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

[Kevin Venzke]

Juho,

--- Juho <juho4880 at yahoo.co.uk> a écrit :
> >> 1000 A>B, 1000 C>D, 1 D>B
> 
> > Yes, I do think D is the proper winner.
> 
> I have many times said that it is possible to support different  
> utility functions. An election method may then implement one of these  
> utility functions as accurately as it can. I must thus say that using  
> winning votes (or something like it) as the ideal utility function  
> must also be ok, although maybe not my first preference.
> 
> 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.

> > 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?
> 
> Yes, but this has nothing to do with the (IRV like or some other  

Even if so I still ask this question.

> >> 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.
> 
> I'd say this is a close race.

I know you would. I don't feel this is a good excuse.

> A wins in margins since it is only two  
> votes short of being a Condorcet winner. That is one possible very  
> sincere measure of who should win an election where the opinions are  
> cyclic. The election of A may leave someone wondering if some  
> strategic insincere moves could have changed (falsified) the outcome,  
> but despite of this it is easy to claim that the algorithm picked the  
> best winner.

As long as you have a "possible measure" then it's easy to claim that
someone is the best winner. In this scenario I don't think this is very
convincing logic; I think many or most people would immediately see an
issue with A winning.

> (1000 A>B, 1000 C>D, 1 D>B)
> > 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.
> 
> Yes, the C>D voters want D to beat A and B. They would be happy if D  
> would be elected instead of A or B (unconditionally without  
> considering how people voted between D and C). But their next  
> question after there is an agreement that D beats A and B would be if  
> they could go even further and elect C instead of D. Their feelings  
> are quite strong/unanimous here.

And I have said repeatedly that in this scenario, you can't get a C win
out of this. Would the C>D voters prefer an A-C coin toss to getting
their second choice? I doubt it. We can't know for sure. Neither can
they; the info isn't on the ballot. This is hardly a basis for a complaint.

I guess you think C>D voters are going to complain about D winning
whether they have a realistic alternative or not!

> >> 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?
> 
> Yes, but in this example it feels more natural to me to think that A  
> and C were tied and consider B and D to be less preferred than the  
> other two.

Again I wonder what the point of second preferences is supposed to be
if the win should be limited to factions' first preferences.

In response to that you may say it isn't about first preferences, that
it's about the matrix. But here we're looking at an actual scenario and
asking what voters were thinking when they voted and how they feel
afterwards.

> (20 A, 15 A>B>C, 10 A>C>B, 35 B>C, 20 C>B)
> >> 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.)
> 
> Do you recommend the "B>C" voters to betary C and vote "B"? Note that  
> according to the poll "C>B" voters were not planning to vote  
> strategically (not yet at least, although they might decide to do so  
> after they hear about this possibility).

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."

I think C>B voters retaliating against this possibility would be quite
stupid. I don't think there is enough ability to gauge what B>C voters
will actually do, since truncation doesn't require much conscious strategy.
I don't think the C>B voters' "counterthreat" to truncate would have an
effect on the B voters. Mostly because the C>B voters are fighting over
nothing but principle. They would be threatening to spoil the race just
to get B voters to express their true second preference (which they 
assume to be C).

> >> - 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?
> 
> I think you didn't do that fully yet. Based on your comment I assume  
> that the sincere opinions could be e.g. 12: B>A and 12: B>C. I assume  
> that B is a centrist candidate and therefore most C supporters might  
> vote C>B (like you said). But this does not explain yet why A voters  
> would (in real life) all be of (sincere) opinion A>B=C. Am I correct  
> to assume that the majority of the A supporters actually feel A>B>C  
> (or is there some explanation why this is not the case).

Yes, you may assume that the A voters' sincere preference order is A>B>C.

However, I do not see B as a "centrist" candidate. B is the major party
opposition to A.

> >> - 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.
> 
> Then why did the B supporters truncate in a situation where they did  
> not know that B is a frontrunner? Why didn't C supportres truncate?

B voters truncated beacuse they DID know that B is a frontrunner, also
that a C win is highly unlikely.

C voters didn't truncate because they had the same information.

