# [EM] Replacing Top Two Primaries

Ted Stern dodecatheon at gmail.com
Tue Oct 12 10:51:52 PDT 2021

```Hi Forest,

Your Harper proposal is similar to an approval primary in which winners are
found by seating the current approval winner, then removing all ballots
that approve that winner and retabulating the remainder. This is a pushover
resistant method.

The difference in your proposal is that voters can have a choice in
several different factions. I'm not sure it's pushover resistant.

It might be beneficial to post both sets of numbers with a non-eliminative
primary.

On Mon, Oct 11, 2021, 23:41 Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> 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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>
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