Arrow, Hausdorff, and ambiguities in the choice of preferred states in complex systems. Issue 2 (17th February 2019)

• Record Type: Journal Article
• Authors: Erber, T.; Frank, M. J.
• Is Part Of: Journal of interdisciplinary mathematics. Volume 22:Issue 2(2019)
• Page Start: 129
• Page End: 137
• Publication Date: 2019-02-17
• Subjects: (2010) 00-XX -- 00Axx -- 00A05 -- 00A79 -- 00A99; 01.55.+b -- 01.90+g -- 01.70.+w; Arrow theorem -- Hausdorff distances -- Preferred states; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.1080/09720502.2019.1583830
• Languages: English
• ISSNs: 0972-0502

Abstract

Abstract: Arrow's 'impossibility' theorem asserts that there are no satisfactory methods of aggregating individual preferences into collective preferences in many complex situations. This result has ramifications in economics, politics, i.e., the theory of voting, and the structure of tournaments. By identifying the objects of choice with mathematical sets, and preferences with Hausdorff measures of the distances between sets, it is possible to extend Arrow's arguments from a sociological to a mathematical setting. One consequence is that notions of reversibility can be expressed in terms of the relative configurations of patterns of sets.