Re: [EM] Improved Instant Pairwise Elimination
Richard,
Good proposal!
However see my in-line starred (***...) comment below.
Sent from my MetroPCS 4G LTE Android Device
-------- Original message --------
From: VoteFair electionmethods@votefair.org
Date: 7/12/21 10:21 AM (GMT-08:00)
To: Susan Simmons suzerainsimmons@outlook.com, election-methods@lists.electorama.com
Subject: Re: [EM] Improved Instant Pairwise Elimination
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).
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.
The
first two steps prevent misunderstandings about step 3.
-
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.) -
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. -
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. -
The upvotes are added across all the ballots to yield a "pairwise
support count" for each candidate. -
The two candidates who have the smallest pairwise support counts
compete against each other in a bottom-two runoff. -
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. -
Candidates are eliminated one at a time until a single candidate remains.
-
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@outlook.com
Date: 7/8/21 12:18 PM (GMT-08:00)
To: election-methods@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
On 7/12/2021 12:14 PM, Susan Simmons wrote:
Good proposal!
...
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.
Indeed. I'm looking for a balance between what "average" voters can
understand and what produces very good -- although not ideal -- results.
Update:
I've written the code for the new method that I recently described in
non-expert terminology.
The results look quite good!
Here's a shorter description that's intended for regular participants here.
-
Eliminate the Condorcet loser when there is one.
-
Sum the pairwise counts in each row (or column depending on
orientation) to calculate a "pairwise support count" for each candidate.
Exclude counts that involve candidates who have already been eliminated. -
Identify the two candidates with the smallest support counts, do an
instant runoff between them, and eliminate the loser.
That's it!
For computation purposes (as opposed to real elections where exact ties
are rare), when the bottom-two step involves a tie, the Condorcet loser
among those tied candidates is eliminated.
Interestingly, doing an instant runoff between the bottom two candidates
is equivalent to finding the Condorcet loser, so the same code does both
the bottom-two runoff and finding the Condorcet loser among 3 or more
tied candidates.
I've added an extra tie resolution method based on recent suggestions
here. When there is still a tie for the bottom-two support counts,
eliminate the tied candidate who has the single smallest pairwise count
(against any other remaining candidate).
Later I'll generate a refined scatter plot showing success rates for
Clone independence and IIA (Independence of Irrelevant Alternatives).
The rough unlabelled version looks nice datawise.
Currently I'm calling this method RCIPE2 (RCIPE version 2.0) with the
expectation that it will replace the RCIPE (version 1.0) method
specified in the Ranked Choice Oregon ballot initiative.
Richard Fobes
The VoteFair guy
On 7/12/2021 12:14 PM, Susan Simmons wrote:
Richard,
Good proposal!
However see my in-line starred (***...) comment below.
Sent from my MetroPCS 4G LTE Android Device
-------- Original message --------
From: VoteFair electionmethods@votefair.org
Date: 7/12/21 10:21 AM (GMT-08:00)
To: Susan Simmons suzerainsimmons@outlook.com,
election-methods@lists.electorama.com
Subject: Re: [EM] Improved Instant Pairwise Elimination
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).
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.
The
first two steps prevent misunderstandings about step 3.
-
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.) -
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. -
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. -
The upvotes are added across all the ballots to yield a "pairwise
support count" for each candidate. -
The two candidates who have the smallest pairwise support counts
compete against each other in a bottom-two runoff. -
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. -
Candidates are eliminated one at a time until a single candidate remains.
-
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@outlook.com
Date: 7/8/21 12:18 PM (GMT-08:00)
To: election-methods@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