Download this Paper Open PDF in Browser

Dominance and Challenging in Abstract Systems

39 Pages Posted: 24 Aug 2015 Last revised: 7 Mar 2016

Scott Moser

School of Politics and International Relations; University of Texas at Austin - Department of Government

Date Written: February 29, 2016

Abstract

In many theories of group choice a dominance relation expressing the ability of alternatives to "defeat" or replace others is the central object on which various solutions are based. I present and argue for the use of a particular sub-relation of the dominance relation called the ultimate challenges relation as a basis for solutions in abstract systems. This derived relation is the largest sub-relation with the property that all win-sets are "self-consistent" with the ultimate challenges relation itself. When a group collectively and iteratively considers alternatives and compares them to possible replacements, the challenges relation is a useful and appropriate device for reasoning about stable outcomes. It reflects a form of iterated reasoning about the replaceability of a status quo by another alternative. Based on this new relation I propose a new solution in abstract systems. I apply it to cooperative majority voting which results in a modification to the tournament equilibrium set, potentially addressing some issues in the original solution.

Keywords: Abstract system, Tournaments, collective choice, social choice theory, retentive

Suggested Citation

Moser, Scott, Dominance and Challenging in Abstract Systems (February 29, 2016). Available at SSRN: https://ssrn.com/abstract=2649425 or http://dx.doi.org/10.2139/ssrn.2649425

Scott Moser (Contact Author)

School of Politics and International Relations ( email )

Nottingham
United Kingdom

University of Texas at Austin - Department of Government ( email )

College of Liberal Arts
1 University Station A1800
Austin, TX 78712
United States

HOME PAGE: http://smoser.webhost.utexas.edu/

Paper statistics

Downloads
20
Abstract Views
98