Defeat strength, Winning Votes vs. Margins, what to do with equally-ranks on ballot?
So this would be about Tideman Ranked-Pairs, or Schulze, or some other Condorcet-compliant method.
It doesn't make much difference if the measure of Defeat Strength is Margins (supporting votes minus opposing votes), but what if Winning Votes is the measure of Defeat Strength
in either RP or Schulze? How should a pair of candidates that are equally-ranked on a ballot be counted? Do you count it (as a winning vote) for both candidates? For neither candidate? (I dislike the idea of a half-vote for both candidates. And I hate the idea of not
allowing equal-ranking in a Condorcet RCV election.)
What is the right way to do this? It seems the most consistent might be to count an equally-ranked votes for neither candidate, since we consider unranked candidates as tied for last place on the ballot, and we would count those as
votes.
But what do you guys think? If we allow for equal-ranking in a Condorcet-compliant RCV, how do we deal with it in terms of vote totals?
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Hi Robert,
In a WV method you can't trace beatpaths through a loss. So if A defeats B you can only trace from A to B, and the strength of the defeat is equal to the number of voters who preferred A>B. (If you added half a vote to A in the case of an equal ranking between A and B, this gives the same effect as margins, assuming you applied this rule everywhere.)
Normally these methods do not show a difference based on whether an equal ranking was explicit, vs. implied via truncation. I would say this is mostly because explicit vs. implicit ranking isn't really native/inherent to the idea of Condorcet. But I'd suggest also because a distinction in treatment doesn't help the voter. A "half vote" treatment turns equal ranking into a "neither here nor there" strategy, where ranking your favorite candidates equal-top is prima facie not optimal regardless of your priorities.
Kevin
Le lundi 20 mai 2019 à 16:06:32 UTC−5, robert bristow-johnson <rbj@audioimagination.com> a écrit :
So this would be about Tideman Ranked-Pairs, or Schulze, or some other Condorcet-compliant method.
It doesn't make much difference if the measure of Defeat Strength is Margins (supporting votes minus opposing votes), but what if Winning Votes is the measure of Defeat Strengthin either RP or Schulze? How should a pair of candidates that are equally-ranked on a ballot be counted? Do you count it (as a winning vote) for both candidates? For neither candidate? (I dislike the idea of a half-vote for both candidates. And I hate the idea of notallowing equal-ranking in a Condorcet RCV election.)
What is the right way to do this? It seems the most consistent might be to count an equally-ranked votes for neither candidate, since we consider unranked candidates as tied for last place on the ballot, and we would count those asvotes.
But what do you guys think? If we allow for equal-ranking in a Condorcet-compliant RCV, how do we deal with it in terms of vote totals?
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Election-Methods mailing list - see https://electorama.com/em for list info
---------------------------- Original Message ----------------------------
Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equally-ranks on ballot?
From: "Kevin Venzke" stepjak@yahoo.fr
Date: Mon, May 20, 2019 6:48 pm
To: election-methods@lists.electorama.com
"robert bristow-johnson" rbj@audioimagination.com
Hi Robert,
In a WV method you can't trace beatpaths through a loss.
I agree with that (but i don't think it speaks to the point). You can include a tie in a beatpath, no? And, if it's RP with WV instead of margins, a tie can be used in the ranking graph, no?
But this is not
about ties in the vote totals. This is about whether we count ties on an individual ballot toward vote totals or do not count them.
So if A defeats B you can only trace from A to B, and the strength of the defeat is equal to the number of voters who preferred A>B.
Only for
WV. For Margins, the strength of the defeat is the number of voters who prefer A>B minus the number of voters who prefer B>A. Now for Margins, that net margin is unchanged if we count equal ranks as votes for both or votes for neither.
But it does make a difference if
we're measuring defeat strength using WV.
(If you added half a vote to A in the case of an equal ranking between A and B, this gives the same effect as margins, assuming you applied this rule everywhere.)
for Margins, adding half a vote (to both A and B) or no vote to either or one
vote for both makes no difference in the defeat strength. but it makes a difference for WV.
Normally these methods do not show a difference based on whether an equal ranking was explicit, vs. implied via truncation.
If we don't count equal ranking as votes for either
candidate, you're correct. But if we do count equal ranked (active ranking, higher than unranked), there is a difference for WV. If two candidates were equally ranked (and not unranked), that WV is in the beatpath. It could end up counting in the net beatpath score, no?
