[Election-Methods] RE : Corrected "strategy in Condorcet" section

[Kevin Venzke]

Juho,

--- Juho <juho4880 at yahoo.co.uk> a écrit :
> I was a bit puzzled when answering this mail. Our terminologies did  
> not yet quite match. There is also still some confusion with what the  
> sincere votes were in your original example (49 A, 24 B, 27 C>B) (see  
> below). And I'm still wondering if you felt that D was the rightful  
> winner in the basic example where sincere opinions were 1000 A>B,  
> 1000 C>D, 1 D>B (or 1000 A>B>C=D, 1000 C>D>A=B, 1 D>B>A=B). The rest  
> of the reactions/comments are embedded below in the mail.

Yes, I do think D is the proper winner.

> > This is why I keep pointing out that this is a Condorcet method and  
> > we're
> > trying to find the best compromise. I really think you are overly
> > impressed with first preferences, and that is why I keep bringing  
> > up IRV.
> > C>D voters are not going to thank you for preventing D from winning,
> > unless C wins instead.
> 
> I don't think I have any interest in the first preferences here. I'm  
> basically interested only in the pairwise matrix that is neutral to  
> where the preferences come from. I didn't understand why IRV is  
> relevant here - I think the C>D voters are not going to thank me for  
> changing the voter from X to Y in any system if they prefer X to Y.
> 
> In the latter example I changed a two way AB tie to a four way tie  
> (either by adding the last vote in wv or by changing the method from  
> margins to wv).
> 
> If people think in the margins way I might get more thanks than  
> blames. But if people feel that wv is the natural measure of  
> preference then the situation is more neutral. Based on this am I  
> right to assume that already in the first example (1000 A>B, 1000  
> C>D, 1 D>B) you found D to be the natural and correct winner  
> (assuming sincere votes)?
> 
> ((Now btw you used a "first place argument" :-).))

Juho, if you think I used a "first place" argument then you didn't get
my point. Also the fact that you used candidates X and Y when discussing
the C>D voters suggests that you didn't get it.

You are saying that the election method should respect the C>D voters'
nearly unanimous belief that C is better than D. If this is not for
the benefit of the C>D voters then for whose benefit is it?

> >>> For an explanation I can see a couple. One is based on the  
> >>> concept of
> >>> approval. This is Condorcet and we are looking for a compromise
> >>> candidate.
> >>> The candidates who received the most votes (of any type) are D and
> >>> B. By
> >>> this concept one of these two should win.
> >>
> >> Yes, approval could be added. But that'd be another voting method.
> >> Voters should be informed about that. They could btw still vote
> >> A>B>C=D instead of A>B>truncate and spoil the election.
> >
> > I didn't say we would add approval. However I believe these is an  
> > implicit
> > sense of approval in casting an explicit vote for a candidate.
> >
> > I do not regard the cast votes A>B>C=D and A>B as meaning the same
> > thing. If you ruin the election when the vote is A>B>C=D then I don't
> > mind as much.
> 
> The vote counting algorithm treats A>B>C=D and A>B in the same way.  
> Voters should be made aware that there is no difference between these  
> two voting styles.

Yes, my comment was hypothetical. Since margins does not distinguish
between those two votes, there are treatments of the vote A>B>C=D that
I would find acceptable normally but which cannot be acceptable under
margins because the same treatments would be necessary given A>B.

> >> One solution would be to make it mandatory to rank all the
> >> candidates. (This would also solve the margins vs. winning votes
> >> debate :-).)
> >
> > I hope this is a joke. That would practically make "betray or risk  
> > being
> > betrayed" a checkbox on the ballot.
> 
> Yes, this was a joke as indicated, but I don't think it would somehow  
> make the method unusable.

Well, it's just as I said. When there are two frontrunners, and some
other candidates, every single voter must decide whether they rank the
lower frontrunner truthfully (which opens you up to being betrayed)
or insincerely low (which prevents you being betrayed but can backfire).

> (I'm not sure but your comment sounds to me a bit like the old  
> argument that use of wv makes Condorcet acceptable while margins keep  
> it unacceptable. My point has been that we should cover all arguments  
> in both directions, and that it is not clear to me why this single  
> argument would be more important and a bigger threat than the others.)

