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

[Kevin Venzke]

Juho,

I'm running short on time to participate in this discussion, so I'm
going to attempt to scale back my responses with the intention of
eventually ending this.

--- Juho <juho4880 at yahoo.co.uk> a écrit :
> 1000 A>B, 1000 C>D, 1 D>B
> >>>> Do you have a verbal (natural language) explanation why D is better
> >>>> than A and C. This scenario could be an election in a school. One
> >>>> class has voted A>B (A and B are pupils of that class), another  
> >>>> class
> >>>> has voted C>D, the teacher has voted D>B. What should the teacher
> >>>> tell the C>D voting class when they ask "didn't you count our  
> >>>> votes"?
> >>>> Maybe this is clear to you. Unfortunately not as clear to me. The
> >>>> teacher vote seemed to be heavier than the pupils votes :-).
> >>>
> >>> The question doesn't make any sense from them, unless first>second
> >>> preferences are really worth so much more than other preferences.
> >>> The C>D
> >>> class didn't just vote C>D, they also voted D>A and D>B. They can
> >>> make the
> >>> same complaint just as easily as long as anybody wins except for C.
> >>>
> >>> And in this scenario you don't get a C win by "counting" C>D.
> >>
> >> Correct, C>D voters want C to win the others. I didn't understand
> >> your last sentence (in winning votes?).
> >
> > My whole point is that C>D voters aren't going to complain about  
> > random
> > things unless they perceive they were harmed somehow. And it isn't  
> > at all
> > clear that C>D voters are *harmed* by the election of their second  
> > choice,
> > unless there was some way that they could have gotten their first
> > choice (that doesn't involve flipping a coin between him and a  
> > candidate
> > not liked at all).
> 
> Even if some voters could not do anything to improve/correct the  
> result of some election method in some particular election, that  
> doesn't make the election method itself or its choices good. 

That's fine, but it's a separate issue.

> Lack of strategic incentives is a good property of an election  
> method, but there are also other criteria like electing good candidates.

That is very vague.

> > Margins thinks a contest is less
> > important the closer the match is. But that's not how people generally
> > determine which contests are the important ones.
> 
> I think the way margins measures the strength of the pairwise  
> comparisons is quite natural. It is possible to discuss if a 55-45  
> result is stronger than a 45-35 result but there may be many  
> opinions. 45-35 could be said to be weaker since some voters found  
> the candidates to be equal. On the other hand 45-35 could be said to  
> be stronger since there were 29% more votes on the winning side than  
> on the losing side (only 22% in 55-45). But roughly I think people  
> are not too far from the margins results.

When you say "stronger" or "weaker" then it feels easier to say whatever
you like. I have no doubt that many, many people can be convinced that
margins is more sensible and more natural on paper.

If you ask instead whether 52-48 or 45-35 seems "more likely to be
important in determining the proper result" then after people think this
through, I think they will take the first one.

> Maybe you claim that the winning votes gives a more natural measure?

I think winning votes gives results that are more in line with what
voters want to see. The method should see votes for strong candidates
and disregard votes for weak candidates.

> Or maybe you assume that strategic voting is so widely spread that  
> therefore the margins would not provide good enough results?

As far as offensive burial, I will let other people make that argument.

I think margins does give a clear reason to not vote for weak candidates,
especially if there's a chance they're strong enough to get a pairwise 
win.

> > It makes no sense to me for A to win when C is in this election.
> > It takes a very obscure explanation to try to argue that the situation
> > of candidate B makes A a better winner than C.
> 
> I don't mean that A would be better than C (just better than B, and C  
> better than D). (After all, the ideal measure, margins thinks they  
> are equal :-).)

I thought we were talking about 7 A>B, 5 B, 8 C here.

I'm trying to remember what you asked me here. I think it was whether
this scenario's outcome (AC tie then) is better if the votes are sincere.
But as far as I remember we never doubted they were sincere.

> >>> I believe a fair number of B>C voters would believe it is a good
> >>> idea to
> >>> betray C; I don't think they would think of it as "betrayal."
> >>
> >> What then, "justified precaution" or "necessary precaution" or "just
> >> regular voting behaviour with this method"?
> >
> > Just "I don't need to vote for that candidate, so why would I."  
> > Note that
> > this is only for supporters of the better-established or more  
> > viable of B
> > and C.
> 
> If that is not strategic, then they have given up their right to  
> express their opinion on some pairwise comparisons in this election.  
> That's allowed but sounds strange if the number of candidates is small.

