Best IRV Tweak
While there remains more than one uneliminated candidate eliminate the remaining one that is weakest relative to the other remaining candidates.
If "weakest" means least top support (relative to the other remaining candidates) then we have IRV.
But if we interpret "weakest" to mean the candidate with the fewest votes in any head-to-head contest (among the remaining candidates) then we have a Condorcet Compliant method.
In fact, the weakest candidate in this sense is a pairwise loser to its opponent in its worst head-to-head contest ... which could not happen to a Condorcet Candidate.
Operationally, this method is much simpler than IRV:
While the pairwise win matrix has more than one remaining entry, wipe out the row and column of the candidate whose row has the smallest remaining entry.
Under this simple method, would NYC still be bogged down in counting?
Sent from my MetroPCS 4G LTE Android Device
On 7/6/2021 1:59 PM, Susan Simmons wrote:
Under this simple method, would NYC still be bogged down in counting?
NYC primary vote counting was delayed by a state law that required a wait before counting absentee ballots, wasn't it?
- Ken Bearman, Minneapolis MN
On Tue, Jul 6, 2021 at 2:00 PM Susan Simmons suzerainsimmons@outlook.com
wrote:
While there remains more than one uneliminated candidate eliminate the
remaining one that is weakest relative to the other remaining candidates.
If "weakest" means least top support (relative to the other remaining
candidates) then we have IRV.
But if we interpret "weakest" to mean the candidate with the fewest votes
in any head-to-head contest (among the remaining candidates) then we have a
Condorcet Compliant method.
In fact, the weakest candidate in this sense is a pairwise loser to its
opponent in its worst head-to-head contest ... which could not happen to a
Condorcet Candidate.
I'm just an amateur, but I think your method is also Smith efficient.
During an elimination round it is possible that the candidate with fewest
votes in a head-to-head contest is in the Smith set, but only by losing a
head-to-head contest against another candidate in the Smith set.
Daniel
We're all amateurs!
You're right ... a Smith candidate cannot be eliminated without suffering a pairwise defeat from another of the remaining candidates, which perforce must be a Smith candidate since Smith candidates cannot be pairwise defeated by non-Smith candidates. When one door shuts another one opens.
Good on you! I didn't even think to ask the question .... so we have a method that is conceptually and operationally simple, while also seamlessly Smith compliant.
It fails mono-raise, but no worse than IRV.
It seems to be clone independent ... if X has little support against Y, then the same will be true for a clone of X, etc.
Compare Yee diagrams. IRV's are chaotic, unlike those of Condorcet methods (including this one) which are composed of ideal convex Voronoi polygons.
IRV uses ranked preference ballots to simulate Hare style runoffs ...this tweak uses the same ballots to simulate a thorough round robin style tournament ... much more thorough than would be practical without the ranked preference ballots.
For example without ranked ballots a round robin contest among ten candidates would require 45 trips to the polls. No wonder there is no tradition of round robin tournaments in the context of public elections.
In the context of sports tournaments it's hard to imagine an analog of runoff without head to head contests because runoff has only one head to head contest ... the final round that takes place after all of the other contestants have been eliminated by a more superficial criterion.
Sent from my MetroPCS 4G LTE Android Device
-------- Original message --------
From: Daniel Carrera dcarrera@gmail.com
Date: 7/6/21 2:21 PM (GMT-08:00)
To: Susan Simmons suzerainsimmons@outlook.com
Cc: election-methods@lists.electorama.com
Subject: Re: [EM] Best IRV Tweak
On Tue, Jul 6, 2021 at 2:00 PM Susan Simmons <suzerainsimmons@outlook.commailto:suzerainsimmons@outlook.com> wrote:
While there remains more than one uneliminated candidate eliminate the remaining one that is weakest relative to the other remaining candidates.
If "weakest" means least top support (relative to the other remaining candidates) then we have IRV.
But if we interpret "weakest" to mean the candidate with the fewest votes in any head-to-head contest (among the remaining candidates) then we have a Condorcet Compliant method.