Maybe I didn't understand your original question here. You ask me why B
is considered a "frontrunner" when he has less first-place support than
C. If I understand this question then the answer is that we determine who
is a "frontrunner" before we know how many first-place votes anybody
gets.

> It would be really helpful to have the sincere opinions, and possibly  
> also recommended strategic voting patterns stable and clearly listed.  
> It is hard to discuss the possibilities if one has only the final  
> outcome of the election available (that is expected to contain  
> strategic votes).

I assume you recall the polling information I suggested.

sincere A>B>C: recommended to truncate
sincere B>A>C: recommended to truncate
sincere B>C>A: recommended to truncate at least if B>C preference gap is
large
sincere C>B>A: recommended to vote C>B>A

The point of the scenario is probably clearer if sincere B>C>A voters
are thought to be B>>>C>A voters. C is supposed to be truly unlikely to
win.

> > 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.
> 
> Correct. That is why I keep asking. I don't expect the sincere  
> opinions of the voters to be as in the votes in the example (they are  
> too extreme), and you seem to agree with this. The sincere opinions  
> are expected to be more balanced in large elections. And that has an  
> impact on the vulnerability and strategic opportunities in the  
> election. My target is to study how high the risks are in real life.  
> That is why I put more weight on scenarios that can be from real life.

But again, you managed to create the same situation using "more balanced"
opinions.

> >> - 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.
> 
> I think it is already a partial failure of the Condorcet method if  
> voters need to vote (counter) strategically.

I would bet that even if you were to invent a method where it is harmless
or even useful to rank both of two frontrunners, *most* voters would still
not do it.

> It looks like the  
> recommended general voting strategy is close to:
> 
> - If you support the strongest candidate (X) of the party, then you  
> should bullet vote
> - If you support the second strongest candidate (Y) of the party,  
> then you should vote Y>X

My recommended general voting strategy for two frontrunners is to not
rank the worse one or anyone liked less.

If your favorite candidate is not a frontrunner but is likely to have
substantial strength, then in WV I *might* suggest compressing the top
ranks so that the better frontrunner is in equal-first. Under margins
I would suggest that you rank your favorite candidate below the better
frontrunner.

Reading this again I guess you are more concerned with candidates of
the same party. I would not say in general that you *should* truncate
if your favorite candidate is the leader. But you can benefit if other
voters believe that you *will* truncate in this situation, because they
will feel forced to support the frontrunner. In margins (or IRV) they may
feel forced to rank the frontrunner in first.

> What if X and Y are about equally strong? Should all X and Y  
> supporters truncate or all rank both candidates? If they truncate,  
> the other party is more likely to win. If they both rank each others,  
> then the strategic risks appear again. Approval has the strategic  
> problem of not allowing the second strongest candidate of a faction  
> grow. Is this true for Condorcet too if truncation is widely used?

If X and Y are about equally strong then I believe it's quite likely that
the race will be spoiled by mutual defection. It doesn't require that
many voters defecting to cause this.

I think this risk is so subtantial that a major party would try very hard
to avoid presenting multiple candidates for the same seat.

Can you clarify what you mean by "Approval has the strategic problem
of not allowing the second strongest candidate of a faction grow"?

I do not think Condorcet (either type, even WV) really allows that much
more potential than Approval for multiple candidates from the same party 
to be viable. I think in practice it would be too dangerous.

> I think Condorcet methods are at their best in situations where  
> voters can vote sincerely, not when strategic considerations start  
> stealing space and time.

I guess I don't understand what you mean by this. People "can" vote
sincerely to the extent that strategic considerations don't force them
to do otherwise.

I guess you are just saying that you wish people would vote sincerely.

> (49 A, 24 B, 27 B>C)
> ...
> (30 A, 9 A>B, 6 A>C, 14 B, 8 B>C, 2 B>A, 25 C>B, 5 C, 1 C>A)
> >> 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.
> 
> The point is that when we take into account the inaccuracy of the  
> polls, opinions that change in time (before the election day),  
> negative reactions to strategic plans, having few such voter groups  
> present that have different targets than what are present in the  
> simplifies scenarios, and having multiple differing opinion poll  
> results available, then the cases become more complex and anything  
> can happen. Reliable strategies become less reliable. In such  
> circumstances the Condorcet methods are expected to perform better.  
> Sincere voting is more often the best strategy to apply. My ideal  
> outcome of this kind of analysis would be that in many societies  
> Condorcet would be practically strategy free. Strategies and counter  
> strategies would not be applied since they would not be considered  
> efficient, and they would maybe be considered bad manners that  
> everyone would try to discourage (e.g. by explaining that it is more  
> likely to lead to worse relults than to better results to the voter  
> in question).

