On 2024-05-21 22:30, robert bristow-johnson wrote:

I think the idea is somewhat like this. I haven't read the paper so I'm
not sure I got it or its preconditions right. (There may be limits to
convergence of the fixed point iteration mechanism.)

You do a preliminary Approval vote - a poll - without further
instructions. The different voters' approval cutoffs fall at various
points because there's zero info and the voters just do whatever.

Now suppose that the winner of the poll is A, and B is in second place.

Next poll, the voters set their cutoff to include A and exclude B (for
those who prefer A to B) or to include B and exclude A (vice versa).

After this happens, candidate C has the highest approval count and D is
in second place. Rinse and repeat.

Do this enough times and (if there's a CW,) some fixed-point candidate,
W, will be in first place, and subsequent approval polls don't change
who's the finisher and who comes in second. Then W is the Condorcet
winner and nobody has any incentive to deviate from setting their
approval cutoff between W and whoever comes in second.

Come the final election, people do as they did in the last poll, and
then W, the Condorcet winner, wins.

So with Approval and enough polls, if there's a Condorcet winner (and
given some assumptions about economic rationality) then Approval should
find it. If there is a sincere cycle, then as I remarked, "round and
round and round it goes; where it stops, nobody knows!" - the ultimate
winner depends on the number of polls conducted and where the cycle started.

Or you could just run a Condorcet method and get the CW in one step
without all this poll business.

Approval has very good method simplicity. But this process complexity --
sheesh, that's something else.

(Before someone says "but Monroe" -- IRV passes his criterion and I see
no reason why a Condorcet prefix should void it.
Actual proofs that Condorcet does or doesn't void NIA would be welcome,
of course... but checking NIA for a method that's part positional and
part pairwise would require synthesizing Monroe's two pivotal strategy
approaches, and that might be pretty tough.
In addition, "NIA-failing methods must fail in practice" does seem a bit
counter to Debian's successful use of Schulze. Or the various other
places and organizations that use it.)

I agree. I find method complexity much more honest than process complexity.

We also really need a way to talk about process complexity in a
principled way. When a method is intended to be the base layer of an
induced method, then the properties of the base method can obscure the
properties of the induced method.

E.g. if the iteration above settles into cycling between members of the
essential set, then the induced method is nonmonotone, even if Approval
itself is monotone. It is also nondeterministic[1] even if Approval isn't.

You could use fractional counting, e.g. if someone votes A=B>C, he gives
half a point to A and half to B. Once either A or B is eliminated, the
vote counts fully for the other candidate. Delemazure and Peters say
that this way of handling ties may break clone independence
(https://arxiv.org/abs/2404.11407), but BTR-IRV already fails it.

A very simple modification to IRV would be Condorcet//IRV. Do you think
that could work? Benham is better but needs more explanation.

The problem with Condorcet//IRV is that it's not cloneproof, and
furthermore it fails in a very obvious way: clone the CW into a
three-cycle and then C//IRV defaults to IRV, after which the cloned
Condorcet winner can fail to be elected. Benham avoids that problem, but
the Condorcet check has to be moved inside the loop, so to speak.

-km

[1] Or related to nondeterminism in the same way a pseudorandom number
generator is related to actual randomness.

not sure I got it or its preconditions right.

Your description gets some of the intuitions correct, but Myerson and Weber
don't assume perfect information; their model includes uncertainty in how
many voters there are of each type (i.e. turnout or polling errors). They
show approval voting 1. has a unique strategic equilibrium, i.e. only one
possible lottery is a result; and 2. that strategic equilibrium elects the
Condorcet winner.

Or you could just run a Condorcet method and get the CW in one step

without all this poll business.

sheesh, that's something else.

No, you can't; that's the point of Gibbard's theorem. It says that no
matter what method you use, you still have to read the polls, because
regardless of the voting system your best vote will depend on the
preferences of others. That's true regardless of the voting system.
Importantly, it's also true for 100% of elections, regardless of the
manipulability rate or voting rule, because you don't know whether you're
in a manipulable election until after you've checked the polls. So,
regardless of the method, you always have to check the polls.

The only ways to reduce the strategic burden of a method are to either A)
make strategy easy to work out or B) make the incentive for strategy so
small, and the difficulty of identifying the correct strategy so large,
that people will just never check the polls. I doubt B can be done, because
the number of candidates in real elections is small, and parties just have
far too strong an incentive to identify strategy. In Hong Kong, parties
will frequently execute *correlated randomized strategies *using apps or
instructions like "vote for the candidate whose height is closest to
yours".

Also, people tend to know who's leading in a race just by hearing news
coverage. I don't think it's possible to know enough about an election to
have an opinion on the candidates, but still have no idea who the
frontrunners are. If nothing else you'd need to know who they are so you
can learn their policy positions.

