by Mark C. Wilson | Oct 20, 2013
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.
by Mark C. Wilson | Oct 12, 2013
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.
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.
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