by crus754 | Mar 23, 2009
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.
by adminnot | Mar 11, 2009
Speaker: Toby Walsh
Affiliation: UNSW and NICTA (Australia)
Title: Where are the really hard manipulation problems?
Date: Wednesday, 18 Mar 2009
Time: 4:00 pm
Location: Building 303, Room 279 (CS seminar room)
Voting is a simple mechanism to aggregate the preferences of agents. Many voting rules have been shown to be NP-hard to manipulate. However, a number of recent theoretical results have suggested that this is only a worst-case complexity, and manipulation may be easy in practice. In this talk, I show that empirical studies are useful in improving our understanding of this issue. I demonstrate that there is a smooth transition in the probability that a coalition can manipulate the result and elect a desired candidate as the size of the manipulating coalition is varied. I argue that for many independent and identically distributed votes, manipulation will be computationally easy even when the coalition of manipulators is critical in size.
by crus754 | Mar 8, 2009
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!
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