Speaker: Matthew Ryan (AUT)
Paper to be presented: “Rationalising Random Choice as Random Consideration”
Date, Time and Venue: Monday, 13 May 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]
Abstract: Attempts to rationalise experimental evidence of pervasive randomness in choice behaviour may be divided into four categories: (i) models of deliberate randomisation; (ii) models of noisy utility maximisation (bounded rationality); (iii) random preferences models; and (iv) random consideration models. Category (i) has largely been explored by economists; (ii) and (iii) are mainly associated with mathematical psychologists and (iv) with researchers in marketing science. Recently, economists have taken an increasing interest in (iv), following the pioneering work of Manzini and Mariotti (Econometrica, 2014). This talk will briefly introduce random consideration models and their relationships with random preference models. A new random consideration model will also be proposed and “axiomatised”. This new model allows preferences to be ill-behaved on subsets of alternatives that are never considered together. In other words, the model is predicated on the implicit (and hopefully plausible) assumption that consideration is necessary to discipline preference.
Speaker: Mariya Teteryatnikova (Department of Economics at the National Research University Higher School of Economics, Moscow)
Paper to be presented: “On the Existence of Perfect Pairwise Stable Weighted Networks” joint with Philippe Bich (Paris School of Economics and University of Paris 1 Pantheon-Sorbonne)
Date, Time and Venue: Monday, 6 May 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]
Abstract: We introduce a new concept of stability in network formation, perfect pairwise stability, and prove that a perfect pairwise stable network exists under very general assumptions. Perfect pairwise stability strictly refines the pairwise stability concept of Jackson and Wolinsky (1996), by transposing the idea of “trembling hand” perfection from non-cooperative games to the framework of cooperative pairwise network formation. The existence result extends that of Bich and Morhaim (2017). We prove that our concept is distinct from strong pairwise stability, a refinement concept introduced by Jackson and Van den Nouweland (2005). We also introduce a sequential framework for network formation and define a natural concept of sequential pairwise stability. By analogy with non-cooperative games, we prove that the sequential framework can be associated with a static one, and that the sequential pairwise stable networks correspond exactly to perfect pairwise stable networks in the static framework.
Short Bio: Mariya Teteryatnikova received her PhD in 2010 from the European University Institute in Florence, Italy. After that, she worked for six years as an Assistant professor at the University of Vienna and for another year at WU- Vienna University of Economics and Business. Since September 2017 she holds a position of an Assistant professor at Higher School of Economics in Moscow and since July 2018 – also a position of a Research associate at WU in Vienna. Her main research fields are (mostly applied) game and network theory and industrial organization.
Speaker: Zach Weber (University of Otago)
Title: “Non-classical logic and inconsistent mathematics”
Date, Time and Venue: Monday, 1 April 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]
Abstract: Faced with logical paradoxes like the liar and the sorites, there are several options, including classical and non-classical (paracomplete and paraconsistent) approaches. I will briefly review some costs and benefits of each. Then I will mainly focus on the paraconsistent approach, using logics that allow for some contradictions. I will outline how paraconsistent logic may be applied in the foundations of mathematics, especially in naive set theory. I’ll conclude with a brief discussion of the wider inconsistent mathematics program as it stands today.
Speaker: Patrick Girard (University of Auckland)
Title: “Mini-Series on Paradoxes”
Date, Time and Venue: Monday, [to start with] 11 and 25 March 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]
Abstract: Patrick will offer 2-3 seminars on paradoxes. He will start with historical/conceptual paradoxes (about God, being bald, and there being no change). He will then talk about modern logical paradoxes that involve truth, set membership and conditionals. He will end with paradoxes involving probability. The journey will take you from a conceptual/historical understanding of paradoxes in philosophy, go via problems in mathematics and logic, and end with more specific paradoxes behind the kind of mathematics that CMSS members are using in social choice theory and the like.
Speaker: Addison Pan (University of Auckland)
Title: “A Note on The Pivotality Condition”
Date, Time and Venue: Wednesday, 23 May 2018, 14:00-15:00, 260-319 [Business School Building, Level 3]
Abstract: This note provides simple derivations of the equilibrium conditions for different voting games with incomplete information. In the standard voting game à la Austen-Smith and Banks (1996), voters update their beliefs only based on the probability that they are pivotal. However, in voting games such as those in Ellis (2016) and Fabrizi and Pan (2017), given a closed and convex set of priors, the ambiguous averse voters select the prior from this set in a strategy-contingent manner. Therefore, it is shown in this paper that in ambiguous voting games the conditional probability of being pivotal alone is not sufficient to determine each voter’s best response.
