Speaker: Arkadii Slinko
Affiliation: University of Auckland
Title: Clone Structures
Date: Tuesday, 4 Jun 2013
Time: 14:00
Location: 303-412
In Economics, a set of linear orders is normally interpreted as a set of opinions of agents about objects in C. Cloning candidates (products) is one of the most sophisticated tools of manipulation of elections (consumer surveys). Unfortunately most common voting rules are vulnerable to this method of manipulation. So clones do matter.
Mathematically, a subset of C which is ranked consecutively (though possibly in different order) in all linear orders is called a clone set. All clone sets for a given family of linear orders form the clone structure. In this talk I will formalise and study properties of clone structures. In particular, I will give an axiomatic characterisation of clone structures, define the composition of those, classify irreducible ones, and show that it is sufficient to have only three linear orders to realise any clone structure.
This is a joint work with Piotr Faliszewski (Krakow) and Edith Elkind (Oxford).
All welcome!
Speaker: Arkadii Slinko
Affiliation: The University of Auckland
Title: Secret sharing schemes 2 (elementary introduction)
Date: Tuesday, 21 May 2013
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building
This is a continuation of my talk on 7 May 2013.
This time I will first introduce two large classes of ideal access structures, namely, conjunctive and disjunctive hierarchical access structures. They are characterised by the fact that users are divided into classes so that users within each class are equivalent but users belonging to different classes have different status with respect to the activity. For example, the UN Security Council with its permanent and non-permanent members is a conjunctive hierarchical access structure (to the passage of a resolution).
The main part of the talk will be focused on the connection between ideal secret sharing schemes and matroids. The theorem of Brickel and Davenport (1991) which describes this connection plays a central role in the theory of secret sharing. A short introduction to matroids will be given, no prior knowledge of matroids will be necessary.
Professor Puppe, Chair of Economic Theory at the Karlsruhe Institute of Technology, visited the CMSS for several weeks in February and March of 2013. Professor Puppe is managing editor of Social Choice and Welfare.
On 20 March 2013, Professor Puppe gave a Public Lecture on “Choosing how to vote: the mathematics of elections”. It gives a non-technical overview of the area. With New Zealand in the midst of a review of the Mixed Member Proportional Representation (MMP) voting system, the CMSS hopes that such events will promote more informed debate on this important topic.
Link to a video record of the talk (audio plus slides) here:
https://dl.dropboxusercontent.com/u/61342635/A201303201801.LTRD253350.REV1-slides.m4v
Speaker: Professor Bettina Klaus
Affiliation: University of Lausanne
Date: Friday 3 May 2013
Time: 12pm
Venue: Room 317, Level 3, Owen G Glenn Building
Abstract: In college admissions and student placements at public schools, the admission decision can be thought of as assigning indivisible objects with capacity constraints to a set of students such that each student receives at most one object and monetary compensations are not allowed. In these important market design problems, the agent-proposing deferred-acceptance (DA-)mechanism with responsive strict priorities performs well and economists have successfully implemented DA-mechanisms or slight variants thereof. We show that almost all real-life mechanisms used in such environments – including the large classes of priority mechanisms and linear programming mechanisms – satisfy a set of simple and intuitive properties. Once we add strategy-proofness to these properties, DA-mechanisms are the only ones surviving. In market design problems that are based on weak priorities (like school choice), generally multiple tie-breaking (MTB) procedures are used and then a mechanism is implemented with the obtained strict priorities. By adding stability with respect to the weak priorities, we establish the first normative foundation for MTB-DA-mechanisms that are used in NYC.
This is a joint Department of Economics/CMSS seminar.
Speaker: Arkadii Slinko
Affiliation: The University of Auckland
Title: Secret sharing schemes (an elementary introduction)
Date: Tuesday, 7 May 2013
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building
Certain cryptographic keys, such as missile launch codes, numbered bank accounts and the secret decoding exponent in an RSA public key cryptosystem, are so important that they present a dilemma. If too many copies are distributed, one may be leaked. If too few, they might all be lost or accidentally destroyed. Secret sharing schemes invented by Shamir (1979) and Blakley (1979) address this problem, and allow arbitrarily high levels of confidentiality and reliability to be achieved. A secret sharing scheme `divides’ the secret S into `shares’ – one for every user – in such a way that S can be easily reconstructable by any authorised subset of users, but an unauthorised subset of users can extract absolutely no information about S. A secret sharing scheme, for example, can secure a secret over multiple servers and it remains recoverable despite multiple server failures.
