On Sun, 12 Nov 2000, Alex Tabarrok wrote: 1. The reason that > dictatorship is the only choice function consistent with Arrow's other > assumptions is that a dictator is an individual! > and 2. If you place the election in the > larger context of a two-stage process in which the parties choose > candidates and then the voters vote - then Arrow's theorem applies full > force. and 3. While in actual fact any number of changes in the electoral system which would be equally democratic (eg. Borda, Approval Voting, Cumulative Voting, etc. etc.) could result in a *completely* different outcome. _____________ These are all excellent and correct points. I'm taking a class with Don Saari on these issues, and I encourage armchair members interested in voting to read his "Basic Geometry of Voting" which provides simple yet very powerful analytical tools for examining these sorts of questions. (BTW Alex - Saari cited a paper of yours in class last week!) Using Saari's tools, Arrow's theorem, Sen's theorem and the Gibbard-Satterthwaite theorem can be proved with a couple of simple pictures and can be easily explained to undergraduates or your grandmother. And the tools can be used to create any crazy paradox you like in a couple of minutes - for example, it becomes trivial to give an example of a preference profile with three candidates, in which A is the plurality winner, B is the Borda count winner, and C is the Condorcet winner! Alex Robson UC Irvine