I still don't know what the others are. You bring up isolated scenarios
involving order reversal, and you make a point about respecting unanimous
opinions which in the examples presented would be an annoyance to the
voters with those opinions.

I believe the "old argument that use of WV makes Condorcet acceptable
while margins keep it unacceptable" usually has to do with order reversal
strategies.

> >>> The other principle is that of unambiguous defeats, where more than
> >>> half of
> >>>
> >>> the voters voted some way on a given issue. D is the only candidate
> >>> not on
> >>> the losing end of one of these.
> >>
> >> Sounds like a "very strong majority requirement". Preference 51-49
> >> (out of the citizens that voted) is considered stronger than
> >> preference 49-0. (Note that also margins could be criticized of
> >> saying that 3-0 is a stronger preference than 51-49 (it depends on
> >> interpretation if this is considered bad or not), but I think the
> >> problems of winning votes are worse here.)
> >
> > Well, I don't know what to say here. I did much better than simply  
> > assert
> > that 51-49 is stronger than 49-0. I pointed out that if the method is
> > equipped to ignore noise then you don't have to rely on the "not
> > catastrophic = OK" doctrine so much.
> 
> What's the "not catastrophic = OK" doctrine? What is considered noise?

"Not catastrophic = OK" is the attitude you seem to present in particular
in response to A winning given 7 A>B, 5 B, 8 C. Basically when a candidate
loses an intuitively important pairwise contest only by a little, it is
OK for that candidate to win anyway.

"Noise" can be said to be votes for candidates who are not likely to win.
If you pull such candidates out of the race, the winner should rarely
change.

> >>> In practical terms I can't see how the C voters could feel cheated
> >>> that D
> >>> wins. If the C voters had not voted for D, then C would still lose
> >>> due to
> >>> the pairwise loss to B.
> >>
> >> I think you are assuming the approval cutoff to be present in the
> >> votes at the end of the listed candidates here. A more straight
> >> forward (and a more "ranking oriented") interpretation might be that
> >> they unanimously said that C is better than D.
> >
> > This is very irritating. How am I assuming there's an approval cutoff?
> > I'm trying to point out that no one in the scenario cares about this
> > issue since everybody is too busy trying to elect the best  
> > candidate they
> > can.
> >
> > Here is a question for you: If this faction really doesn't want their
> > second choice to win (since it goes against their unanimous  
> > preference for
> > their first choice), why do they even vote for him?
> 
> You are again using the "first choice" argumentation. I'm not. Maybe  
> your thinking based on the wv philosophy (and mine is one step closer  
> to the margins) and that is why the terminology looks a bit  
> different. Lets be explicit in the wordings to understand what we mean.
> 
> I'm just saying that from the rankings point of view 100% of the C>D  
> voters ranked C above D. They want C to win D but they want D to win  
> the others. (And as should already be clear I don't assume that the  
> votes carry a message that the candidates that are marked in the  
> ballot are somehow "approved".)

I didn't assume that either here.

This isn't "first choice" argumentation, as I explained above.

If you agree that C>D voters want D to beat the other candidates, then
they should be allowed to elect D. From *their* perspective it makes no
sense to require that D must have some support against C to beat other
candidates.

> >>> In the second scenario you suppose equally-sized factions voting
> >>> A>B>C>D,
> >>> E>F>G, H>I, J. (Again, this is not a realistic scenario.) Under WV
> >>> a single
> >>> additional voter has at least some way to vote that can turn any
> >>> one of
> >>> these candidates into the winner. You say:
> >>>
> >>> "The question thus is if it is acceptable that winning votes
> >>> doesn't put
> >>> any weight on the unanimous opinion on the order of candidates set
> >>> by the
> >>> voters of each party to the candidates of that party."
> >>>
> >>> This is a Condorcet method. We're looking for a compromise  
> >>> choice, not
> >>> selecting a representative of voters belonging to one party. When
> >>> people
> >>> want to attach weight to many voters' first preferences then they
> >>> use IRV.
> >>
> >> I don't see the link to IRV. The first preferences were not the
> >> deciding element here but truncation.
> >>
> >> It is characteristic to Condrocet methods to elect a good compromise
> >> candidate. In this case I think A, E, H an J would maybe have been
> >> better compromises than the others.
> >
> > I don't know what you think "compromise" means. AEHJ are not  
> > compromises
> > at all; they are the first preferences of each large faction.
> 
> Ok, now I understand a bit where you see me promoting the first  
> choices. But still I say I have no interest in putting some specific  
> weight on the first preferences. It just happens to be so that if a  
> voter marks some candidate at the #1 position, then that candidate  
> gets lots of points in the matrix (=preferred to all others).
> 
> In this election I don't thing there were candidates that could be  
> called "good compromise candidates" since all voters except one gave  
> support to the candidates of their own party and left all the others  
> tied at the last position.