I would say this is mostly because explicit vs. implicit ranking isn't really native/inherent to the idea of Condorcet. But I'd suggest also because a distinction in treatment doesn't help the voter. A "half vote" treatment turns equal ranking into a "neither here nor there"
strategy, where ranking your favorite candidates equal-top is prima facie not optimal regardless of your priorities.
This last statement I can't figure out.
bestest,
r b-j
Le lundi 20 mai 2019 à 16:06:32 UTC−5, robert bristow-johnson rbj@audioimagination.com a écrit :
So this would be about Tideman Ranked-Pairs, or Schulze, or some other Condorcet-compliant method.
It doesn't make much difference if the measure of Defeat Strength is Margins (supporting votes minus opposing votes), but what if Winning Votes is the measure of Defeat Strength in either RP or Schulze? How should a pair of candidates that are equally-ranked on a ballot be counted?
Do you count it (as a winning vote) for both candidates? For neither candidate? (I dislike the idea of a half-vote for both candidates. And I hate the idea of not allowing equal-ranking in a Condorcet RCV election.)
What is the right way to do this? It seems the most consistent might be to count an equally-ranked votes for neither candidate, since we consider unranked candidates as tied for last place on the ballot, and we would not count those as votes.
But what do you guys think? If we allow for equal-ranking in a Condorcet-compliant RCV, how do we deal with it in terms of vote totals?
Hi Robert,
I'll add a bit below but the long story made short is that under WV, you traditionally don't add any tally to the pairwise matrix for a single ballot's tied rankings, no matter whether the equality is implicit or explicit.
Also, the conventional wisdom is that voters don't want to create strong defeats among the candidates they like. So if you had different treatment for implicit or explicit equality, you might if anything want to add the tally for ties among truncated candidates, not explicitly ranked candidates. (But I don't actually think you should do that.)
Le lundi 20 mai 2019 à 23:06:57 UTC−5, robert bristow-johnson <rbj@audioimagination.com> a écrit : ---------------------------- Original Message ----------------------------
Hi Robert,
In a WV method you can't trace beatpaths through a loss.
I agree with that (but i don't think it speaks to the point). You can include a tie in a beatpath, no? And, if it's >RP with WV instead of margins, a tie can be used in the ranking graph, no?
Generally no... With RP in particular I can't imagine it, because you are locking defeats in descending order of strength. Even if you assign a defeat strength to a tie, there is no way to say in which direction it can be locked.
I wonder if you're thinking of the Schwartz set which has kind of a tricky definition. To be in the Schwartz set you need a path of wins to those candidates that have such a path to you. So you don't need a path to everyone. Tied contests can help you, but you don't actually trace through them.
But this is notabout ties in the vote totals. This is about whether we count ties on an individual ballot toward vote totals or do not count them.
So if A defeats B you can only trace from A to B, and the strength of the defeat is equal to the number of voters who preferred A>B.
Only forWV. For Margins, the strength of the defeat is the number of voters who prefer A>B minus the number >of voters who prefer B>A. Now for Margins, that net margin is unchanged if we count equal ranks as votes for both or votes for neither.
But it does make a difference ifwe're measuring defeat strength using WV.
(If you added half a vote to A in the case of an equal ranking between A and B, this gives the same effect as margins, assuming you applied this rule everywhere.)
for Margins, adding half a vote (to both A and B) or no vote to either or onevote for both makes no difference in the defeat strength. but it makes a difference for WV.
What I mean is that if you always add half votes for (both types of) equality under WV, the method will give the same result as margins.
Normally these methods do not show a difference based on whether an equal ranking was explicit, vs. implied via truncation.
If we don't count equal ranking as votes for eithercandidate, you're correct. But if we do count equal ranked >(active ranking, higher than unranked), there is a difference for WV. If two candidates were equally ranked (and >not unranked), that WV is in the beatpath. It could end up counting in the net beatpath score, no?
If you used such a rule then yes. But typically there is no concept of ranked vs. unranked.
I would say this is mostly because explicit vs. implicit ranking isn't really native/inherent to the idea of Condorcet. >>But I'd suggest also because a distinction in treatment doesn't help the voter. A "half vote" treatment turns equal >>ranking into a "neither here nor there"strategy, where ranking your favorite candidates equal-top is prima facie >>not optimal regardless of your priorities.
