Vol. 12, No. 1, 2019

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Fair choice sequences

William J. Keith and Sean Grindatti

Vol. 12 (2019), No. 1, 13–30

We consider turn sequences used to allocate of a set of indivisible items between two players who take turns choosing their most desired element of the set, with the goal of minimizing the advantage of the first player. Balanced alternation, while not usually optimal, is fairer than alternation. Strategies for seeking the fairest choice sequence are discussed. We show an unexpected combinatorial connection between partition dominance and fairness, suggesting a new avenue for future investigations in this subject, and conjecture a connection to a previously studied optimality criterion. Several intriguing questions are open at multiple levels of accessibility.

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social choice, fair division, permutations, fairness, egalitarian, partitions, dominance
Mathematical Subject Classification 2010
Primary: 91A05
Secondary: 05A17
Received: 8 July 2016
Revised: 10 December 2017
Accepted: 30 December 2017
Published: 31 May 2018

Communicated by Kenneth S. Berenhaut
William J. Keith
Department of Mathematical Sciences
Michigan Tech University
Houghton, MI
United States
Sean Grindatti
Department of Mathematical Sciences
Michigan Tech University
Houghton, MI
United States