by Mark C. Wilson | Oct 4, 2013
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.
by Mark C. Wilson | Sep 19, 2013
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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.
by Mark C. Wilson | Sep 11, 2013
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.
by Mark C. Wilson | Aug 23, 2013
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.
by Mark C. Wilson | Aug 16, 2013
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.
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