Speaker: Samin Aref
Affiliation: Department of Computer Science
Title: Measuring Partial Balance in Signed Networks
Date: Tuesday, 29 Sep 2015
Time: 5:00 pm
Location: CAG15/114-G15 (Commerce A)

Is the enemy of an enemy necessarily a friend, or is a friend of a friend a friend? If not, to what extent does this tend to hold? Such questions were formulated in terms of signed (social) networks and necessary and sufficient conditions for a network to be “balanced” were obtained around 1960. Since then the idea that signed networks tend over time to become more balanced has been widely used in several application areas, such as international relations. However investigation of this hypothesis has been complicated by the lack of a standard measure of partial balance, since complete balance is almost never achieved in practice.

We formalise the concept of a measure of partial balance, compare several known measures on real-world and synthetic datasets, as well as investigating their axiomatic properties. We use both well-known datasets from the sociology literature, such as Read’s New Guinean tribes, and much more recent ones involving senate bill co-sponsorship. The synthetic data involves both Erdős-Rényi and Barabási-Albert graphs.

We find that under all our measures, real-world networks are more balanced than random networks. We also show that some measures behave better than others in terms of axioms. We make some recommendations for measures to be used in future work.

Everyone welcome!

Speaker: Nina Anchugina & Arkadii Slinko
Affiliation: The University of Auckland
Title: Two talks see titles below
Date: Thursday, 7 May 2015
Time: 5:00 pm
Location: Room 260-325, Owen Glenn Building

1. Speaker: Nina Anchugina.
Title: A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting
Time: 30 min.

Abstract: The main goal of this talk is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting in inter-temporal decision-making. Exponential discounting has a well-established axiomatic foundation originally developed by Koopmans (1960) with subsequent contributions by several other authors. Hayashi (2003) and Olea and Strzalecki (2014) axiomatize quasi-hyperbolic discounting. In this talk we provide an alternative foundation for exponential and quasi-hyperbolic discounting, with simple, transparent axioms and relatively straightforward proofs. Using techniques by Fishburn (1982) and Harvey (1986), we show that Anscombe and Aumann’s (1963) version of Subjective Expected Utility (SEU) theory can be readily adapted to axiomatize the aforementioned types of discounting, in both finite and infinite horizon settings.

This is a joint work with Matthew Ryan.

2. Speaker: Arkadii Slinko
Title: Condorcet Domains and Median Graphs
Time 30 min

Abstract: A set of linear orders D is called a Condorcet domain if every profile composed from preferences from D has acyclic majority relation. Maximal Condorcet domains have been a subject of intense investigation, especially by Fishburn and Monjardet. Demange (2012) generalized the classical single-crossing property to the intermediate property on median graphs and proved that for every intermediate profile R with an odd number of voters on a median graph G there is a representative voter whose preference order coincides with the majority relation. We complement her result with proving that the linear orders of any profile which is intermediate on a median graph form a Condorcet domain. We prove that for any median graph there exists a profile that is intermediate with respect to that graph and that one may need at least as many alternatives as vertices to construct such a profile. We provide a polynomial-time algorithm to recognise whether or not a given profile is intermediate with respect to some median graph.

This is a joint work with Adam Clearwater (The University of Auckland) and Clemens Puppe (Karlsruhe Institute of Technology, Germany).

Everyone welcome!

The video from the seminar “Non-transitive Games in Business” by Valery Pavlov is now available on the CMSS YouTube channel.

Speaker: Valery Pavlov
Affiliation: Information Systems and Operations Management
Title: Non-transitive games in business
Date: Tuesday, 24 Mar 2015
Time: 5:00 pm
Location: Owen Glen building, room 260-321

This paper studies a model of competition between two players who are concerned not only with their expected profits but also with their chance of earning more than the other player. As a result, the game has some similarities with the well-known Rock-Paper-Scissors game. We conduct an experiment that tests (i) the hypothesis that such competition may arise without monetary rewards, purely as a result of intrinsic competitiveness and (ii) whether such social preferences can be easily mitigated. The experimental data provide strong evidence of the intrinsic competitiveness hypothesis and indicate some possibilities for its mitigation.
We hope this study may be of interest for practicing managers. First, it broadly captures a number of common situations in which “popular” decisions clash with “good” ones. Popular decisions bring pleasing results more often than good decisions but the difference in such is not that big whereas when outcomes of good decisions result in much higher gains albeit less often. Second, the competition mechanism we analyzed may explain why employees may be reluctant to share their own decisions and when decisions of the best employees are shared with the rest the overall performance of the company may be driven away from the optimum.

Everyone welcome!

Speaker:     Konstantin Sorokin
Affiliation: Higher School of Economics (Moscow)
Title:       Candidate utility invariance under stochastic voting
Date:        Friday, 16 Jan 2015
Time:        3:00 pm
Location:    Room 412, Science Centre (303)

Previous work by the authors (Zakharov, 2012, Sorokin and Zakharov, 2014) demonstrated
that the shape of the functions that translate vote shares into payoffs does have an effect on
the equilibrium actions of candidates in two-candidate voting games with a finite number of
stochastic voters. In particular, we have shown that the „mean voter theorem‰ that predicts
candidates choosing identical policy positions in fact holds only for a small set of candidate
utility functions (a set that includes both winner-take-all and proportional utility).

In this work, we take our research one step further. First, we show that, as the number of
voters becomes large, the outcome of an electoral competition game is invariant with respect
to the candidate utility functions. Second, we show that this invariance holds only if the votes
are cast independently. If there is, say, a common shock to the utilities that all voters receive, then candidate payoffs will affect the equilibrium even in the limiting games when the number of voters is infinite.

Everyone welcome!

Title:
Overview of the Centre for Mathematical Social Sciences

Speaker:
Mark Wilson, Computer Science and Centre for Mathematical Social Sciences (accompanied by Valery Pavlov)

Abstract:
The Centre for Mathematical Social Sciences at the University of Auckland is sometimes confused with COMPASS by outsiders. Although our structure, research methods and levels of funding have been quite different, it does seem that more collaboration could be explored.
I will give a quick overview of CMSS and discuss a few current research projects.

Date, Time, Venue: Friday September 12, 1-2, COMPASS meeting room (second floor, Fale Pacifika building)