Before someone says "but Monroe" -- IRV passes his criterion and I see

Condorcet//IRV passes his criterion, but I doubt it has a unique
equilibrium on the Condorcet winner because it's not weakly-sincere in the
Myerson-Weber equilibrium like score or approval are. It's entirely
possible you can't identify the sincere Condorcet winner from the polls.
Same reason the Condorcet winner can (and often does) lose under FPP with
strategic voting, even though the Condorcet winner is a strong Nash
equilibrium in FPP.

I agree. I find method complexity much more honest than process complexity.

...

As I have said, I have sorta soured on the "modify IRV language to make it Condorcet consistent" approach.  The simplest Condorcet-consistent modification to Hare IRV is BTR-IRV.  I'm pretty sure that is.

Okay, I will try to stick with the semantics from Wikipedia:

• Condorcet methods fit within two categories:

** Two-method systems, which use a separate method to handle cases in which there is no Condorcet winner.
** One-method systems, which use a single method that, without any special handling, always identifies the winner to be the Condorcet winner.

I think that they call that "separate method" a "completion method".  At least this Canadian MP does: https://condorcet.ca/ .

No the advantage of a One-method Condorcet system is that it doesn't need a completion method in the legislative language and we're done with it.  If there is no CW, we just take what we get.  I think that BTR-IRV might be the simplest One-method Condorcet system to encode into law with words.  Probably the One-method system I would prefer most, if I were king of the world, would be Ranked-Pairs.  (Still agnostic about Working Votes vs. Margins.)  But I am not sure we can get Ranked Pairs passed into law.

But I think that transparency in marketing is important, because this is one of my biggest criticisms of FairVote.  So I see some value in the Two-method Condorcet systems because the first method is the simple application of the Condorcet criterion to examination of every single pairing of candidates:

1. Begin with every candidate not labeled as a loser.

2. For every possible pairing of candidates; if more voters mark their ballots ranking Candidate A higher than Candidate B than the number of voters marking their ballots ranking Candidate B higher than Candidate A, then Candidate B is labeled a loser.

3. After examination of every pairing of candidates, the candidate left not labeled a loser is the candidate elected.

4. If, after examination of every pairing of candidates, no candidate is not labeled a loser then the following Completion Method determines which candidate is elected:

(Condorcet-Plurality --- 5. Completion method: The candidate with the Plurality of first-choice rankings is elected

(Or Condorcet-TTR --- 5. Completion method: The two candidates with the most first-choice rankings shall face each other in a runoff in which the candidate that has more voters ranking that candidate higher than the other candidate is elected.)

Now this Condorcet-TTR is going to work very much like Condorcet-IRV, but it doesn't refer to all of the IRV semantics, just for the sake of a completion method.  Can't that be good enough?

I really don't want policy makers and public thinking that we're trying to pull a sophisticated scam over them.  I want these people to see that we're applying the Condorcet principle directly to the election tallies.

And then we simply have to explain to them that, when excrement hits the fan and there is no Condorcet winner, we do the best that we can and blame this on Arrow, et. al.  We make a decision, with simple principles, about which candidate has the best claim to having the most voter support, even though we know there is always going to be another more preferred and there will be a spoiler, no matter who we elect.

Unlike MO and CLC, I am not concerned about a "feeding-frenzy 🦈 of burial."  Cycles are going to be extremely rare and spotty.  And when they happen, there will be no little deception; we'll be clear that there is no Condorcet winner and that we have to elect someone who isn't the CW and that in this contingency there are prior agreed-to rules that spell out who that is.

See, the problem is FairVote advocates a simpler One-method system (that doesn't always elect the CW even when such exists).  Simple method (more complicated than FPTP), but no simple principle.  What's the one-sentence principle (that's actually true) that describes IRV?  There isn't any.  Why should we fight and die on the hill for IRV?  At least FPTP has a very simple principle: "Candidate with the most votes is elected."

Condorcet has a simple, one-sentence principle that defines it and it's a hard ethic to disagree with:  If more voters mark their ballots preferring A to B, then what possibly can justify electing B?  IRV or even STAR advocates have to answer that, and they cannot.  If we can, at all, avoid it, there is no good reason to elect B.  Doing so will directly inflate the effectiveness of votes coming from the B voters over those of the A voters and we will not have equally-valued votes.  Not One-person-one-vote at the end of the day.

So Condorcet expresses a better, clearer principle of democracy than does Hare.  Or Borda.  Or FPTP.  Or STAR.  Or Approval.  What is needed is legislative language that doesn't scare the policy makers nor the public away.  And IRV and STAR have also scared away some people because of the perceived complexity of the method in legislation.  I don't want Condorcet language to be unnecessarily complex and not opaque at all.  (Like Schulze and some of these other ideas of your, Kristofer, would be opaque.  They are not sufficiently concise.)  I want people to know exactly what they are getting with the language defining the method encoded in law.

