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SPEAKER:  Matthew Ryan (Economics)

 

DAY & TIME: 11am, 30 April

 

VENUE: OGGB Room 6115

 

TITLE: “Stochastic Choice and Expected Utility”

 

DESCRIPTION/ABSTRACT:  This talk will survey some recent developments in the theory of probabilistic choice, a branch of decision theory that treats the act of choice as inherently stochastic.  Much of this theory has applications in econometrics.  For example, McFadden’s logit model is based on a famous result by R. D. Luce.  Most stochastic choice models are probabilistic extensions of models of utility over deterministic objects.  Two recent papers (one by Dagsvik in Mathematical Social Sciences in 2008, and another by Gul and Pesendorfer in Econometrica in 2006) extend these ideas to choice amongst gambles, obtaining stochastic versions of expected utility.  This talk will mostly discuss the contribution by Dagsvik.  I hope to give a follow-up talk to the MSS Group later in May, which will discuss an alternative proof of one of Dagsvik’s results.

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Speaker: Reyhaneh Reyhani
Affiliation: Computer Science Department, The University of Auckland
Title: New measures of the difficulty of manipulation of voting rules
Date: Monday, 27 Apr 2009, 3:00 pm
Location: Room 401

Voting systems as a method for aggregating different opinions of group members are used extensively in different fields. Except for dictatorships, all voting systems are susceptible to strategic manipulation. From the perspective of mechanism design, it is generally regarded desirable to minimize the occurrence of strategic manipulation of voting rules.

One method for designing a safer voting system against strategic manipulation is to find rules that minimize the number of situations in which manipulation can succeed.

In this talk, we introduce new measures of manipulability of anonymous voting rules and argue for their superiority over some commonly used measures. We give a simple common framework that describes these measures and connects them to recent literature. We discuss their computation and present numerical results that allow for comparison of various common voting rules. This is joint work with Geoffrey Pritchard and Mark Wilson.

Finally, I will mention some issues that I intend to consider in future for my PhD thesis.

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Speaker: Geoff Pritchard
Affiliation: The University of Auckland
Title: Impartial-culture asymptotics: a central limit theorem for manipulation of elections
Date: Monday, 30 Mar 2009
Time: 4:00 pm
Location: Room 401 (small math seminar room)

We consider the problem of manipulation of elections using positional voting rules under Impartial Culture voter behaviour. We consider both the logical possibility of coalitional manipulation, and the number of voters that must be recruited to form a manipulating coalition. It is shown that the manipulation problem may be well approximated by a very simple linear program in two variables. This permits a comparative analysis of the asymptotic (large-population) manipulability of the various rules. It is seen that the manipulation resistance of positional rules with 5 or 6 (or more) candidates is quite different from the more commonly analyzed 3- and 4-candidate cases.

This is joint work with Mark Wilson, to appear in Mathematical Socal Sciences. Slides for the talk are available.

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Noam Nisan is one of the authors of the recent book Algorithmic Game Theory and his blog at http://agtb.wordpress.com/ is focused on this topic. It should be of interest to members of this group. He has a recent post on the history of this very active new field, in which he says:

“As the Internet was growing around the mid-to-late 1990’s, several threads of research emerged that somehow connected three key elements: Computer Science, Economics & Game-Theory, and the Internet.    Within the networking community, several researchers started worrying about the non-cooperative nature of the Internet, and started considering the issue of incentives.  Within the AI community, the coordination between multiple software “agents” became an area of study.  Electronic commerce started flourishing, and the underlying basic questions started emerging. A few economists started studying Internet-related economic questions.  Around the late 1990’s the different groups of people with these different motivations started talking to each other, and a joint field started emerging.  “

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Modelling Health Care: Combining real-world data in an “expert system” to test policy scenarios

Peter Davis, Director, COMPASS

There is increasing interest in the application of computational techniques in the social sciences, particularly in the area of modelling social processes. We present preliminary work in building a micro-simulation model of the system of decision-making in health care in the community whereby people experience illness and go to the doctor, who then responds. We combine data from different sources to give this model a solid base in the “real world” and we test it against external data. Policy scenarios are foreshadowed. There are major opportunities for collaborative work across disciplinary boundaries.

Note: COMPASS (www.compass.auckland.ac.nz) is a research group at UoA that uses quantitative, computational techniques in social sciences. The main purpose of this talk is to explore collaborative possibilities between the two groups.

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Speaker:     Arkadii Slinko
Affiliation: The University of Auckland
Title:       Axioms for ex-post rationality
Date:        Monday, 9 Mar 2009
Time:        3:00 pm
Location:    Room 401 (small math seminar room)

A Decision Maker (DM) must choose at discrete moments from a finite set of actions that result in random rewards.  The environment is complex in that she finds it impossible to describe the states of the world and is thus prevented from application of standard Bayesian methods of expected utility maximisation. The DM can however be ex-post rational. If she knows the utilities of the prizes she may, at each step, maximise the “expected utility” of each action using empirical frequencies of the rewards. We give axioms for such ex-post rational behaviour.

Mathematical apparatus used is that of multisets and multiset rankings developed by the presenter in a paper with Murat Sertel (2002).

We also consider the topic of utility elicitation which requires the apparatus of random walks on a non-standard grid. An interesting open question will be formulated that may be a topic for a research project or an Honours dissertation.

The paper is written jointly with Murali Agastya (UNSW, Australia and NUS, Singapore).

Everyone welcome!