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Download Borda Scores and Aggregation of Preference: A Geometric-Combinatoric and a Topological Approach
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The University of Chicago Department of Statistics Statistics Colloquium JUN ZHANG Department of Psychology University of Michigan, Ann Arbor Borda Scores and Aggregation of Preference: A Geometric-Combinatoric and at Topological Approach MONDAY, April 23, 2012, at 4:00PM 133 Eckhart Hall, 5734 S. University Avenue Refreshments following the seminar in Eckhart 110. ABSTRACT Borda scores are defined over ranking probabilities (“voter profiles”), that is, the probability distribution over all rankings of a set of candidates. It will first be shown that the space of Borda scores form a convex polytope called “permutahedron”. Investigating the various ways a permutahedron as a geometric-combinatoric object may arise allows one to appropriately define Borda scores for binary choice probabilities, for subset choice probabilities, and for rank-position probabilities. A topological approach is then adopted to study aggregation of preference under interval-scaled utilities. It turns out that any well-behaved (continuous, anonymous, and respecting unanimity) aggregation map (“social choice function”) has to allow for null outcome in the social choice while not allowing for null preference by an individual voter. This result complements Chilchilnisky and Heals (1983) topological rendition of impossibility theorems of K. Arrow. For further information and inquiries about building access for persons with disabilities, please contact Dan Moreau at 773.702.8333 or send him an email at [email protected]. If you wish to subscribe to our email list, please visit the following website: https://lists.uchicago.edu/web/arc/statseminars.