It is strategic, it's just not consciously strategic. Every day I refrain
from doing a million things that couldn't help me and might hurt me,
and while this is strategic, it takes no thought from me.

I don't know what the number of candidates has to do with it.

> >> I proposed one set of sincere opinions below. If they are not what
> >> you thought the sincere votes are, please propose an alternative set
> >> (this is your scenario after all, so you take the lead).
> >
> > I want to reiterate that I don't find the sincere votes to be  
> > important
> > here. This is because I'm not aware of any set of sincere preferences,
> > polling information, or resulting strategic voting where the result of
> > the 49 24 27 scenario seems acceptable.
> 
> Note that I was talking about sincere opinions, not about sincere  
> votes. Sincere opinions exist (irrespective if there are polls or  
> not) and I think they are important. I gave two sets of possible  
> sincere opinions that both can lead to the actual votes that you  
> proposed. The explanation of voter behaviour and their reactions and  
> strategic opportunities are very different in these two cases. It is  
> essential to understand what the intentions of the voters are to  
> comment why they voted as they did (too difficult to cover all the  
> possible sincere opinion alternatives).

I don't see why it is essential, provided that there is at least one
scenario behind the cast votes that is realistic.

> >> Yes, the basic relations are the same, but the strengths are
> >> different, and in real life there are many kind of voters with many
> >> kind of opinions, and the probability of some (extreme) scenarios
> >> appearing may be low.
> >
> > strengths are different: But this didn't make any difference.
> 
> I think that makes a difference. Probabilities, number of strategic  
> voters etc. are relevant when one considers what will happen in real  
> life.
> 
> > there are more types of voters: Didn't make any difference.
> 
> Also this may make a difference (depends on what kind of additional  
> voter types there are).

I'm talking about this one scenario that you created from mine.

> >>> My recommended general voting strategy for two frontrunners is to  
> >>> not
> >>> rank the worse one or anyone liked less.
> >>
> >> If you can, it would be nice to get a formal strategy recommendation
> >> for this (you had something in this direction earlier in this mail).
> >> Generic strategy guidance would be really useful. (Approval has some
> >> quite well described strategies.) Now I still struggle a bit e.g.
> >> with "frontrunner" (how to measure it).
> >
> > Approval strategy involves estimating likelihood of a pair of  
> > candidates
> > being in a crucial tie. That is hard to measure as well.
> >
> > In real life I believe it will be pretty clear who the "two  
> > frontrunners"
> > are, and if there aren't two clear frontrunners, then we have a real
> > multi-candidate race and should be grateful.
> >
> > One basis for this strategy under WV is that if there are two  
> > frontrunners,
> > and people have the sense not to rank the worse one, then the less
> > preferred frontrunner can never win the election, and nobody has to  
> > lie
> > about who their favorite candidates are.
> >
> > If you only added this feature to FPP I think it would be a halfway
> > decent method. It's basically a guarantee that an (essentially) two-
> > candidate race won't get screwed up.
> 
> Ok, that means bullet voting for the strongest.

I'm sorry what? I'm talking about adding functionality to FPP, not using
a certain strategy under FPP.

> Note that my tradition is multi-party with 3-4 realistic candidates  
> and nowadays a two-round runoff. I want Condorcet to perform better  
> than just allow voting one's favourite and bullet vote the strongest  
> ones since people do that already today. Such fully strategic  
> Condorcet elections may have some benefits when compared to two-round  
> runoff, but expecting people to use different voting strategies  
> depending on the estimated strength of the candidates would be also  
> quite a mess for the regular voters.

I don't remember if I said this, but I believe a two-round election makes
a huge difference. Your favorite candidate doesn't have to have nearly
as much support going into the first round; if he's strong enough to get
top two then he can gain more support later, when he has everyone's
attention.

> > I would say under plurality very few people vote sincerely, and  
> > those that
> > do mainly vote for candidates that we wouldn't expect to become viable
> > anyway, even if it were safe to vote for them.
> >
> > Even with a top-two runoff I think you see a lot more sincerity  
> > than under
> > FPP.
> 
> Yes, my experience with top-two runoff is that most voters vote  
> sincerely. I think I have not heard anyone saying that they would  
> have voted strategically, nor have I seen recommendations to vote  
> strategically. I think I have seen one strategic nomination when the  
> far left party didn't name their own candidate for the election but  
> nominated the moderate left candidate as their candidate. Top-two  
> runoff can be said to be at least as vulnerable to strategic voting  
> than Condorcet. If the two-round runoff would be changed to Condorcet  
> I'd expect the sincere voting tradition to continue. Your background  
> may be different and different countries and political systems may be  
> different but I think there are places where Condorcet could be used  
> successfully and practically without any strategic voting. The  
> theoretical problem cases exist, but they do exist in two-round  
> runoff as well, and people don't seem to mind.

