Notes for Session 7, Basic Voting Theory, Summer School 2011 T.Seidenfeld 1 Notes for Session 7 Basic Voting Theory Summary: Notes for Session 7, Basic Voting Theory, Summer School 2011 T.Seidenfeld 1 Notes for Session 7 ­ Basic Voting Theory We follow up the "Impossibility" (Session 6) of pooling expert probabilities, while preserving unanimities in both unconditional and conditional probabilities. Here we explore the power of group voting as a substitute for group pooling. Assume that the group decision problem involves m-many, pairwise exclusive social acts, e.g., the options might be candidates in an election, or (exclusive) bills before a legislature. And there are n-many citizens, or voters, or legislators in our group. Each voterj (j = 1, ..., n) has an ORDINAL ranking of the m-options, as summarized in the table below. The quantities r·j are the ranks assigned by voterj to the m- many acts. We'll let a rank of 1 be best, and a rank of m be worst. Ties are allowed by sharing the average rank for those tied in the ranking. For example, if two acts tie for best position they share rank 1.5 ( = (1+2) / 2), etc. Thus, for each voter, the sum of the ranks equals m(m+1)/2. Notes for Session 7, Basic Voting Theory, Summer School 2011 T.Seidenfeld 2 TABLE of n-many Voters' Rank Order of m-many acts Act1 Act2 Acti Actm Collections: Mathematics