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.