[EM] High5 voting (~ Smith//Approval on a reduced set)

[Ted Stern]

I've been mulling over ways to get a Smith/Approval method into a somewhat
practical form, and have taken some cues from Jameson Quinn's Vote-321.

Vote-321 is a pretty method, with a lot of strategy resistance, and if it
were among the options for a new voting system (with no Condorcet method
available), I would choose it immediately.

However, I have a few issues with it: vulnerability to cloning; lack of
expression; and what I consider a too-small provisional subset. The latter
is more of a psychological / media problem, and what I mean by "too-small"
is that if only the top three first-place candidates make it past the first
pass, public attention could be excessively focused on the front-runners at
the cost of addressing issues raised by less popular candidates. But the
too-small subset is also what enables Vote-321's vulnerability to cloning.
By including at least one or two more candidates in the first pass of
candidate reduction, cloning risk is reduced.

Following is what I call the *High 5 *method for three or more candidates:

*Ballot Expression:*
I prefer a 6 slot ranked ballot, equal-ranking and gaps allowed, with the
rank/tiers named as follows:


Tier Name

Approval Status

Description

A

Approved

Most Preferred / Best / Favorite

B

Approved

Good

C

Approved

OK / Acceptable

D

Disapproved

Not Preferred, but would be in their coalition (i.e. Compromise)

E

Disapproved

Mostly Unacceptable but Lesser Evil

Reject

Dispapproved

Completely unacceptable

Summarized, there are 3 approved ranks (Most Preferred, Good, OK), 2
disapproved ranks (compromise, lesser of two evils), and Reject. Blank
ballots are counted as rejection.

*Tabulation:*

   - Total most-preferred votes per candidate (i.e. "A" votes).
   - Approval / Disapproval totals per candidate
   - Pairwise preference array
   - Optional:
      - Tied-Approval pairwise
      - Tied-Disapproval (above reject) pairwise
      - Approved vs Disapproved/Reject pairwise

*First-pass subset:*

   - *Top 5 candidates by most-preferred votes*

*Procedure:*

   - Of the top 5 most-preferred candidates are found, drop the
   least-approved candidate.
   - Among the remaining candidates, use the pairwise preference array to
   find the Smith Set
   - If more than one candidate is in the Smith Set, pick the most approved
   member of the set as the winner.

If you start with 3 candidates, this method reduces to top-two approval.

Starting with 4 candidates, this method reduces to sorting the candidates
by Approval and doing a top-three tournament: the winner is the pairwise
winner of A1 versus (the pairwise winner of A2 versus A3).

For 5 or more candidates, the method has a very high probability of finding
the CW (if one exists) among the top five favorites, while falling back to
approval in the event of a cycle among the four most-approved of those top
five.

In a "jungle-primary" type of situation (though no primary is necessary),
media attention would be given to at least the top 5 candidates instead of
just the top two, ensuring attention to a range of viewpoints. And in the
event of a large number of candidates, it would not be necessary to
tabulate pairwise preferences for more than 7 or 8 top-first-ranked
candidates as determined by pre-election polling, reducing tabulation
complexity while retaining summability.

Using most-preferred votes for the first pass has a slight anti-cloning
effect, as a preference ballot would lead to a tendency toward vote
splitting if one faction has too many candidates. The anti-cloning pressure
is greater than in Vote-321 because of the larger range of expression.

Finally, the Smith//Approval method, when combined with the explicit
approval cutoff ballot, allows enough strategy to reduce burial incentive.

I'm calling this "High 5" voting because it's descriptive of both the
ranking method and the top-five most preferred first-level truncation, and
it's easier to remember than Smith//Approval.

Thoughts?
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