If an election is tied, isn't it okay for one more voter to break the 
tie?

Wouldn't you *especially* want to listen to a voter whose preferences 
cross parties? I think it would hardly be more encouraging if the
tiebreaking voter simply voted "A".

> >>> In the third post you bring up the scenario 20 A, 15 ABC, 10 ACB,
> >>> 35 BC,
> >>> 20 CB and note that the latter faction can use order reversal to
> >>> steal the
> >>> win.
> >>>
> >>> The order reversal here backfires and elects A if the 35 BC voters
> >>> don't
> >>> vote for C. If even 6 BC voters truncate, it backfires. As I  
> >>> discussed
> >>> earlier, I don't see why B voters would vote for C anyway. (Nor  
> >>> why A
> >>> voters vote for B or C, but that does not seem to be essential to  
> >>> the
> >>> scenario.)
> >>
> >> Yes but the point of the example is that in this type of (realistic!)
> >> situations margins doesn't encourage strategic voting but winning
> >> votes does. With winning votes the use of the (working) strategy
> >> might lead to a counter strategy that may well further lead to a
> >> "catastrophe" and elect A.
> >
> > This situation doesn't encourage strategic voting under WV. Did you  
> > not
> > notice it only takes *six* out of 35 to make the strategy backfire?  
> > It is
> > not reasonable at all for C voters to think this is a reliable  
> > strategy.
> 
> Someone called this a game of chicken. Not a nice feature of a voting  
> system. If the newspapers publish the results of the poll and tell  
> that C>B voters have the option to vote strategically C>A>B, what  
> should the B>C voters do? Should they truncate in order to eliminate  
> the risks? Those C>B voters that want C to win more that they fear A  
> to win (utilities e.g. C=100, B=50, A=40) may vote strategically even  
> if there would be a risk of some B>C voters using the counter strategy.

The same newspapers would say that B>C voters should truncate. And then
it doesn't work. (This is assuming not just that B voters do plan to give
that many votes to C, but that C voters trust that they will.)

> >> To me the easiest explanation to why B supporters voted C and the
> >> other way around was that they were the two candidates of one party
> >> (e.g. Republicans). They are both average Republicans (not extremists
> >> in any direction). B is just a bit more competent for the job than C.
> >> This applies to A voters (Democrats) too.
> >
> > Incidentally, I don't see it as likely that one party will nominate  
> > two
> > candidates, exactly because of the defection and betrayal  
> > incentives that
> > exist. If there are two candidates of the same ideology, I think it is
> > likely that one is better established than the other, and the  
> > supporters
> > of the better established candidate are in a much better position to
> > force the other candidate's supporters to aid them.
> 
> Are you recommending a two-party system or two-candidate elections?  
> That would make the Condorcet strategies disappear :-). The one  
> candidate per party idea could be extended to having one candidate  
> for the left wing parties and one for the right wing parties.

There is a big difference between "recommending" something and predicting
that something will be the case.

Just because good Condorcet methods can handle clones doesn't mean it
makes sense for parties to try to nominate them. I think voters would be
far too tempted to defect.

I think the real value of good methods is to permit viability of 
independents, centrists, or candidates representing a position on a 
different political axis that would otherwise be neglected.

But it would also be very nice to reduce the phenomenon of weak candidates
spoiling elections.

> If this would be the preferred mode of operation, then the "tree  
> voting" style where candidates are organised in a tree like  
> structure. See e.g. my mails on tree structures at March 11th 2007.  
> That is one strong but a bit limiting way of getting rid of the cycle  
> based strategies.

