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

[Juho]

On Aug 8, 2007, at 4:53 , Kevin Venzke wrote:

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. We could  
for example have a method that takes a random ballot and then picks a  
random candidate from that ballot giving slightly decreasing  
probabilities/weight to candidates towards the end of the ballot.  
That method could pick the worst candidate from this voter's point of  
view and the voter would have no way of improving the results. But  
that doesn't mean that the candidate (chosen by the method) and the  
method itself are good and the candidate would not be harmed by the  
method. I think the candidate can complain and ask some other method  
to be used.

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

Maybe I misunderstood what you meant.

> 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.

Maybe you claim that the winning votes gives a more natural measure?  
Or maybe you assume that strategic voting is so widely spread that  
therefore the margins would not provide good enough results?

> 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 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.

>> 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).

>> 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).

>>> 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.

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 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.

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.

>> 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. 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.

> 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.

Juho




	
	
		
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