This last statement I can't figure out.
Compare this with the concept of giving half-approvals under Approval. In most scenarios it's not possible to calculate that giving a candidate half an approval is strategically optimal. Similarly if you use a treatment of equal ranking such that a vote for A=B is simply midway, in effect, between voting A>B and B>A, then you should imagine that one of A>B or B>A must be a better vote than equality. I see this as a loss because ordinarily WV comes quite close to meeting the principle that you can rank your true favorite candidate equal-top with your compromise choice without thereby making the compromise choice lose to somebody worse.
Kevin
Robert,
Another Condorcet-compliant method that might interest you, from a Kevin
Venzke webpage:
Jobst Heitzig's River method is identical to Tideman's method,
except that one additionally ignores (without locking) defeats against
candidates against whom some defeat has already been locked. This is
possibly the easiest of the three to work out by hand.
The other two he is referring to are Schulze and Tideman RP. Nearly all
the time it will elect the same candidate and as far as I know is at
least as good.
I strongly suggest that the measure of defeat strength should be Losing
Votes and that ballots that equal-rank A and B above bottom should
contribute a whole vote
to each in the A-B pairwise comparison. Ballots that rank A and B
equal-bottom (or truncate both A and B) should contribute nothing to the
A-B pairwise comparison.
I'll be posting more on this soonish, but since you asked the question I
thought I'd just give you some food for thought to be going along with.
Chris Benham
On 21/05/2019 6:36 am, robert bristow-johnson wrote:
So this would be about Tideman Ranked-Pairs, or Schulze, or some other
Condorcet-compliant method.
It doesn't make much difference if the measure of Defeat Strength is
Margins (supporting votes minus opposing votes), but what if Winning
Votes is the measure of Defeat Strength in either RP or Schulze??? How
should a pair of candidates that are equally-ranked on a ballot be
counted??? Do you count it (as a winning vote) for both candidates???
For neither candidate? (I dislike the idea of a half-vote for both
candidates.?? And I hate the idea of not allowing equal-ranking in a
Condorcet RCV election.)
What is the right way to do this??? It seems the most consistent might
be to count an equally-ranked votes for neither candidate, since
we consider unranked candidates as tied for last place on the ballot,
and we would count those as votes.
But what do you guys think??? If we allow for equal-ranking in a
Condorcet-compliant RCV, how do we deal with it in terms of vote totals?
--
r b-j?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ??rbj@audioimagination.com
"Imagination is more important than knowledge."
Election-Methods mailing list - see https://electorama.com/em for list info
This email has been checked for viruses by AVG.
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---------------------------- Original Message ----------------------------
Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equally-ranks on ballot?
From: "Chris Benham" cbenhamau@yahoo.com.au
Date: Wed, May 22, 2019 2:35 pm
To: election-methods@lists.electorama.com
Another Condorcet-compliant method that might interest you, from a Kevin
Venzke webpage:
Jobst Heitzig's River method is identical to Tideman's method,
except that one additionally ignores (without locking) defeats against
candidates against whom some defeat has already been locked. This is
possibly the easiest of the three to work out by hand.
maybe someone needs to explain this more to me. i can think of a plausible example where it may differ from RP, but i can't think of what the motivating principle is. if River and RP disagree, why is the River winner a
better choice?
The other two he is referring to are Schulze and Tideman RP. Nearly all
the time it will elect the same candidate and as far as I know is at
least as good.
well, we know when there are only 3 in the Smith Set, that Schulze and Tideman pick the same winner. dunno about this River method, though.
I strongly suggest that the measure of defeat strength should be Losing
Votes and that ballots that equal-rank A and B above bottom should
contribute a whole vote
to each in the A-B pairwise comparison. Ballots that rank A and B
equal-bottom (or truncate both A and B) should contribute nothing to the
A-B pairwise comparison.
that's an interesting proposal i hadn't heard before. i'll be interested in hearing the motivation of it. i presume you mean that the defeat strength should be a strictly decreasing function of the losing votes, perhaps -LV (and the greatest
defeat strength is the least negative -LV). in principle, why is this better than Winning Votes or Margins? (seems like Margins is the midpoint compromise between WV and LV since it is WV-LV.)