Speaker: Arkadii Slinko (University of Auckland)
Title: “What Do Multiwinner Voting Rules Do? Some Simulations Over the Two-Dimensional Euclidean Domain”, joint work with Edith Elkind, Piotr Faliszewski, Jean-Francois Laslier, Piotr Skowron and Nimrod Talmon
Date, Time and Venue: Wednesday, 9 May 2018, 14:00-15:00, 260-319 [Business School Building, Level 3]
Abstract: We visualize aggregate outputs of several multiwinner voting rules—SNTV, STV, Bloc, k-Borda, Monroe, Chamberlin–Courant, and PAV—for elections generated according to the two-dimensional Euclidean model. We consider three applications of multiwinner voting, namely, parliamentary elections, portfolio/movie selection, and shortlisting, and we use our results to understand which of these rules seem to be best suited for each application. In particular, we show that STV (one of the few nontrivial rules used in real high-stake elections) exhibits excellent performance, whereas the Bloc rule (also often used in practice) performs poorly. We also visualise three approximation algorithms for the computationally hard Chamberlin–Courant and Monroe rules. Our results show that the best approximation algorithms on offer (one of which is introduced in this paper) can be safely used instead of the original rules themselves.
Speaker: Matthew Ryan (AUT)
Title: The Jury Paradox
Date, Time and Venue: Wednesday, 7 March 2018, 14:00-15:00, 260-319 [Business School Building, Level 3]
Abstract: This talk is a sequel to last year’s discussion of Condorcet’s Jury Theorem, which is a classic result on the “wisdom of crowds”. Timothy Feddersen and Wolfgang Pesendorfer (Am. Pol. Sci. Rev., 1998) showed that raising the hurdle for conviction (e.g., from simple majority to unanimity) may increase the probability of convicting an innocent defendant, even when all jurors regard this error as worse than that of acquitting a guilty defendant and all vote “rationally”. The talk will explore the logic behind this “Jury Paradox”.
Speaker: Piotr Faliszewski (Krakow)
Date, Time and Venue: Monday, 26 February 2018, 15:00-16:00, CaseRoom4/260-009 [Business School Building, Level 0]
Abstract: We start from examples of multiwinner voting rules, then dwell on a particular class of those rules, called committee scoring rules, which we consider in detail from axiomatic, algorithmic and experimental perspective. We promise beautiful pictures!
Speaker: Han Bleichrodt (Erasmus University Rotterdam and ANU)
Date, Time and Venue: Friday, 23 February 2018, 12:00-13:00, room 260-6115 [Business School Building, Level 6]
Title: Testing Hurwicz Expected Utility
Abstract: Gul and Pesendorfer (2015) propose a new theory of ambiguity, they dub Hurwicz expected utility (HEU). HEU is the first axiomatic theory that is consistent with most of the available empirical evidence on decision under uncertainty. We show that HEU is also tractable and a particular subclass can readily be estimated and tested. We do this by requiring the probability weighting functions in the HEU representation to come from a two-parameter family. We investigate two predictions of HEU. The first prediction is that ambiguity aversion is constant across different sources of ambiguity. We investigate this utilizing the data of Abdellaoui et al. (2011). We observe support for it in their most extensive data set, but not in the other data set. The second prediction is that ambiguity aversion and first-order risk aversion (Segal and Spivak, 1990) are positively correlated. We perform an experiment to test this prediction. As the positive correlation revealed in the data is only slight to fair we conclude the evidence of a positive relation between ambiguity aversion and first order risk aversion is not conclusive.
Speaker: Matthew Ryan (AUT)
Date, Time and Venue: Thursday, 26 October 2017, 2:00-3:00 pm, room 260-323 [Business School Building, Level 3]
Title: The Condorcet Jury Theorem: An Introduction
Abstract: Back in August, Simona Fabrizi presented her work with Addison Pan on the so-called “Jury Paradox”. The present talk provides an introduction to some of the background literature on group decision-making. The “Condorcet Jury Theorem” is an 18th century result due to the Marquis de Condorcet, which anticipates modern notions of the wisdom of crowds. It is also important in political theory as a rationale for democratic decision-making. The theorem asserts that (under suitable conditions) a group of relatively uninformed voters will make better decisions by majority rule than a single expert deciding unilaterally, provided the group is large enough. We introduce Condorcet’s result and its limitations, as well as a few extensions. Condorcet assumed “sincere” voting, while the modern research on group choice requires that votes be cast “rationally” – that is, the profile of votes should be an equilibrium (in the sense of Harsanyi) of the voting game. It is well-known that sincere voting need not be rational in this sense. Does the essence of the Jury Theorem survive strategic voting? Come along and find out!