In fact, the weakest candidate in this sense is a pairwise loser to its opponent in its worst head-to-head contest ... which could not happen to a Condorcet Candidate.
I'm just an amateur, but I think your method is also Smith efficient. During an elimination round it is possible that the candidate with fewest votes in a head-to-head contest is in the Smith set, but only by losing a head-to-head contest against another candidate in the Smith set.
Daniel
On 7/6/2021 11:59 AM, Susan Simmons wrote:
...
While the pairwise win matrix has more than one remaining entry, wipe
out the row and column of the candidate whose row has the smallest
remaining entry.
Under this simple method, would NYC still be bogged down in counting?
What you are describing sounds similar to Instant Pairwise Elimination
(IPE), except reversing the order of looking for the highest opposition
count versus the lowest support count.
https://electowiki.org/wiki/Instant_Pairwise_Elimination
The extra step of looking for Condorcet losers is needed because the
Condorcet loser does not always have the lowest support count.
The winner is not always the Condorcet winner, so it's not a Condorcet
method.
This approach of using pairwise counts is "precinct summable" so each
precinct can convert the ballot rankings into pairwise counts, send that
table of numbers to multiple locations, and summing those tables yields
the (same) results in multiple counting locations.
What's bogging down the counting in NYC is several complications. Notice
that most journalists are only reporting first-choice counts because
that's what they know how to do.
Also consider that government counts in the U.S. often defer to a
consortium of journalists who collaborate to ensure that different news
sources are not reporting different election results. ("It's complicated.")
The method you suggest is very close to what I've been using as an
approximation for the Condorcet-Kemeny method for cases that involve,
say, 50 or more choices (which means candidates if it's an election).
Yes it's much better than IRV. And it's easy to explain:
Each ballot gives a candidate the number of upvotes equal to the number
of remaining candidates who are ranked lower than that candidate.
(Unmarked candidates are virtually marked at the lowest preference level.)
I happen to be in the process of creating an animation for this
pairwise-support method, where the candidate with the lowest support
count is eliminated -- except when there is a "pairwise losing
candidate" (aka Condorcet loser), in which case the latter is eliminated
instead.
If you happen to have a good name for this method, please share it.
Thanks for pushing forward with election-method reforms that voters can
understand!
Richard Fobes
The VoteFair guy
On 7/6/2021 11:59 AM, Susan Simmons wrote:
While there remains more than one uneliminated candidate eliminate the
remaining one that is weakest relative to the other remaining candidates.
If "weakest" means least top support (relative to the other remaining
candidates) then we have IRV.
But if we interpret "weakest" to mean the candidate with the fewest
votes in any head-to-head contest (among the remaining candidates) then
we have a Condorcet Compliant method.
In fact, the weakest candidate in this sense is a pairwise loser to its
opponent in its worst head-to-head contest ... which could not happen to
a Condorcet Candidate.
Operationally, this method is much simpler than IRV:
While the pairwise win matrix has more than one remaining entry, wipe
out the row and column of the candidate whose row has the smallest
remaining entry.
Under this simple method, would NYC still be bogged down in counting?
Sent from my MetroPCS 4G LTE Android Device
Election-Methods mailing list - see https://electorama.com/em for list info
It appears that this IRV Tweak satisfies independence from Smith dominated alternatives.(ISDA)
Sent from my MetroPCS 4G LTE Android Device
-------- Original message --------
From: Susan Simmons suzerainsimmons@outlook.com
Date: 7/6/21 4:03 PM (GMT-08:00)
To: Daniel Carrera dcarrera@gmail.com, election-methods@lists.electorama.com
Cc: election-methods@lists.electorama.com
Subject: Re: [EM] Best IRV Tweak
We're all amateurs!
You're right ... a Smith candidate cannot be eliminated without suffering a pairwise defeat from another of the remaining candidates, which perforce must be a Smith candidate since Smith candidates cannot be pairwise defeated by non-Smith candidates. When one door shuts another one opens.
Good on you! I didn't even think to ask the question .... so we have a method that is conceptually and operationally simple, while also seamlessly Smith compliant.
