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Quantifying the Classical Impossibility Theorems from Social Choice
October 21, 2015 @ 2:00 pm - 4:00 pm
Social choice theory studies mathematically the processes involved when groups of people make choices. There are a number of beautiful and astonishing qualitative results in this area, for example Arrow’s Theorem about the non-existence of ideal voting schemes, and the Gibbard-Satterthwaite Theorem about the manipulation of elections. These classical theorems have had tremendous impact on the field of social choice. More recently, a sequence of stronger, quantitative versions of such theorems, by Gil Kalai, Ehud Friedgut, Elchanan Mossel et al., has entered into the picture. These results depend on the theory of Fourier analysis on the Boolean cube. In this talk, we will review some of these results and techniques, and put them in a broader context. Some questions we will address include: What are the implications of the aforementioned results for real-life applications? How grievous is Arrow’s Theorem really, and how should we cope with it? Finally, we will look at possible future research. Inspired by Daniel Kahneman’s work on cognitive biases, we introduce a new and simple model to simulate the various biases that manifest themselves in small meetings involving sequential voting.