies another compelling principle known as the bloc postulate. We also propose a distinction between two separate aspects of voting power: power as share in a fixed purse (P-power) and power as influence (I-power).

The 2010 International Conference on Computer Engineering & Systems, 2010

We examine three binary voting algorithms used with computer replication for fault tolerance and ... more We examine three binary voting algorithms used with computer replication for fault tolerance and separately observe the resultant reliability and security. We offer insights to answer the question: Can a voting algorithm provide a system with both security and reliability? We show that while random dictator (i.e., randomly choosing one of the replicas) provides good security and majority rule yields

Theory and Decision, 2005

Consider an election in which each of the n voters casts a vote consisting of a strict preference... more Consider an election in which each of the n voters casts a vote consisting of a strict preference ranking of the three candidates A, B, and C. In the limit as n → ∞, which scoring rule maximizes, under the assumption of Impartial Anonymous Culture (uniform probability distribution over profiles), the probability that the Condorcet candidate wins the election, given that a Condorcet candidate exists? We produce an analytic solution, which is not the Borda Count. Our result agrees with recent numerical results from two independent studies, and contradicts a published result of Van Newenhizen (1992).

The Journal of Symbolic Logic, 1982

The Journal of Symbolic Logic, 1991

Social Choice and Welfare, 2003