Monthly Archives: February 2010

Two Interesting Observations about Voting I Hadn’t Seen Until Recently

By “voting”, I mean the following general problem:  Suppose there are n candidates and m voters.  Each voter produces a total ordering of all n candidates.  A voting procedure is a function which takes as input all m orderings, and produces an output ranking of all n 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).

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Quantish Physics: A Discrete Model of Quantum Physics

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.

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