Frontiers in Decision Theory & Experimentation
Source: The caterpillar symbol of ambiguity in ''Alice's Adventures in Wonderland''.
Contact the Editor of this blog, Matthew Ryan
papers and presentations (under construction)
"Fair market value could have contributed to the crash" (and slides)
This paper by ATE member Jack Stecher and co-authors Radhika Lunawat, Kira Pronin and Gaoqing Zhang examines (both theoretically and experimentally) how fair market value accounting in the absence of actual market prices may lead to market collapse."Choosing how to vote: the mathematics of elections"
ATE member, Clemens Puppe (Karlsruhe Institute of Technology) visited Auckland for several weeks in February and March of 2013. Clemens is managing editor of Social Choice and Welfare. Above is the title of a Public Lecture that Clemens delivered at the University of Auckland on 20 March 2013. The link is to the CMSS website, where you can find a recorded version of the lecture (audio plus slides)."The Condorcet Set: Majority Voting over Interconnected Propositions".
(Presentation by Clemens Puppe, KIT).
Abstract: Judgement aggregation is a model of social choice where the space of social alternatives is the set of consistent evaluations ('views') on a family of logically intercon- nected propositions, or yes/no-issues. Yet, simply complying with the majority opin- ion in each issue often yields a logically inconsistent collection of judgements. Thus, we consider the Condorcet set: the set of logically consistent views which agree with the majority on a maximal set of issues. The elements of this set are exactly those that can be obtained through sequential majority voting, according to which issues are sequentially decided by simple majority unless earlier choices logically force the opposite decision. We investigate the size and structure of the Condorcet set and hence the properties of sequential majority voting for several important classes of judgement aggregation problems. While the Condorcet set verifies McKelvey's (1979) celebrated 'chaos theorem' in a number of contexts, in others it is shown to be very regular and well-behaved.
selected ongoing research (under construction)
Matthew Ryan (AUT): With colleagues in the Centre for Mathematical Social Science (CMSS) I have an on-going research project looking at applications of abstract (or generalised) convexity to social and individual choice. For example, abstract convex geometries for discrete spaces are intimately connected with path independent choice functions (Koshevoy, MSS, 1999). My homepage has further notes and slides on this topic. I'm aware of some other ATE members who share this interest (such as Arkadii Slinko and Clemens Puppe). I'm always keen to hear from others who may be interested in this area -- so please let me know. At some point it would be nice to organise a workshop on this theme. Let me also say a little bit about the CMSS. This is an interdisciplinary group with core participants from mathematics, computer science, economics and philosophy. We also have contacts in engineering science, statistics and ISOM (Information Systems and Operations Management). We study a range of topics in social science from a mathematical or computational perspective, including decision theory and social choice. We are always keen to establish links with other individuals and groups in the region. We would be particularly keen to hear from researchers in mathematical politics. Several CMSS members have an interest in the design of voting systems but we don't currently have anyone with a background in political science engaged with the Centre.