[EM] Another Proposed Single-winner Method

[William WAUGH]

*Goals*

My design goals here are:

1. The election method I am proposing must (like Score Voting) remove
the strategic
need for candidates to expensively convince voters they are one of the "2
most likely to win" <https://rangevoting.org/Cash3.html>.

2. The method should be perceived to provide the perceived benefit of IRV
over Score, at least as well as IRV is perceived to, that a voter can
support a compromise candidate without diluting the voter's support for the
voter's favorite candidate.

To obtain the above two benefits, I am willing to accept the following
costs:

- The method need not be precinct-summable.

*Grammar of the Ballot*

The voter fills the ballot with an ordered list of stanzas.

Each stanza lists a candidate or some candidates.

Furthermore, each stanza is marked "Interpretation Category A" or
"Interpretation Category B". The default is "A".

*Procedure for the Tally*

As a preliminary step for the tally, the tallying agent must scan the
ballots to collect the names written in. Then the candidate set is
initialized to include all the written-in names.

The tallying proceeds in rounds.

Each round receives as an argument, a set of candidates who are said to be
"still in the running". For the first round, this is the entire set of
candidates.

Each round uses a set of accumulators. One accumulator is associated to
each candidate who is still in the running. At the start of the round,
these accumulators are initialized to zero.

The next step for executing the round of tallying requires going through
the ballots, visiting each one.

The first step during a visit to a ballot in the context of a round of
tallying is to scan down the stanzas on the ballot to find the first one
that applies to the current set of candidates still in the running.

If a stanza is marked for interpretation category "A", such a stanza
applies if and only if any of the candidates named in the stanza is still
in the running.

Otherwise, the stanza applies if and only if and only if any of the
candidates who were in the full candidate set at the start of the tally who
are *not* named in the stanza is still in the running.

The accumulator associated to each candidate named in the stanza (if the
candidate is still in the running) is incremented by one. Once this is done
based on this one stanza, the procedure for the round of tallying proceeds
to the next ballot.

When the procedure for the round of tallying has visited all the ballots,
said procedure carries out the summing-up of the round, as follows.

Halve the count of the candidates remaining in the running. If the result
is not a whole number, round it down to the next lower whole number. So for
example, if there are three candidates in the running, half that is 1 1/2,
and we round that down to 1. The rounded-down result is the count of
candidates who have to be eliminated from the running by this round of the
tally. Eliminate the that-many candidates having the lowest values in their
accumulators.

After elimination, if only one candidate remains, yield that candidate as
the winner.

Otherwise, proceed to the next round of tallying, using the not-eliminated
candidates as the candidates in the running for that next round.

*Questions*

1. Can you point out a simpler election method that you think would work at
least as effectively as the one I propose above, to unseat oligarchy?
(Score Voting is simpler, since it is precinct-summable).

*Analysis*

You may be wondering why I included the possibility for the voter to choose
Interpretation Category "B". No doubt when you first read it, it sounded
strange and arbitrary.

I believe that in order to remove the strategic need for candidates to
expensively convince voters they are one of the "2 most likely to win"
<https://rangevoting.org/Cash3.html>, an election method must meet two
constraints:

1. Frohnmayer balance; and

2. Sufficient expressivity.

I don't know where to draw the line for sufficiency of expressivity, but I
think the above proposed method does have sufficient expressivity, and I
think that vote-for-and-against and vote-for-or-against (a. k. a. Negative
Vote) don't.

Frohnmayer balance means that every vote that can be cast in the system has
an antivote. "Antivote" means a vote such that if the original vote and its
antivote are entered in the election, the winner is the same as though
neither the original vote nor its antivote had been entered.

The choice between the two interpretation categories I provide for stanzas
permits me to construct for any given vote its antivote.

Starting with the original vote, we construct its antivote stanza by
stanza. Each stanza in the antivote corresponds to the stanza in the same
position in sequence in the original vote. The antistanza of a given stanza
uses the opposite interpretation category and names the complement of the
set of candidates named by the original stanza under the complete set of
candidates in the election QED
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