[EM] Improved Instant Pairwise Elimination

[VoteFair]

I like Susan's suggestions (below).

As a result of these suggestions and other recent developments, 
currently I'm writing software that implements the following method, 
which is an improvement over IPE (Instant Pairwise Elimination). The 
first two steps prevent misunderstandings about step 3.

1. When a voter does not rank a candidate, that candidate is ranked at 
the lowest preference level shown on the ballot. (This fairness 
compromise is designed to not alienate fans of write-in candidates.)

2. When a voter marks multiple ranking levels for the same candidate, 
the highest rank is used and the other marks for that candidate are ignored.

3. On each ballot each candidate receives the number of upvotes equal to 
the number of not-yet-eliminated candidates who are ranked lower than 
that candidate.

4. The upvotes are added across all the ballots to yield a "pairwise 
support count" for each candidate.

5. The two candidates who have the smallest pairwise support counts 
compete against each other in a bottom-two runoff.

6. During the bottom-two runoff each ballot indicates which of the two 
candidates is ranked at a lower level compared to the other candidate, 
and the candidate who is ranked lower on more ballots is eliminated.

7. Candidates are eliminated one at a time until a single candidate remains.

8. If this method is used in a US primary election for one of the two 
largest political parties (currently the Republican and Democratic 
parties), the last candidate to be eliminated also progresses to the 
general election as a second nominee. (This provision defeats the 
money-based tactics of blocking, concentration, and splitting.)

I'm still working out details about how best to resolve ties. Currently 
I like Susan's idea of eliminating the candidate with the smallest 
single pairwise count (against any other candidate).

On rare occasions this method can fail to elect the Condorcet winner. 
Under current conditions this is an advantage. That's because the 
FairVote organization has convinced large numbers of voters that 
Condorcet methods are bad.

After writing the code for this method I'll measure its success rates 
for Clone independence and IIA (independence of irrelevant alternatives).

Note that step 3 provides a fairer way to accomplish what STAR voting 
does with scores.

In case it isn't obvious, this method allows two (or more) candidates to 
be marked at the same preference level, and the counts are precinct 
summable. These advantages overcome two of the biggest disadvantages of 
FairVote's version of IRV.

Again, thank you Susan for your useful suggestions!

Richard Fobes
The VoteFair guy


On 7/8/2021 6:04 PM, Susan Simmons wrote:
> Simplified version:
>
> At each elimination step eliminate from among the remaining candidates
> the pairwise loser between (1) the candidate whose maximum margin of
> support is minimal, and (2) the loser in the pairwise contest with
> fewest losing votes.
>
> (1) is the Condorcet Loser if there is one, else (arguably) the
> candidate closest to that distinction in the sense that its max win
> margin is as close to zero as possible. [A candidate will have at least
> one positive margin of sjpport if and only if it is not the CL.]  So
> let's call it the NCL, Nearest thing to Condorcet Loser.
>
> (2) is the Gross Loser from Benham's version of Reynaud, BRGL.
>
> So Improved Instant Pairwise Elimination eliminates (at each step) the
> pairwise loser between the NCL and the GL.
>
> If the NCL and the GL are different, then the eliminated candidate is
> beaten by the other one. If they are the same, then the eliminated
> candidate is the GL, which is never a Condorcet candidate.  In neither
> case is a Condorcet candidate eliminated ... so the method meets the
> Condorcet Criterion.
>
> Note that the pairwise margins matrix is simply the pairwise support
> matrix minus its transpose, so the whole thing is efficiently precinct
> summable.
>
> My preferred version of the pairwise support matrix is this: the (i, j)
> entry is the number of ballots on which candidate i is ranked strictly
> ahead of j, plus the number of ballots on which both are ranked Top,
> plus half the number of ballots on which both are ranked together (i.e.
> equal to each other) strictly between Bottom and Top.
>
> This convention for equal rankings makes good sense, for example, when
> interpreting the diagonal elements of the matrix as implicit approvals,
> and in other similar contexts.
>
> Thanks for listening!
>
>
>
> Sent from my MetroPCS 4G LTE Android Device
>
>
> -------- Original message --------
> From: Susan Simmons <suzerainsimmons at outlook.com>
> Date: 7/8/21 12:18 PM (GMT-08:00)
> To: election-methods at lists.electorama.com
> Subject: Improved Instant Pairwise Elimination
>
>
> At each elimination step IPE eliminates the Condorcet Loser if there is
> one, otherwise it eliminates the loser of the pairwise contest with the
> most winning votes.
>
> We propose eliminating (at each elimination step among those not
> eliminated previously) the Condorcet Loser if there is one, else the
> pairwise loser between (1) the candidate whose maximum support for any
> of its pairwise wins is minimal, and (2) the loser from the pairwise
> contest with the fewest losing votes (i.e. the Gross Loser).
>
> In other words eliminate the CL when there is one, otherwise eliminate
> whichever is less preferred... the GL or the closest thing to a CL.
>
> Is this better than BRGL which simply eliminates the GL at each step?
>
> Yes and no. On the one hand it is more aggressive and thorough about
> getting rid of the least desireable remaining candidate as soon as
> possible. On the other hand it is probably a harder sell to a public
> lacking patience in these matters ... who tend to assume that the order
> of elimination of "losers" doesn't make much difference, if any.
>
>
>
>
> Sent from my MetroPCS 4G LTE Android Device
>
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info
>