It fails mono-raise, but no worse than IRV.
It seems to be clone independent ... if X has little support against Y, then the same will be true for a clone of X, etc.
Compare Yee diagrams. IRV's are chaotic, unlike those of Condorcet methods (including this one) which are composed of ideal convex Voronoi polygons.
IRV uses ranked preference ballots to simulate Hare style runoffs ...this tweak uses the same ballots to simulate a thorough round robin style tournament ... much more thorough than would be practical without the ranked preference ballots.
For example without ranked ballots a round robin contest among ten candidates would require 45 trips to the polls. No wonder there is no tradition of round robin tournaments in the context of public elections.
In the context of sports tournaments it's hard to imagine an analog of runoff without head to head contests because runoff has only one head to head contest ... the final round that takes place after all of the other contestants have been eliminated by a more superficial criterion.
Sent from my MetroPCS 4G LTE Android Device
-------- Original message --------
From: Daniel Carrera dcarrera@gmail.com
Date: 7/6/21 2:21 PM (GMT-08:00)
To: Susan Simmons suzerainsimmons@outlook.com
Cc: election-methods@lists.electorama.com
Subject: Re: [EM] Best IRV Tweak
On Tue, Jul 6, 2021 at 2:00 PM Susan Simmons <suzerainsimmons@outlook.commailto:suzerainsimmons@outlook.com> wrote:
While there remains more than one uneliminated candidate eliminate the remaining one that is weakest relative to the other remaining candidates.
If "weakest" means least top support (relative to the other remaining candidates) then we have IRV.
But if we interpret "weakest" to mean the candidate with the fewest votes in any head-to-head contest (among the remaining candidates) then we have a Condorcet Compliant method.
In fact, the weakest candidate in this sense is a pairwise loser to its opponent in its worst head-to-head contest ... which could not happen to a Condorcet Candidate.
I'm just an amateur, but I think your method is also Smith efficient. During an elimination round it is possible that the candidate with fewest votes in a head-to-head contest is in the Smith set, but only by losing a head-to-head contest against another candidate in the Smith set.
Daniel
On Tue, Jul 6, 2021 at 9:58 PM Susan Simmons suzerainsimmons@outlook.com
wrote:
It appears that this IRV Tweak satisfies independence from Smith dominated
alternatives.(ISDA)
I'm really impressed. The method I was discussing a few days ago was not
ISDA, was not independent of clones, and your method is easier to
implement. Even for a fairly complex election anyone can quickly compute
the winner with pencil and paper. I have no idea how to prove that a voting
method satisfies ISDA but I've thought carefully about the independence of
clones and I'm pretty sure I can confirm that yours is indeed independent
of clones.
Your method naturally extends to one that produces a full ranking: The
candidate that is removed first is the lowest rank, and so on. It seems to
me like this ranking satisfies local independence from irrelevant
alternatives. If you remove the lowest or highest ranked candidate, the
order of the remaining candidates does not change. I'm not sure how to
prove this because to me it looks self-evident, but it's weird because very
few methods satisfy LIIA. The table on Wikipedia only lists Ranked Pairs
and Kemeny-Young as satisfying LIIA.
I'm actually surprised that this isn't a well-known method already. You'd
think someone would have thought of it before.
Daniel.
On 07.07.2021 09:05, Daniel Carrera wrote:
On Tue, Jul 6, 2021 at 9:58 PM Susan Simmons
<suzerainsimmons@outlook.com mailto:suzerainsimmons@outlook.com> wrote:
It appears that this IRV Tweak satisfies independence from Smith
dominated alternatives.(ISDA)
I'm really impressed. The method I was discussing a few days ago was not
ISDA, was not independent of clones, and your method is easier to
implement. Even for a fairly complex election anyone can quickly compute
the winner with pencil and paper.I have no idea how to prove that a
voting method satisfies ISDA but I've thought carefully about the
independence of clones and I'm pretty sure I can confirm that yours is
indeed independent of clones.
