Monday talk (for general audience):
Mathematical vs. statistical models in social science
Mathematical arguments can give insights into social phenomena but, paradoxically, tend to give qualitative rather than quantitative predictions. In contrast, statistical models, which often look messier, can introduce new insights. We give several examples of interesting, but flawed, mathematical models for examples including political representation, trench warfare, the rationality of voting, and the electoral benefits of moderation. We consider ways in which these models can be improved in these examples. We also discuss more generally why mathematical models might be appealing and why they commonly run into problems.
Tuesday talk (for math/stat majors and other interested parties):
Coalitions, voting power, and political instability
We shall consider two topics involving coalitions and voting. Each topic involves open questions both in mathematics (probability theory) and in political science.
(1) Individuals in a committee or election can increase their voting power by forming coalitions. This behavior yields a prisoner’s dilemma, in which a subset of voters can increase their power, while reducing average voting power for the electorate as a whole. This is an unusual form of the prisoner’s dilemma in that cooperation is the selfish act that hurts the larger group. The result should be an ever-changing pattern of coalitions, thus implying a potential theoretical explanation for political instability.
(2) In an electoral system with fixed coalition structure (such as the U.S. Electoral College, the United Nations, or the European Union), people in diferent states will have different voting power. We discuss some flawed models for voting power that have been used in the past, and consider the challenges of setting up more reasonable mathematical models involving stochastic processes on trees or networks.
If people want to read anything beforehand, here’s some stuff for the first talk:
http://www.stat.columbia.edu/~gelman/research/unpublished/trench.doc
http://www.stat.columbia.edu/~gelman/research/unpublished/rational_final5.pdf
http://www.stat.columbia.edu/~gelman/research/published/chance.pdf
and here’s some stuff for the second talk:
http://www.stat.columbia.edu/~gelman/research/published/blocs.pdf
http://www.stat.columbia.edu/~gelman/research/published/STS027.pdf
http://www.stat.columbia.edu/~gelman/research/published/gelmankatzbafumi.pdf