I believe major political establishments would tell you that this is
indeed the "preferred mode of operation" assuming they understood the
question.

> >>> You say the point of your sixth post is that you describe a scenario
> >>> where "strongish natural cycles" could be possible. Your scenario
> >>> involves each third of the electorate voting A>B>C, B>C>A, C>A>B,  
> >>> with
> >>> this vote reflecting their sincere preferences. That's fine, but I
> >>> don't
> >>> see why such a cycle is more plausible than a cycle that arises  
> >>> solely
> >>> because of truncation (which was the case in my scenario).
> >>
> >> This example (March 23, 2005 8:29:18 GMT+02:00, "Re: majority rule,
> >> mutinous pirates, and voter strategy") was just part of a discussion
> >> on if "strongish natural cycles" are possible in the first place (not
> >> intended to discuss margins vs. winning votes).
> >>
> >> In your example (see below) I couldn't find a plausible (real life)
> >> explanation to why some groups truncated so strongly while one group
> >> didn't truncate at all.
> >
> > Well I can help you out. A and B factions truncated because they were
> > the frontrunners. C voters didn't truncate because they didn't expect
> > C to win, and therefore needed a second preference as a compromise.
> 
> Ok, this is a clear explanation but I have some questions still.
> 
> - I can't really comment the strategies if I don't know what the  
> sincere opinions of the voters were. Could you give some set of  
> sincere opinions that led to these strategic votes.

I did this already. What did you not like? That I didn't clearly specify
the division of the 24 B voters between B>A sincere and B>C sincere?

> - Why is B considered a frontrunner with less first place support  
> than C had?

Because the election results are only available after the election is
held.

I don't know why you ask this. Information isn't perfect; your modification
of my scenario to make it "more realistic" seemed to primarily have as
its goal, to make the point that the results of the election are not
very certain.

> - Why did A supporters decide to truncate? Being one of the  
> frontrunners is not yet a good enough reason.

When I first encountered this scenario the candidates were labeled Bush,
Gore, and Nader. The situation is that Nader turns out to be oddly strong.
It makes little sense to me to imagine that a substantial number of voters
would vote "Bush>Gore" just because Nader is in the race.

I'm not sure why it matters whether A voters truncate. If they vote for
B, as I've said, then they can make A lose. But this doesn't really save
the scenario because it directly answers why A supporters should truncate.

> - Why did B supporters decide to truncate? Is this a winning votes  
> counter strategy?

It's a Condorcet strategy. If B voters believe C voters will give a
second preference to B (because C is not considered a likely winner) and
especially if they don't expect second preferences from A voters, giving
a second preference to C is not optimal since it can make C the voted CW.

Actually, I'm not sure I know a method where it is clearly a good 
strategy for the B voters (supporting the better-established candidate B)
to give a second preference to C. Under IRV it is technically harmless,
but if B voters aren't expected to vote for C then this makes C voters
more likely to just let B win via a B>C vote.

This is assuming still that B is better-established than C.

> >>> 49 A
> >>> 24 B
> >>> 27 C>B
> >>
> >> The numbers of this example are so unlikely to occur in real life
> >> that I modified the example a bit to get values that would be more
> >> probable. This was the first one that I found to be close enough to
> >> be realistic (maybe not yet fully realistic, maybe there are others
> >> that serve the strategic needs better).
> >>
> >> 30 A
> >> 9  A>B
> >> 6  A>C
> >> 14 B
> >> 8  B>C
> >> 2  B>A
> >> 25 C>B
> >> 5  C
> >> 1  C>A
> >>
> >> Vulnerability to the margins strategy was kept => similar cycle with
> >> appropriate differing strengths with margins and with winning votes.
> >> One C>B voter can change the result by voting B>C.
> >>
> >> I tried to keep the original number of first place supporters of each
> >> candidate. => 49/24/27. But I had to assume that some C supporters
> >> will truncate (since some B voters did so too) and as a result the
> >> number of A supporters had to be dropped to 43. In order to make C
> >> win B I donated these votes to C. => 45/24/31.
> >
> > Just a note. There is no need to assume some C voters will truncate,
> > unless you are trying to trick yourself into thinking this is a real
> > election or something. C voters didn't truncate because they knew C  
> > was
> > not a frontrunner. In real life, some C voters would truncate, sure.
> > But "I had to assume that some C supporters will truncate since some
> > B voters did so too" is ridiculous logic.
> 
> These were intended to be sincere opinions that could be from real  
> life. I thus planned to consider any any possible strategies (and  
> strategic truncations) based on these sincere opinions.
> 
> (These votes were intended to be a more realistic example of sincere  
> opinions than your original example. Now I learned that the original  
> example was not intended to be sincere. The example is however still  
> valid as a more realistic set of sincere opinions.)

