By “voting”, I mean the following general problem: Suppose there are candidates and voters. Each voter produces a total ordering of all candidates. A voting procedure is a function which takes as input all orderings, and produces an output ranking of all candidates. Arrow’s impossibility theorem states that there is really no satisfactory voting procedure when the number of candidates is greater than 2 (majority rule is a good voting procedure when there are two candidates).
Monthly Archives: February 2010
In the book Good and Real, author Gary Drescher, who received his PhD from MIT’s AI lab, defends the view that determinism is a consistent and coherent view of the world. In doing so, he enters many different arenas: ethics, decision theory, and physics.
In his chapter on quantum mechanics, he defends the “many-worlds” interpretation (although he doesn’t think the term accurately describes the concept) versus the Copenhagen interpretation. In the process of doing so, he does something I thought was extraordinary: he comes up with a simple model of quantum mechanics in which all of the standard concepts you read about: the two-slit experiment, the Heisenberg uncertainty principle, etc., are represented. This model requires no prerequisites from physics and actually uses almost totally discrete mathematics!
(Edit: I somehow missed this when originally writing this post, but Drescher also outlines quantish physics in an online paper.)
I’ll sketch it below.