Well, in a two-round runoff you might want to vote strategically in the
first round if you fear that neither of the top two candidates will be
any good. If you're not afraid of that then why not vote sincerely?

I think if you converted a two-round runoff into IRV where all but the
top two candidates are immediately eliminated, you'd immediately see
a major hit to sincerity. More importantly I think, you'd see a major hit
to the number of candidates who can get votes.

> 49 A, 24 B, 27 B>C
> >>>> An alternative explanation to these actual votes could be that the
> >>>> sincere opinions were:
> >>>> 49 A>B=C
> >>>> 24 B>C>A
> >>>> 27 C>B>A
> 
> > I
> > keep pointing out that WV consistently avoids favorite betrayal
> > incentive in these situations, and in response you point out that in
> > margins, one faction here shouldn't have truncation incentive. If  
> > margins
> > consistently has that quality then sure, that would be noteworthy.
> 
> I think all the vulnerabilities are equal.

I don't. If a vulnerability won't occur to a voter to use, it's not as
important. If the vulnerability doesn't harm the result or even makes the
result better, it's not as important. Etc.

> >> Do I read this right. "Condorcet with widespread truncation is better
> >> than Approval, and Condorcet can't do better than this"?
> >
> > It sounds ok, but I'm not sure what you mean by "this."
> 
> "This" just referred to the discussion before.
> 
> > If voters under Condorcet don't use offensive strategies  
> > (specifically,
> > burial of rival frontrunners below worse candidates) and don't use
> > favorite betrayal, then even if these voters truncate at the same rank
> > they would under Approval, I believe Condorcet would be far better  
> > than
> > Approval.
> >
> > I do not believe you can design a Condorcet method where filling out a
> > complete ranking is generally a good strategy. (If that is what you  
> > are
> > asking here.) And as I've said, even if you managed to design one I  
> > think
> > you would have an extremely difficult time convincing many voters  
> > to take
> > advantage of it.
> 
> Yes, I meant sincere voting in Condorcet. I don't believe I can  
> provide you a method that would be immune to strategic voting, but I  
> do believe that in some environments most people would vote sincerely  
> anyway. This is because on average sincere voting can be claimed to  
> bring them the best results. 

This is not really true with respect to votes for candidates that you do
not think can win.

> Hunting for the not so common and not so  
> certain strategic opportunities and then taking part in such "plots"  
> may not be tempting to them. I have seen relatively sincere behaviour  
> in two-round runoff too, so why not in Condorcet. The strategies are  
> a bit different but maybe not that much different.

Two rounds. If you split a Condorcet method into two rounds I think you
will get more sincerity, since more candidates could be considered
viable, and voters have a chance to adjust for mistakes that they 
otherwise couldn't react to.

> > I don't especially want to promote other methods here, but it seems
> > reasonable to note that my ICA method precisely intends to bring as
> > much Condorcet efficiency to Approval as possible, without inviting
> > favorite betrayal or much offensive burial.
> >
> > Using approval to solve cycles isn't as sophisticated as determining
> > defeat strength, but approval does have in common with WV that  
> > candidates
> > or contests are considered more important when more people are  
> > involved
> > in voting for them.
> 
> Ok, you are preparing for the highly strategic environment. That may  
> be good for the strategic environments. Obviously I'm more relaxed  
> with the risk of Condorcet becoming highly strategical.
>
> I note that in addition to discussing the vulnerability of margins  
> vs. winning votes and their other weaknesses and strengths we now  
> have also the environments with wide spread strategic voting and  
> marginal strategic voting on the table. Answers to the first question  
> in these two environments may be somewhat different.

If you assume sincere voting then you just don't have to deal with
arguments about negative incentives.

In response to your second mail, I have read it, but my point was not to
ask you to further study that example, but to note my list of reasons
for criticizing the result of the original scenario. It is not the simple
fact that margins shows a vulnerability in a situation.

Kevin Venzke


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