[EM] Single Non-Transferable voting + Approval (or Approval Sorted Margins) as a primary

[Ted Stern]

Over the years a number of people on this list (e.g. Rob Lanphier, myself
and others) have proposed various methods for using Approval in primary
elections.

There are arguments to be made for using other PR methods, but it seems to
me that SNTV is ideally suited to be a primary method, since it resists
pushover and doesn't tend to overrepresent parties.

Using Approval as a base method, single non-transferable approval voting
would look like

   - Advance Approval winner and Approval runner-up
   - Deweight to zero all ballots approving of AW.
   - Repeat until some threshold (e.g. 90%) of ballots have been used up:
      - Advance approval winner on the current remaining ballots
      - Deweight ballots approving of latest winner to zero

The advantages here are

   - Relative simplicity -- No complicated reweighting algorithms, so each
   recount for the next approval winner is faster than the previous, and can
   even be done by hand.
   - Each winner (other than the first approval runner-up) will tend to be
   from a different party or faction of a party.  There may be some overlap
   from also advancing the overall Approval runner-up, but if the total AW and
   ARU are from the same party, it gives them an advantage under Approval to
   have a similar candidate for comparison.
   - Most groups will be represented in the General election.
   - Pushover strategy is disincentivized by complete deweighting, so
   parties should not be threatened by strategic promotion of their worst
   candidate. There is some possibility that voters would do that regardless,
   but the effect should be no worse than in current top-two elections.
   - Modifications could include:
      - Stop advancing candidates when the highest approval on remaining
      ballots drops below a threshold. For example, if the total deweight
      threshold is 90%, if the latest winner has less than 5% approval on
      remaining ballots (half the complement of 90%), break the loop.
      - Stop when a certain number of candidates have advanced. For
      example, if using the 5% rule above, it is possible that 10 to 15
      candidates could advance to the General, defeating the winnowing
purpose of
      a primary. It seems reasonable to stop at 5 or 6 candidates.
      - Use a different method other than simple Approval.

I would be perfectly satisfied to have SNTAV as a primary method, but if
one can handle a bit more complexity (say in smaller groups), it would be
reasonable to use Approval Sorted Margins as the base method:


   - Use Ranked or Rated ballots with explicit Approval Cutoff. If not
   explicitly specified, cutoff is at zero-rating or last ranking.
   - Advance Approval Sorted Margins winner to general election
   - Deweight to zero all ballots approving of AW.
   - Repeat until some threshold (e.g. 90%) of ballots have been used up:
      - Advance ASM winner on the current remaining ballots
      - Deweight ballots approving of latest winner to zero

For public elections, I think the SNTAV approach I outline above, with a
90% threshold, 5% minimum remaining approval, and limited to 6 candidates
(4 approval winners and 1 top approval runner-up) gives enough room to
enable more parties to develop.
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