Your method naturally extends to one that produces a full ranking: The
candidate that is removed first is the lowest rank, and so on. It seems
to me like this ranking satisfies local independence from irrelevant
alternatives. If you remove the lowestor highest ranked candidate, the
order of the remaining candidates does not change.I'm not sure how to
prove this because to me it looks self-evident, but it's weird because
very few methods satisfy LIIA. The table on Wikipedia only lists Ranked
Pairs and Kemeny-Young as satisfying LIIA.
Call the two first candidates to be eliminated X and Y (Y is eliminated
first), and the last one to be eliminated (i.e. the winner) A.
Suppose that Y's worst matchup is against A, but that X's worst matchup
is against someone else, and slightly worse than Y's next worst matchup.
Then eliminating A (the winner) may cause X to be eliminated first,
instead of Y. This is a violation of LIIA.
LIIA is just very hard to pass :-)
-km
On 06.07.2021 20:59, Susan Simmons wrote:
While there remains more than one uneliminated candidate eliminate the
remaining one that is weakest relative to the other remaining candidates.
If "weakest" means least top support (relative to the other remaining
candidates) then we have IRV.
But if we interpret "weakest" to mean the candidate with the fewest
votes in any head-to-head contest (among the remaining candidates) then
we have a Condorcet Compliant method.
In fact, the weakest candidate in this sense is a pairwise loser to its
opponent in its worst head-to-head contest ... which could not happen to
a Condorcet Candidate.
That sounds like Raynaud, which is Minmax-elimination.
More information here: https://electowiki.org/wiki/Raynaud
-km
Yes, Kristofer, specifically it is Benham's "Raynaud(Gross Loser)" the version of Reynaud that Chris Benham devised to satisfy Plurality.
Let's call it BRGL to avoid the question of Reynaud versus Raynaud.
BRGL succinctly stated: until only one candidate remains the loser of the (remaining) pairwise contest with the fewest losing votes is eliminated.
As Daniel noted, this is much simpler and cleaner (at least computationally) than the "BTR" patched version of IRV. And yet, from one point of view, it only differs from IRV on the question of which remaining candidate at each step is to be deemed "weakest" ... the Plurality loser or the pairwise loser with the least support.
To see that BRGL is an ISDA method, consider that no matter the order of elimination of the candidates up to any stage of the process, the next Smith candidate to be eliminated will be due to its defeat by the other remaining Smith member against which it musters the fewest votes.
VoteFair points out that IPE is similar to BRGL and probably superior to BRDL in simulations. But IPE lacks the clean simplicity of BRDL, espcially when IPE is hybridized with the BTR patch, as proposed by VoteFair.
It's proabably too late for Robert B-J to shift from BTR-IRV to BRDL in his presentation in Burlington, and not necessary, because his main point is that a conceptually and operationally small tweak of IRV totally fixes IRV's lack of Condorcet compliance. In fact, as suggested by "Robla," he should forget BTR and just graft a Condorcet check onto the front of IRV. [From there it's an easy future step to check for a CW among the remaining candidates at each round of the instant runoff ... a frequent proposal on the EM list].
Forest
(from my wife's phone)
Sent from my MetroPCS 4G LTE Android Device
-------- Original message --------
From: Kristofer Munsterhjelm km_elmet@t-online.de
Date: 7/7/21 8:26 AM (GMT-08:00)
To: Susan Simmons suzerainsimmons@outlook.com, election-methods@lists.electorama.com
Subject: Re: [EM] Best IRV Tweak
On 06.07.2021 20:59, Susan Simmons wrote:
While there remains more than one uneliminated candidate eliminate the
remaining one that is weakest relative to the other remaining candidates.
If "weakest" means least top support (relative to the other remaining
candidates) then we have IRV.
But if we interpret "weakest" to mean the candidate with the fewest
votes in any head-to-head contest (among the remaining candidates) then
we have a Condorcet Compliant method.
In fact, the weakest candidate in this sense is a pairwise loser to its
opponent in its worst head-to-head contest ... which could not happen to
a Condorcet Candidate.
That sounds like Raynaud, which is Minmax-elimination.
More information here: https://electowiki.org/wiki/Raynaud
-km