I'll be posting more on this soonish, but since you asked the question
I
thought I'd just give you some food for thought to be going along with.
i am digesting.
Thank you, Chris.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Hi Robert,
A few comments on this exchange...
Another Condorcet-compliant method that might interest you, from a Kevin
Venzke webpage:
Jobst Heitzig's River method is identical to Tideman's method,
except that one additionally ignores (without locking) defeats against
candidates against whom some defeat has already been locked. This is
possibly the easiest of the three to work out by hand.
maybe someone needs to explain this more to me. i can think of a plausible example where it may differ from
RP, but i can't think of what the motivating principle is. if River and RP disagree, why is the River winner a better choice?
There are theoretical arguments for each method, but for me the appeal of River is not that it gives a
better winner but that it's easier to find the result. You don't have to look at as many pairwise contests
as with RP.
The other two he is referring to are Schulze and Tideman RP. Nearly all
the time it will elect the same candidate and as far as I know is at
least as good.
well, we know when there are only 3 in the Smith Set, that Schulze and Tideman pick the same winner.
dunno about this River method, though.
Yes, it's the same.
i have to say i am still not convinced of WV. probably Schulze-Margins is still the best, but
RP-Margins good enough and possibly easier to sell to policy makers and the public.
I really wonder. Could you sell A winning the below election? Especially to someone who doesn't know
about pairwise matrices. The IRV or Bucklin advocate will find this absurd I would guess.
7 A>B.
5 B.
8 C.
i like Margins in principle: The percentage Margin is (WV-LV)/(WV+LV) and is a measure of the
decisiveness of defeat, without respect to the size of the election. So 5% defeat is a more decisive
defeat than a 4% defeat.
But if you consider every Condorcet pair as it's own little election, then the salience of the election
would be the number of voters that weigh in on it, which is WV+LV.
I feel the loser of the most "salient" election should not be elected. I think this is in the same vein as
saying that elections shouldn't be vulnerable to spoilers. E.g. if less salient contests affect the outcome
it's likely they do so without benefit to the winners of those contests. (As there is only one prize to give
out.)
Kevin
I think the problem with Schulze versus Ranked Pairs or River is that Schulze is more complicated to understand/explain, and also it's not even obviously a method. Also, realistically you'll probably never encounter an election where any of these three would give a different result. I've often heard people say that these methods can give different results, but I don't think I've ever seen an example, and this suggests to me that it would have to be pretty contrived and complex.
But about Schulze not obviously being a method - have a look at the Wikipedia article under "Computation" - https://en.wikipedia.org/wiki/Schulze_method#Computation
And it's that last bit that sticks out:
"It can be proven that and together imply .[1]:§4.1 Therefore, it is guaranteed (1) that the above definition of "better" really defines a transitive relation and (2) that there is always at least one candidate with for every other candidate ."
"It can be proven..." I don't necessarily mind if it takes a complex proof to show that a method obeys certain criterion like monotonicity etc. But this is just about it being a method that can elect a winner. How complex is this proof? I'm just taking it on trust that it works as a method. With Ranked Pairs or River, it's pretty trivial.
And on Warren Smith's rangevoting.org, https://rangevoting.org/SchulzeComplic.html
"(4) If the strongest path from L to W, is stronger than, or at least as strong as, the strongest path from W to L, and if this is simultaneously true for every L, then W is a "Schulze winner." Schulze proved the theorem that such a W always exists (at least using "margins"; I am confused re the "winning-votes" enhancement)."
So even Warren is confused about the proof for winning votes. And bear in mind, this isn't a proof about some property of the method, but that it is even a method.
Toby
From: robert bristow-johnson <rbj@audioimagination.com>
To: election-methods@lists.electorama.com
Sent: Wednesday, 22 May 2019, 23:14
Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot?
---------------------------- Original Message ----------------------------
Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equally-ranks on ballot?
From: "Chris Benham" cbenhamau@yahoo.com.au
Date: Wed, May 22, 2019 2:35 pm
To: election-methods@lists.electorama.com
Another Condorcet-compliant method that might interest you, from a Kevin
Venzke webpage:
Jobst Heitzig's River method is identical to Tideman's method,
except that one additionally ignores (without locking) defeats against
candidates against whom some defeat has already been locked. This is
possibly the easiest of the three to work out by hand.maybe someone needs to explain this more to me. i can think of a plausible example where it may differ from RP, but i can't think of what the motivating principle is. if River and RP disagree, why is the River winner abetter choice?