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

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Robert,

I think Condorcet//IRV would work fine, and surely could get some
support from IRV supporters.

Until one candidate remains, one-at-a-time eliminate the favorite
(among remaining candidates) of the fewest.

The palaver about a "majority" is just to shorten the counting process,
and also fits in with the marketing.

Since you are obsessed with "clear and simple language"  am I right in
assuming that for you selling and explaining the concept of the "Smith
set" (or top cycle) is out?

What is your problem with  Condorcet//Approval?    If you don't like the
"implicit" version (where all candidates ranked above bottom are
considered approved), then what about the "explicit" version?

One fairly simple way of doing that was proposed in April 2002  on EM by
Adam Tarr.  That was to use ABC-DEF grading ballots, with only
candidates given an A or B or C considered to be approved.

http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html

But several other ballot styles have been suggested for this type of
method.  Someone liked having a Yes/No box next to every candidate.  The
approval cutoff being a "virtual candidate" has been suggested, a 0-100
score ballot with scores above 50 counting as approval and so on.  I
suggested that the voters could mark the lowest ranked candidate they
approve, and so that candidate plus the ones they rank not below that
candidate are counted as approved.

Chris B.

On 23/05/2024 11:54 am, robert bristow-johnson wrote:

Robert,

I think Condorcet//IRV would work fine, and surely could get some
support from IRV supporters.

Until one candidate remains, one-at-a-time eliminate the favorite
(among remaining candidates) of the fewest.

The palaver about a "majority" is just to shorten the counting process,
and also fits in with the marketing.

Since you are obsessed with "clear and simple language"  am I right in
assuming that for you selling and explaining the concept of the "Smith
set" (or top cycle) is out?

What is your problem with  Condorcet//Approval?    If you don't like the
"implicit" version (where all candidates ranked above bottom are
considered approved), then what about the "explicit" version?

One fairly simple way of doing that was proposed in April 2002  on EM by
Adam Tarr.  That was to use ABC-DEF grading ballots, with only
candidates given an A or B or C considered to be approved.

http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html

But several other ballot styles have been suggested for this type of
method.  Someone liked having a Yes/No box next to every candidate.  The
approval cutoff being a "virtual candidate" has been suggested, a 0-100
score ballot with scores above 50 counting as approval and so on.  I
suggested that the voters could mark the lowest ranked candidate they
approve, and so that candidate plus the ones they rank not below that
candidate are counted as approved.

Chris B.

On 23/05/2024 11:54 am, robert bristow-johnson wrote:

Can you imagine legislative language, first defining the Smith set and then the actual reference to the Smith set in the verbiage of the law?

I just want Condorcet in law, that spells out plainly who the Condorcet winner is and how that candidate is identified from the ballot data.  Now, being a two-method system, the law will also have to spell out what to do when there is no Condorcet winner.  Condorcet-Approval is pretty simple and implicitly defining any ranked candidate as having received an Approval vote is simple enough.  Perhaps it could be a better law than Condorcet-Plurality or Condorcet-TTR.

What are the tactical/strategic voting implications of Condorcet-Approval?  How is it better to disincentivize strategic or tactical voting?  What are the pitfalls?

I'm a bit concerned about the loss of voter expressivity in the case of a cycle, with Condorcet-Approval.

I am a little concerned about two candidates, say George W Bush and Donald Trump, neither whom I approve, but I may very well rank W one rung higher than the corrupt, criminal, mendacious, narcissistic demagogue.  So I would have to rank W which would imply approval if the election goes into a cycle.

I think anything more than just asking voters to rank their preferences is asking too much.  It requires or burdens the voters to think tactically.

I'm still thinking perhaps Condorcet-TTR might be best.  It's within epsilon of Condorcet-IRV (like that California bill from a few years ago) but it doesn't carry the semantic baggage of all of the IRV elements (like "active candidates" or "continuing candidates" or transferred votes, etc.).

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

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On 2024-05-23 04:24, robert bristow-johnson wrote:

I see your point, and I'd say that "modify IRV language" is mainly good
for two things:
- If the jurisdiction is already used to IRV, it might be easier to
pass, and
- If you really need strategy resistance, Condorcet-IRV hybrids will
provide. (Not applicable to BTR-IRV.)

The election methods area of Wikipedia has been pretty heavily edited
lately, but that seems reasonable enough.

How about Minmax as an approximation to RP?

The difficult part would be to explain its underlying reasoning: that in
the absence of someone who wins every pairwise matchup, we take the one
who loses the least no matter who he's paired up with.

