Speaker:     Sergey Ozernikov
Affiliation: The University of Auckland
Title:       Public-Key Infrastructure: trust metrics in the Web of Trust
Date:        Tuesday, 25 Mar 2014
Time:        5:00 pm
Location:    Room 412, Science Centre (303)

Public Key Insrastructure (PKI) is an arrangement that provides its users with means for confident and effective utilisation of public-key cryptography. An overview of non-hierarchical example of PKI – Pretty Good Privacy (PGP) – will be given, which uses the concept of a Web of Trust – a structure where any user can act as a certificate authority and assert validity of other users’ certificates.

A user A of PGP before sending a message to another user X must calculate the validity of the other user’s certificate using the public information about the network and their private information about the trustworthiness of the users on the certification paths from A to X. This is normally done on the basis of the so-called trust metric. Trust metrics and decision rules based on them are a field of active research – it is unlikely that anyone will invent a single perfect decision rule since there are many conflicting desiderata. In particular, it is desirable that such a decision rule
– be immune to various attacks;
– be easily computable;
– satisfy nice normative properties (axioms).

This is an introductory talk on this subject. No specific knowledge of cryptography will be assumed. Social networks people are especially invited.

Speaker:     Adam Clearwater
Affiliation: The University of Auckland
Title:       The single-crossing property on a tree
Date:        Tuesday, 11 Mar 2014
Time:        5:00 pm
Location:    Room 412, Science Centre (303)

We generalize the classical single-crossing property to single-crossing property on trees and obtain new ways to construct the so-called Condorcet domains which are sets of linear orders which possess the property that every profile composed from those orders have transitive majority relation. We prove that for any tree there exist profiles that are single-crossing on that tree; moreover, that tree is minimal in this respect for at least one such profile. Finally, we provide a polynomial-time algorithm to recognize whether or not a given profile is single-crossing with respect to some tree. We also show that finding winners for Chamberlin-Courant rule is polynomial  for profiles that are single-crossing on trees.

This paper is a product of Adam’s Summer Scholarship project. The research was conducted jointly with Clemens Puppe (KIT, Germany) and Arkadii Slinko.

Speaker:     Arkadii Slinko
Affiliation: The University of Ackland
Title:       Swensson’s theorem and its failed generalisations
Date:        Tuesday, 25 Feb 2014
Time:        5:00 pm
Location:    Room 412, Science Centre (303)

Swensson’s theorem is one of the many impossibility theorems in mathematical economics. These impossibility theorems give you an idea of what is possible and what is impossible to achieve. Imagine that you have to allocate state houses to families who need them and that those families have preferences on the set of houses. What should the allocation mechanism be? Swensson (1999) proved that if we impose just three simple desirable properties on the allocation mechanism we will be left only with a serial disctatorship under which a random queu (permutation) will be chosen and each family will be asked to choose their house when their term in the queue comes.

During Piotr Skowron’s visit in January we tried to generalise Swensson’s theorem to more general class of mechanisms called social assignment rules. We produced a bunch of counterexamples instead. In my talk I will prove Swensson’s theorem and present our counterexamples.

Speaker: Andy Philpott (Department of Engineering Science)
Topic: A Primer on Supply-Function Equilibrium
When: 2:30-3:30, Tuesday 29 October
Where: Room 5115, OGGB
Abstract: Supply function equilibrium models arise when agents offer a schedule of prices and quantities to an auction for a single divisible good. They were first developed in the setting of treasury auctions, but have become useful models for studying auctions of electricity, where uncertainty plays a key role. This talk will attempt to give an elementary account of supply function equilibrium, focusing on the mathematics underlying the model.

Slides are available.

Speaker: Matthew Ryan (Department of Economics)
Topic: Belief Functions (Part II)
When: 2:30-3:30, Tuesday 22 October
Where: Room 5115, OGGB
Abstract:

Belief functions generalise the notion of probability by relaxing additivity, while retaining a weaker property called infinite monotonicity. Belief functions allow us to quantify beliefs in a manner which is sensitive to the strength of the evidential support. I’ll focus on how to update such beliefs; more generally, how to perform statistical inference when the prior is described by a belief function. Many puzzles and problems arise when considering the issue of updating/inference. This talk will be informal (i.e., ill-prepared!) and will raise questions rather than provide answers.

Speaker: Shaun White (PhD student, Department of Mathematics)
Topic: William Riker’s “Liberalism Against Populism”
When: 2:30-3:30, Tuesday 15 October
Where: Room 5115, OGGB
Abstract:

I will give an overview of William Riker’s “Liberalism Against Populism”. William Riker was a hugely influential political scientist. His “Liberalism Against Populism” (1982) is often said to be his seminal work. In it, Riker explores the implications of social choice theory for the theory of democracy. He argues that there are two ways to interpret voting. According to the liberal interpretation we vote merely to restrain elected officials. According to the populist interpretation we vote so that we can establish the general will of the electorate. Riker claims that the results of social choice theory imply that we must reject the populist interpretation. I will outline Riker’s reasoning. I will also discuss the very robust response made by Gerry Mackie (Democracy Defended, 2003).

Slides are available.

Speaker: Matthew Ryan (Economics)
Topic: Belief Functions (Part I)
When: 2:30-3:30, Tuesday 8 October
Where: Room 5115, OGGB
Abstract:

Belief functions are used to quantify degrees of belief. They provide a more flexible alternative to the usual (in Economics) quantification by probabilities. Any probability is a belief function, but not conversely. This talk will introduce belief functions and discuss an unexpected connection between the mathematics of belief functions and David Kreps’ (1979) famous axiomatisation of expected indirect utility. In a subsequent talk, I will discuss the updating of belief functions – how to perform statistical inference when the prior is described by a belief function.

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Speaker: Andrew Withy (Philosophy)
Topic: Truth is never enough.
When: 2:30-3:30, Tuesday 24 September
Where: Room 5115, OGGB
Abstract:

Humans always bear in mind more factors than simply truth when deciding what to say, which theorems to prove, or which conclusions to draw from a data set. Standard reasoning models treat all conclusions from valid arguments equally, while humans show distinct preferences for simple, consistent, and informative conclusions. I will introduce some formal information norms, and discuss their relationship with a class of intuitive syntactic preference relations over conclusions. One surprising ‘co-incidence’ is that the diverse and seemingly unrelated properties of ceteris paribus informativity, equilinear distributivity, propositional inclusion, and deductive finitude appear to be equivalent under these norms. Time permitting, some practical consequences of these norms will be sketched, as well as applications in linguistic pragmatics or philosophy of science, depending on audience interest.