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<div>Richard, </div>
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<div>Good proposal!</div>
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<div>However see my in-line starred (***...) comment below.</div>
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<div style="font-size:85%;color:#575757" dir="auto">Sent from my MetroPCS 4G LTE Android Device</div>
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<div>-------- Original message --------</div>
<div>From: VoteFair <electionmethods@votefair.org> </div>
<div>Date: 7/12/21 10:21 AM (GMT-08:00) </div>
<div>To: Susan Simmons <suzerainsimmons@outlook.com>, election-methods@lists.electorama.com
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<div>Subject: Re: [EM] Improved Instant Pairwise Elimination </div>
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<div class="PlainText">I like Susan's suggestions (below).<br>
<br>
As a result of these suggestions and other recent developments, <br>
currently I'm writing software that implements the following method, <br>
which is an improvement over IPE (Instant Pairwise Elimination).</div>
<div class="PlainText">********************************</div>
<div class="PlainText">An improvement in simplicity & in conformity to the kind of form currently in vogue in naive reform circles ... though not a technical improvement over the version of IPE quoted below.</div>
<div class="PlainText">************************************</div>
<div class="PlainText"><br>
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<div class="PlainText"><br>
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<div class="PlainText"> The <br>
first two steps prevent misunderstandings about step 3.<br>
<br>
1. When a voter does not rank a candidate, that candidate is ranked at <br>
the lowest preference level shown on the ballot. (This fairness <br>
compromise is designed to not alienate fans of write-in candidates.)<br>
<br>
2. When a voter marks multiple ranking levels for the same candidate, <br>
the highest rank is used and the other marks for that candidate are ignored.<br>
<br>
3. On each ballot each candidate receives the number of upvotes equal to <br>
the number of not-yet-eliminated candidates who are ranked lower than <br>
that candidate.<br>
<br>
4. The upvotes are added across all the ballots to yield a "pairwise <br>
support count" for each candidate.<br>
<br>
5. The two candidates who have the smallest pairwise support counts <br>
compete against each other in a bottom-two runoff.<br>
<br>
6. During the bottom-two runoff each ballot indicates which of the two <br>
candidates is ranked at a lower level compared to the other candidate, <br>
and the candidate who is ranked lower on more ballots is eliminated.<br>
<br>
7. Candidates are eliminated one at a time until a single candidate remains.<br>
<br>
8. If this method is used in a US primary election for one of the two <br>
largest political parties (currently the Republican and Democratic <br>
parties), the last candidate to be eliminated also progresses to the <br>
general election as a second nominee. (This provision defeats the <br>
money-based tactics of blocking, concentration, and splitting.)<br>
<br>
I'm still working out details about how best to resolve ties. Currently <br>
I like Susan's idea of eliminating the candidate with the smallest <br>
single pairwise count (against any other candidate).<br>
<br>
On rare occasions this method can fail to elect the Condorcet winner. <br>
Under current conditions this is an advantage. That's because the <br>
FairVote organization has convinced large numbers of voters that <br>
Condorcet methods are bad.<br>
<br>
After writing the code for this method I'll measure its success rates <br>
for Clone independence and IIA (independence of irrelevant alternatives).<br>
<br>
Note that step 3 provides a fairer way to accomplish what STAR voting <br>
does with scores.<br>
<br>
In case it isn't obvious, this method allows two (or more) candidates to <br>
be marked at the same preference level, and the counts are precinct <br>
summable. These advantages overcome two of the biggest disadvantages of <br>
FairVote's version of IRV.<br>
<br>
Again, thank you Susan for your useful suggestions!<br>
<br>
Richard Fobes<br>
The VoteFair guy<br>
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<br>
On 7/8/2021 6:04 PM, Susan Simmons wrote:<br>
> Simplified version:<br>
><br>
> At each elimination step eliminate from among the remaining candidates<br>
> the pairwise loser between (1) the candidate whose maximum margin of<br>
> support is minimal, and (2) the loser in the pairwise contest with<br>
> fewest losing votes.<br>
><br>
> (1) is the Condorcet Loser if there is one, else (arguably) the<br>
> candidate closest to that distinction in the sense that its max win<br>
> margin is as close to zero as possible. [A candidate will have at least<br>
> one positive margin of sjpport if and only if it is not the CL.] So<br>
> let's call it the NCL, Nearest thing to Condorcet Loser.<br>
><br>
> (2) is the Gross Loser from Benham's version of Reynaud, BRGL.<br>
><br>
> So Improved Instant Pairwise Elimination eliminates (at each step) the<br>
> pairwise loser between the NCL and the GL.<br>
><br>
> If the NCL and the GL are different, then the eliminated candidate is<br>
> beaten by the other one. If they are the same, then the eliminated<br>
> candidate is the GL, which is never a Condorcet candidate. In neither<br>
> case is a Condorcet candidate eliminated ... so the method meets the<br>
> Condorcet Criterion.<br>
><br>
> Note that the pairwise margins matrix is simply the pairwise support<br>
> matrix minus its transpose, so the whole thing is efficiently precinct<br>
> summable.<br>
><br>
> My preferred version of the pairwise support matrix is this: the (i, j)<br>
> entry is the number of ballots on which candidate i is ranked strictly<br>
> ahead of j, plus the number of ballots on which both are ranked Top,<br>
> plus half the number of ballots on which both are ranked together (i.e.<br>
> equal to each other) strictly between Bottom and Top.<br>
><br>
> This convention for equal rankings makes good sense, for example, when<br>
> interpreting the diagonal elements of the matrix as implicit approvals,<br>
> and in other similar contexts.<br>
><br>
> Thanks for listening!<br>
><br>
><br>
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> Sent from my MetroPCS 4G LTE Android Device<br>
><br>
><br>
> -------- Original message --------<br>
> From: Susan Simmons <suzerainsimmons@outlook.com><br>
> Date: 7/8/21 12:18 PM (GMT-08:00)<br>
> To: election-methods@lists.electorama.com<br>
> Subject: Improved Instant Pairwise Elimination<br>
><br>
><br>
> At each elimination step IPE eliminates the Condorcet Loser if there is<br>
> one, otherwise it eliminates the loser of the pairwise contest with the<br>
> most winning votes.<br>
><br>
> We propose eliminating (at each elimination step among those not<br>
> eliminated previously) the Condorcet Loser if there is one, else the<br>
> pairwise loser between (1) the candidate whose maximum support for any<br>
> of its pairwise wins is minimal, and (2) the loser from the pairwise<br>
> contest with the fewest losing votes (i.e. the Gross Loser).<br>
><br>
> In other words eliminate the CL when there is one, otherwise eliminate<br>
> whichever is less preferred... the GL or the closest thing to a CL.<br>
><br>
> Is this better than BRGL which simply eliminates the GL at each step?<br>
><br>
> Yes and no. On the one hand it is more aggressive and thorough about<br>
> getting rid of the least desireable remaining candidate as soon as<br>
> possible. On the other hand it is probably a harder sell to a public<br>
> lacking patience in these matters ... who tend to assume that the order<br>
> of elimination of "losers" doesn't make much difference, if any.<br>
><br>
><br>
><br>
><br>
> Sent from my MetroPCS 4G LTE Android Device<br>
><br>
><br>
> ----<br>
> Election-Methods mailing list - see <a href="https://electorama.com/em" target="_BLANK">
https://electorama.com/em</a> for list info<br>
><br>
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