Consensus-halving via theorems of Borsuk-Ulam and Tucker

Forest W. Simmons and Francis Edward Su

In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believe the portions are equally split. Moreover, the division takes at most n cuts, which is best possible. This extends prior work using methods from combinatorial topology to solve fair division problems. Several applications of consensus-halving are discussed.

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Year of publication:	2001 ; Manuscript version, February 2001
Authors:	Simmons, Forest W. ; Su, Francis Edward
Publisher:	Claremont, CA : Claremont Graduate University
Subject:	Mathematische Optimierung \| Mathematical programming \| Gerechtigkeit \| Justice \| Spieltheorie \| Game theory \| Theorie \| Theory