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Voting in Agreeable Societies

Student-Run Applied & Math Seminar

Speaker: Anthony Caine, UC Davis
Location: 2112 MSB
Start time: Wed, Feb 3 2016, 12:10PM

Consider a one dimensional political specturm like liberal versus conservative. Did you know that in a society where every two people can find a common ground then there is a stance that will be agreed upon by all people? While this is interesting, such a society does not model, say, the presidential election. Indeed, there exists people in America who cannot agree. However, maybe out of every 10 people, there are 3 that agree. This motivates the following definition and question, let's call a society (k,m)-agreeable if there are at least m people and for every subset of m people at least k of them agree on a candidate. Then what is the maximum number of people we can satisfy in the election? We can further generalize this to multidimensional "candidates", i.e. we have two dimensional political spectrum (control over property)x(control over person).