Vol. 12, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12, 1 issue

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Addresses
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Fair choice sequences

William J. Keith and Sean Grindatti

Vol. 12 (2019), No. 1, 13–30
Abstract

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.

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

Communicated by Kenneth S. Berenhaut
Authors
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