The Role of Orthogonal Decomposition in Collective Decision-Making

Suppose several teachers are assessing the level of preparation of their common students, with the goal of splitting them into one group ready to tackle more abstract and challenging concepts, and a second group needing more review.  Each teacher submits a recommended division, and these views will be aggregated in some way, into a single collective decision as to the best split.  This context seems quite different from that of an election in which voters submit ballots, each of which ranks candidates for President, and the collective decision identifies the winner. However, in both cases we are aggregating several input binary relations of a specified type into a single binary relation of a possibly different type.

We’ll discuss two “universal” rules for aggregating binary relations, each of which generates a surprising diversity of well-known aggregation rules as special cases.  Differences between general rules may arise from an orthogonal decomposition that separates input information into two components, with one rule using both components and the other discarding one of them.  We’ll discuss two decompositions, related to the two types of collective decisions mentioned above, and to a single voting rule proposed by John Kemeny.

This seminar is one of a series of seminars in the Whitaker Ideas Forum seminar series.  Professor Bill Zwicker, Union College, USA will be speaking on behalf of the Group Decision Making research cluster.