I just don't see the point yet. You've added in some other ballot
possibilities and you made C a bit more viable.

> >> It looks to me that B must be more centric than C. I expect A voters
> >> to truncate since they are not interested in the right wing internal
> >> battle. B voters truncate since many of them are so close to the left
> >> wing that A and C are about equal in preference to them. C voters do
> >> not truncate much since for them the other right wing candidate B is
> >> clearly better than A.
> >
> > This paragraph makes a lot of sense.
> >
> >> The most unrealistic point in this (one step more realistic) scenario
> >> is maybe the fact that so few A supporters find B better than C
> >> (although as I said, B appears to be closer to the centre than C).
> >> But let's go forward.
> >>
> >> These votes are sincere.
> >
> > It might be unrealistic that these are sincere, but it's not  
> > unrealistic
> > that so few A voters would vote for their main opposition.
> 
> Do you mean that voting "A>B>C" would be giving support to B and that  
> A supporters should by default vote "A" (if B is considered "main  
> opposition")? My basic thinking is that vote "A>B>C" differs from  
> vote "A" only in that the voter takes position on if B is better than  
> C. (Without strategic considerations) this should have no impact on  
> how much the voter prefers A over B and C.

Yes, if there are two frontrunners, I do not believe it is good advice
to rank the frontrunner you like less, or anyone worse than him. This is
because this truncation makes it an unreliable strategy for the other 
frontrunner's supporters to try to use order reversal against your
preferred candidate. And ranking the worse frontrunner will hardly ever
be of any use anyway.

Under margins, this may not be very effective as a deterrent, but I
still think it is extremely likely voters will not generally rank the
lesser frontrunner.

> >> I used ties only at the end of the ballot (=> truncation).
> >>
> >> The difference to the original scenario is that the thresholds to all
> >> kind of changes are in this type of more realistic scenarios smaller
> >> than in the original example. In this case it seems that the
> >> strategic opportunity would not exist if any of the voter groups
> >> would gain or lose 1 to 4 votes (with the exception of "B>A" voters
> >> who can not lose more than 2 votes and that is not yet enough, and
> >> there would have to be 5-6 more "C" voters for the strategy to become
> >> void).
> >>
> >> C has now also a considerable chance of winning the election. If e.g.
> >> there would be 3 less "A>B" voters or three more "C>B" voters in the
> >> actual election C would win. Applying the original strategy would
> >> eliminate this possibility. C supporters would thus voluntarily give
> >> up the chance of winning. Opinion polls are unreliable and the
> >> opinions will change by the elections day. That makes the situation
> >> more balanced from C's point of view. Should one try to win with the
> >> help of strategic voting or by promoting one's own candidate. Note
> >> that recommending strategic voting may also turn some voters against
> >> the plotting candidate.
> >>
> >> There are many possibilities of changes in the voting behaviour, many
> >> different types of changes are likely to occur before the election
> >> day, and they are quite difficult to analyze and guess.
> >>
> >> It may be difficult for the C supporters to give up the idea of C
> >> winning the election. Throwing one's favourite candidate out without
> >> even really participating the election (where the candidate is close
> >> to winning the race) doesn't sound very tempting (to humans with
> >> optimistic and self-confident attitudes :-).
> >>
> >> The point of this modified example is that in real life the situation
> >> is likely to be much less clear due to multiple opinion groups, more
> >> balanced (less extreme) votes of large elections, inaccurate polls,
> >> changes in opinions between the poll and the election, possible other
> >> strategies etc. In this situation the C supporters might as well
> >> conclude that even though some polls show that strategic voting could
> >> be possible it may be a better bet to vote sincerely and concentrate
> >> on promoting C instead. (maybe even to state that sincere voting is
> >> recommended even if some strategists would recommend strategic  
> >> voting)
> >
> > So you say a scenario becomes more realistic when information is very
> > poor? Or it becomes realistic when all three candidates have a  
> > chance of
> > winning?
> 
> None of these. My intention is to say that a large population is  
> likely to have more than three types of sincere opinions (with three  
> candidates). A strong bias in the opinions (from random distribution)  
> also needs to be explained to make the scenario credible.

