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.

Speaker: Shaun White (PhD student, Department of Mathematics)
Topic: Applications of the Gibbard-Satterthwaite Theorem to voting systems
When: 2:30-3:30, Tuesday 17 September
Where: Room 5115, OGGB
Abstract:

The Gibbard-Satterthwaite Theorem is one of social choice theory’s most notable results. Social choice theorists usually present the theorem as a statement about voting systems. Consequently, political scientists have shown considerable interest in the theorem and its applications.

The theorem applies to many voting systems, but it doesn’t apply to all voting systems. If we ask “which systems does the theorem apply to?”, the social choice theorist and the political scientist will give what appear to be different answers. This is partly because social choice theorists and political scientists use voting-terminology differently.

In this talk I will state the Gibbard-Satterthwaite Theorem in purely mathematical terms; the statement will refer to sets, relations, and functions. I will give an overview of the framework in which Gibbard originally presented the theorem; this framework features voters, preferences, strategies, and game forms. I will then use these two tools — the purely mathematical theorem, Gibbard’s framework — to build an interdisciplinary method for applying the Gibbard-Satterthwaite Theorem.

Speaker: Benjamin Hadjibeyli (ENS de Lyon)
Topic: Geometry of distance-rationalization
When: 2:30-3:30, Tuesday 27 August
Where: Room 5115, OGGB
Abstract: Representing voting rules in the unit simplex by considering only the distribution of voter preferences is a classical approach to voting theory, for example in the books of Donald Saari. However, it has not yet been applied to the distance-rationalization framework. We aim to analyse general properties of distance-rationalizable voting rules by looking at the geometry of their consensus and metric under this representation. This leads to interesting geometric questions involving metric spaces.

Slides are available.

Speaker: Mark Wilson (Computer Science)
Topic: “Distance rationalization of voting rules”
When: 2:30-3:30, Tuesday 20 August
Where: Room 5115, OGGB
Abstract:
A promising unifying framework for social choice involves the concept of measuring how far a preference profile is from an acknowledged consensus, with respect to some distance measure. This has been actively studied recently, particularly by Elkind, Faliszewski, and Slinko.

This is an introductory talk, giving basic definitions, examples, and results, to set the scene for next week’s talk.

Slides are available.

Speaker: Patrick Girard (Philosophy)
Topic: “Belief revision and the limit assumption: Tension between static belief and belief dynamics”
When: 2:30-3:30, Tuesday 13 August
Where: Room 5115, OGGB
Abstract:
…so there’s this assumption called the limit assumption which basically says that doxastic orders are well-founded. If you only consider beliefs as being static, the assumption is philosophically implausible. However, when you do belief change, than it becomes crucial for a lot of doxastic operations. Without it, you can’t be sure that revising a belief set returns a belief set. Which considerations is more important? Static or dynamic? I will try and explain what that all means.

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.