The other two he is referring to are Schulze and Tideman RP. Nearly all
the time it will elect the same candidate and as far as I know is at
least as good.well, we know when there are only 3 in the Smith Set, that Schulze and Tideman pick the same winner. dunno about this River method, though.
I strongly suggest that the measure of defeat strength should be Losing
Votes and that ballots that equal-rank A and B above bottom should
contribute a whole vote
to each in the A-B pairwise comparison. Ballots that rank A and B
equal-bottom (or truncate both A and B) should contribute nothing to the
A-B pairwise comparison.that's an interesting proposal i hadn't heard before. i'll be interested in hearing the motivation of it. i presume you mean that the defeat strength should be a strictly decreasing function of the losing votes, perhaps -LV (and the greatestdefeat strength is the least negative -LV). in principle, why is this better than Winning Votes or Margins? (seems like Margins is the midpoint compromise between WV and LV since it is WV-LV.) > I'll be posting more on this soonish, but since you asked the questionI
thought I'd just give you some food for thought to be going along with.i am digesting.Thank you, Chris.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
----
Election-Methods mailing list - see https://electorama.com/em for list info
Good question Robert!
Does anyone know of a publication that addresses this topic? On the site
that Canadian MP Ron McKinnon published to promote Ranked Pairs, it appears
the approach is to add voters' indifferent votes to both candidates when
computing winning votes.
The “majority vote” is the number of votes in which the given majority
candidate is more-preferred-than the given minority candidate plus the
no-preference value. The “minority vote” is the number of votes in which
the minority-candidate is more-preferred-than the given majority candidate
plus the no-preference value.
https://condorcet.ca/see-how-it-works/how-it-works/
(Click "Ranking the Pairs", then click "Notes")
While I have ideas about the reasoning for the approach, I don't know for
certain. I'll email him about it. MP's tend to be busy, so it may take a
while to get a response. To speed things up, does anyone have a connection
to Mr. McKinnon or the expert(s) he worked with? I would be interested in
learning more about their reasoning for this approach.
All the best,
Carl
On Mon, May 20, 2019, 4:06 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
So this would be about Tideman Ranked-Pairs, or Schulze, or some other
Condorcet-compliant method.
It doesn't make much difference if the measure of Defeat Strength is
Margins (supporting votes minus opposing votes), but what if Winning Votes
is the measure of Defeat Strength in either RP or Schulze? How should a
pair of candidates that are equally-ranked on a ballot be counted? Do you
count it (as a winning vote) for both candidates? For neither
candidate? (I dislike the idea of a half-vote for both candidates. And I
hate the idea of not allowing equal-ranking in a Condorcet RCV election.)
What is the right way to do this? It seems the most consistent might be
to count an equally-ranked votes for neither candidate, since we
consider unranked candidates as tied for last place on the ballot, and we
would count those as votes.
But what do you guys think? If we allow for equal-ranking in a
Condorcet-compliant RCV, how do we deal with it in terms of vote totals?
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Election-Methods mailing list - see https://electorama.com/em for list
info
On Mon, May 20, 2019, 4:06 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
So this would be about Tideman Ranked-Pairs, or Schulze, or some other
Condorcet-compliant method.
It doesn't make much difference if the measure of Defeat Strength is
Margins (supporting votes minus opposing votes), but what if Winning Votes
is the measure of Defeat Strength in either RP or Schulze? How should a
pair of candidates that are equally-ranked on a ballot be counted? Do you
count it (as a winning vote) for both candidates? For neither
candidate? (I dislike the idea of a half-vote for both candidates. And I
hate the idea of not allowing equal-ranking in a Condorcet RCV election.)
What is the right way to do this? It seems the most consistent might be
to count an equally-ranked votes for neither candidate, since we
consider unranked candidates as tied for last place on the ballot, and we
would count those as votes.
But what do you guys think? If we allow for equal-ranking in a
Condorcet-compliant RCV, how do we deal with it in terms of vote totals?
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Election-Methods mailing list - see https://electorama.com/em for list
info