But your more realistic scenario with more than three types of sincere
opinions manages to present the precise scenario I complained about. So
I don't see why you need to have it justified, why I left miscellaneous
voters out of the original scenario.

> > I'm not sure you understand my point with this scenario. If the C  
> > voters
> > vote sincerely in this scenario, then A wins and the C voters wish  
> > they
> > had betrayed their candidate (who wasn't expected to win anyway). If
> > we give people incentive to betray candidates who aren't frontrunners,
> > what do we even need a better election method for?
> 
> Ok, after the election some group notes that they could have  
> falsified the result to something better from their point of view by  
> voting strategically. That is not yet a serious problem. What happens  
> at the election day is more serious. I tried to demonstrate that with  
> good probability there are no easy strategic options available, and  
> that in a large population that probability decreases. I'm trying to  
> find such sincere opinions where the basic scenario that you  
> presented could be realistic in normal large scale elections (and  
> then analyse that case, to see the probabilities, the damage level,  
> ease of applying the strategy, risk of getting worse results than  
> planned etc.).

And I disagree (that "with good probability there are no easy strategic
options available") because as I pointed out, it is almost always a
safe strategy to use favorite betrayal, under any method, when you don't
think your preferred candidates are contenders.

So the more unsafe it is, under a given method, to vote for a sincere
favorite, the more voters will be driven to just forget them.

> In the modified scenario that I presented the success of the strategy  
> was one vote away but still the strategic plan appeared to be less  
> than clear due to the numerous uncertainties with controlling the  
> strategy, changes in the opinions before the election day, reactions  
> to the strategic voting plans (counter strategies, reduced support to  
> the plotters) etc.

You are talking like it's a positive thing if the C>B voters decide not
to use a betrayal strategy. It's not positive; it's the other side of a
bad coin. Whether they betray C now or just remember to do it in the
future, an incentive is or will be apparent.

> >> This kind of observations apply to many strategic examples, not only
> >> this margins based strategy. The vulnerability of Condorcet methods
> >> to strategic voting is a fact but in most cases the vulnerabilities
> >> are quite marginal and seldom (or in some cases practically never)
> >> occur in real life. If the voters do not (maybe mistakenly) trust the
> >> method and/or if the society finds strategic voting natural and
> >> recommendable the risks are higher than in situations where voters
> >> already trust the method and find strategic voting unpleasant (this
> >> does not require that the voters would not be very competitive).
> >
> > Not sure what you're getting at here since the strategic voting in  
> > this
> > scenario is just favorite betrayal by supporters of weak candidates;
> > this strategy is practically never risky if you know who the  
> > frontrunners
> > are.
> >
> > Not to mention that using the strategy here actually improves the  
> > result.
> > If you want voters to be sincere, don't force them to strategize.
> >
> > I see it as crucial that we not give voters reasons to stick to voting
> > for frontrunners.
> 
> My ideal outcome of these studies would be to find out that Condorcet  
> methods are not too vulnerable to strategic voting and as a result  
> all voters could safely vote sincerely. The conclusions may be  
> different in different societies depending e.g. on the level of  
> interest in strategic voting. If the voters are forced to strategic  
> (or counter strategic) votes, that is already a problem to me. A good  
> method should allow sincere voting. Also electing some other  
> candidate than the best one (with sincere votes) is a problem that  
> should be avoided. I'm thus more interested in sincere voting than  
> allowing strategies and counter strategies to take place.
> 
> The last paragraph talked about Condorcet in general, not about this  
> particular example.

Everybody wants sincere voting. I guess you can just assume you get it.
Otherwise you need to have proper incentives in place to get it.

Kevin Venzke


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