Secret sharing schemes are a sort of cooperative games where the information and not money is being distributed among players. The set of authorised coalitions of a secret sharing scheme is a simple game so there is a rich connection to the theory of games.
In my talk I will give an elementary introduction to secret sharing.
Speaker: Dr Ben Greiner
Affiliation: University of New South Wales
Title: Bargaining, Asymmetric Information, and Communication – An Experiment
Date: Tuesday, 9 Apr 2013
Time: 12:00 pm
Location: Lab 04, Level 0, Owen Glenn Building
(note the unusual time and venue)
This paper explores the effect of communication on negotiation behavior in a stylized bargaining environment with asymmetric information. In particular, we study an Ultimatum Game in which the total amount to be bargained over (the pie) might be unknown to one party. We systematically vary whether both parties are informed about the pie size (baseline), or only the proposer, or only the responder. In addition, we vary whether there is no communication before the bargaining procedure, or whether the informed party can send a message about the pie size before decisions are made. In one communication condition, the message sender is free to choose the correct or the wrong message (cheap talk), while in the second communication condition the sender can only choose whether to reveal or not to reveal the true pie size (“true talk”). We find that contrary to the theoretical prediction cheap talk has a significant positive effect on efficiency, while true talk is less effective than expected.
Speaker: Kathryn E. Lenz
Affiliation: Department of Mathematics and Statistics, University of Minnesota Duluth
Title: Voting Methods for Municipal Elections: Propaganda, Field Experiments and what USA Voters Want from an Election Algorithm
Date: Tuesday, 19 Mar 2013
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building
Within the past two decades various cities across the USA have experimented with instant run-off voting (IRV) for political elections. These experiments demonstrate a public desire for replacing plurality voting with a better method and they give insight into what voters want from an election algorithm. This talk will briefly review several standard election algorithms, properties and public reaction to them. Examples will be given of IRV city election results, pro-IRV propaganda found on websites, misrepresentations in newspaper opinion pieces and discussions with mathematicians and non-mathematicians. Though disheartening, misinformation about IRV propagating in the public arena and suppression of full IRV election results do provide opportunities for the mathematically minded to engage in civic dialogue and to raise awareness concerning election algorithm options.
Slides are available.
Speaker: Matthias Ehrgott
Affiliation: The University of Auckland
Title: Multiobjective Optimization for Supporting Radiation Therapy Treatment Planning
Date: Tuesday, 5 Mar 2013
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building
The choice of a plan for radiotherapy treatment for an individual cancer patient requires the careful trade-off between the goals of delivering a sufficiently high radiation dose to the tumour and avoiding irradiation of critical organs and normal tissue. To support the treatment planner in this task it is necessary to visualize these trade-offs. The treatment planning problem can be formulated as a multi-objective optimization problem. We present a method to compute the optimal trade-offs for this problem and plot them in three dimensions. Furthermore, by computing a finite set of treatment plans that are well distributed across the entire trade-off surface, we support the treatment planner in identifying the best available plan for the patient under consideration.
Slides are available
The title of an article in The Economist. Very relevant to CMSS.
Speaker: Dov Samet
Affiliation: Tel Aviv University
Title: Interim agreements: In the footsteps of Zeno, Parkinson, and Nash
Date: Thursday, 14 Feb 2013
Time: 10:30 am
Location: Room 317, Owen Glenn Building
Zeno’s paradoxes of motion, which claim that moving from one point to another cannot be accomplished in finite time, seem to be of serious concern when moving towards an agreement in utility space is concerned. Parkinson’s Law of Triviality implies that such an agreement cannot be reached in finite time. By explicitly modeling dynamic processes of reaching interim agreements, we show that if utilities are von Neumann-Morgenstern, then no such process can bring about an agreement in finite time in linear bargaining problems. To extend this result for all bargaining problems, we characterize a particular path illustrated by Raiffa, and show that no agreement is reached along this path in finite time. When deadlines are set, then agreements are reached exactly at the deadline, proving Parkinson’s Law that work expands so as to fill the time available for its completion.