It's the two level quantifier that makes it hard to understand: find the
candidate whose worst defeat is the least. If seen from the right
perspective (someone who beats everybody handily is better than someone
who beats by just a little), it seems kinda obvious, but it's hard to
phrase it in a way that makes this perspective evident.

It's pretty easy to find the winner once you have the Condorcet matrix,
though.

I guess that's the thing. You can't easily pass an outright
pairwise-based method unless the people understand the logic to
considering things pairwise. The language is secondary in that sense.

This is comparable to my fpA-fpC method except simpler to understand but
not monotone. Its main problem, I think, is that if irrelevant
candidates hog the first preferences, then first preferences are not a
good measure of strength. E.g. in the 2021 City Council Ward 2
Minneapolis election results, Smith//fpA-fpC (and presumably Smith//TTR)
gave a result that agreed with minmax, whereas plain Condorcet//
wouldn't have. This could also have clone independence implications if
there's no CW.

If, on the other hand, cycles (dishonest or honest) are rare, then
there's no problem, and we just need something that doesn't horribly
break the few times cycles exist.

It might be good enough. I'm just saying where its limits are :-)

Here's an attempt to define the Smith set operationally. It doesn't seem
too complex - as I mentioned above, the sticking point seems rather to
be whether policy makers and the public understand that the Condorcet
way of doing things is sensible to begin with.

1. If more voters prefer a candidate A to another candidate B, we say
   that A beats B.

2. The method first finds the admissible candidates, then performs a
   calculation as if only the admissible candidates had run.

3. Start by admitting the candidate who beats the most other candidates.
   If there is a tie by that measure, admit all of the tied candidates.

4. Check if there is another candidate who beats an admissible
   candidate. If so, admit that candidate and check again.

5. Repeat the checking and admitting process for as long as there exists
   a candidate who beats an admissible candidate.

6. Once there are no more non-admissible candidates who beat admissible
   candidates, eliminate the candidates who have not been admitted.

7. Count the ballots again, ignoring preferences for candidates who have
   not been admitted.

8. Of the two candidates with the most first preferences in this second
   count, elect the one who beats the other. If there is a tie, break the
   tie randomly.

(Smith//TTR)

Of course, this might be overengineering. If it is, then Condorcet//
would be good enough.

I'm under no illusion that my methods are simple. I'm definitely more of
a research type, trying to figure out what's possible rather than what's
implementable.

If someday the public places as much trust in Condorcet methods as the
NZ voters do in Meek's method, or the Norwegian voters do in the (pretty
complex) top-up seat algorithm, then point them in my direction. Or
Schulze's :-)

-km

One-sentence definition of RP:

Elect the candidate who isn’t beaten among all of the strongest defeats
that don’t contradict (cycle with) eachother.
—-

That’s unambiguous, clear & explicit. There’s only 1 meaning that it could
have.

The following wording is longer, but it entirely spells out the procedure.

List the pairwise defeats one at a time, stronger ones first.

But, if the next-strongest one forms a cycle with already-listed defeats,
then skip that one.

When all defeats have been listed or skipped, elect the candidate who isn’t
defeated in any listed defeat.
—-

You might offer, with it, MinMax:

Elect the candidate whose greatest defeat is the least.
—-

RP is better. MM is simpler.

(Obviously both methods need the usual preliminary definitions.)

On Thu, May 23, 2024 at 10:19 robert bristow-johnson <
rbj@audioimagination.com> wrote:

Good luck explaining that to a low engagement voter.
On Thu, May 23, 2024 at 8:21 PM Michael Ossipoff email9648742@gmail.com
wrote:

Robert,

Are you seriously suggesting another round of voting?   Why?

Hare is much better than TTR.  And you already collected the all the
ranking information you need to operate either in the first round.

I am not a lawyer and know nothing about whatever is special or
distinctive about US "legislative language".   But nonetheless I can't
see why it would be an insurmountable challenge.

It makes Burial strategy more likely to backfire than to succeed.   And
it is less likely to fail Favorite Betrayal for voters who rank their
Lesser Evil compromise equal-top with their sincere Favorite.

Aren't they used to that?    TTR would introduce a lot of extra Pushover
strategy opportunities, which of course (via your crazy primaries
system) US voters are well used to.

I suggest that the default placement of the approval cutoff could be
just below equal-top.  Then to the extent that the voters don't bother
with it the method defaults to Condorcet//FPP(whole), or Condorcet//Top
Ratings, which may not be a huge shock.

Also I think it is easier to vote sincerely with
Condorcet//Approval(explicit) than with the explicit version. Because
you can sincerely rank all the candidates without being concerned about
being forced to approve candidates you don't like.

Then just make a judgement call (or be guided by someone's advice) on
where to put your approval cutoff (which probably most of the time will
be irrelevant).

Chris B.

On 24/05/2024 2:48 am, robert bristow-johnson wrote: