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Computer Science Department ColloquiumThe Median Procedure – a Universal Aggregation Rule? |
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Tuesday, October 01, 2024, 12:30pm - 02:00pm |
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Speaker: William S. Zwicker
Bio
William S. Zwicker. Union College Mathematics Department and Murat Sertel Center for Advanced Economic Studies.
Location : CoRE 301
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Event Type: Computer Science Department Colloquium
Abstract: The median procedure MP (Barthélemy and Monjardet, 1981) aggregates a sequence of binary relations from some input class I into a single relation (with ties allowed) in some output class O. Varying the choice of I and O gives rise to a remarkable range of known rules as special cases of MP, including:(1) Plurality voting,(2) Approval voting,(3) Kemeny voting,(4) Borda voting (with outcome a winner), (5) Mirkin aggregation of equivalence relations (a form of cluster analysis),but not (6) Borda voting (with outcome a ranking),(7) The Mean Rule (Duddy and Piggins),(8) j,k-Kemeny (a version of Kemeny for weak orders), or(9) Any of the known Condorcet extensions: Copeland, minimax, etc.MP is usually defined by choosing the relation in O "closest" (using a form of Hamming distance) to the inputs. But an alternative formulation using inner (aka, "dot") product and orthogonal decomposition is better equipped to explain how and why computational complexity varies among the rules listed above, and why rules (6), (7) and (8) – but not (9) – also arise from MP when an extra projection step is inserted. This formulation suggests that rules (1) - (8) all aggregate information in essentially the same way, but differ with regard to which dimensions of information are taken into account.
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Contact Professor David Pennock
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