[EM] Replacing Top Two Primaries

[Forest Simmons]

I like the idea of trying to make a second round unnecessary as much as
possible.  For this reason, I suggest electing the approval winner of the
first round if the winning approval is greater than 50 percent. Gilding the
lily does not seem necessary to me.

However, if no candidate attains majority approval in the first round, I
suggest publishing the Martin Harper Lottery probabilities before the
second round to better inform the voters' approvals. The approval winner of
the second round wins the election.

In 2002 Martin Harper suggested a simple vote transfer formulation of
ordinary Approval to satisfy the superstitions of  STV proponents ... your
single vote transfers to the candidate (among those approved by you) that
has the greatest approval from other voters.

The Martin Harper Lottery probability for candidate X is the percentage of
the votes that X ends up with after the completion of all of the transfers.

This helps inform the voters' approval choices in the second round.

Furthermore, although the first round is not supposed eliminate anybody,
what harm in advancing to the second round only the support of the Harper
Lottery from the first round?

A weighted geometric mean of the Martin Harper Lottery probabilities is
given by the product ...

Product (over candidates k) of P(k)^P(k)

The Shannon entropy of the lottery is the base two log of the reciprocal of
this product.

So if E is the Shannon entropy of L measuresd in bits, then the above
(weighted geometric mean) product is given by

P = 1/2^E.

FWS
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