Well, again, I am focused mainly on favorite betrayal incentive, because
it is such a safe and reliable strategy. I don't think it would be
realistic to guess that people wouldn't be able to determine who the
frontrunners likely are, and that is all you need to know for this
strategy.

Then I can't see how favorite betrayal would generally be considered
"bad manners that everyone would try to discourage"; under FPP at least
when you don't use favorite betrayal (when you realistically should)
it's called "wasting your vote." And I can hardly see how "wasting your
vote" in this way leads to a better result even though it is sincere.

> - - - - -
> 
> I'll now approach your old example from a somewhat new angle, taking  
> also the sincere opinions into account. Maybe this approach explains  
> a bit better what I'm after. The idea is that strategic voting with  
> margins and winning votes is a sword that has two edges. I now  
> understand your original (exaggerated) example (49 A, 24 B, 27 C>B)  
> to be a result of strategic considerations in a typical left-centre- 
> right set-up.

I don't view the scenario that way. If B were really seen to be center,
then I would expect more A voters to support him. Specifically, if B
were "center" then I would expect that A voters would not trust that
A would beat C.

> The original (intended, exaggerated) sincere opinions could have been:
> 49 A>B>C
> 12 B>A>C
> 12 B>C>A
> 27 C>B>A
> 
> Both margins and winning votes would elect B with sincere votes.
> 
> In this situation the A and B supporters decide to vote (counter)  
> strategically and truncate (with more or less valid reasons). (The  
> end result / actual votes are exaggerated, but more realistic votes  
> can be discussed later if needed.)
> 49 A
> 24 B
> 27 C>B
> 
> Margins will elect A and winning votes will elect B. Your opinion  
> seemed to be that winning votes is better since with margins C  
> supporters would be tempted to vote B>C and thereby make B the  
> winner. (Note that with these numbers at least 48 out of the 49 A  
> supporters would have to vote strategically to generate the  
> temptation for the C supporters to vote strategically.)

We could also adjust it to e.g. 49 A, 5 B, 46 C>B, with a significant
number of the 49 voting A>B.

My issue is not simply that C voters have strategic incentive here. It's
that the incentive is to abandon candidates who aren't frontrunners; 
that it is practically risk-free; and that if the C voters don't use
the strategy, their sincere votes confuse margins into picking the wrong
winner.

> 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
> 
> This is a typical (exaggerated) left-right-right set-up. Both margins  
> and winning votes would elect C with sincere votes.
> 
> In this alternative the B supporters vote strategically and truncate.  
> The actual votes are exactly the same as in the first case - this is  
> thus just an alternative explanation to them.

This is what I prefer.

> Now the fact that winning votes elects B makes it possible for the B  
> supporters to apply the strategy while margins do not encourage  
> strategic voting.

I don't see this as a wash. In both cases under margins (C voters using
strategy or B voters not using strategy) the effect is achieved basically
by threatening the voters to either vote someone as CW, or else be punished
by having margins resolve the cycle badly.

I don't know, could we call it an "advantage" of margins if it gives
people incentive to avoid cycles?

> It is thus difficult to avoid all the strategic voting scenarios  
> whichever preference strength measurement function one uses (margins  
> or winning votes). It is possible to try to defend against one kind  
> of threat and open doors to others while doing so (the two edges in a  
> small space) . What choice should the election method do if there are  
> problems in whatever choice one makes?
>
> In principle one needs to evaluate all possible cases and then  
> estimate which function is better. And of course one has to add to  
> the final election method evaluation also the other factors (e.g.  
> performance with sincere votes, ref. the 1000 A>B, 1000 B>C, 1 D>B  
> example).
>
> (A third explanation to the actual votes would btw be that the actual  
> votes are actually sincere. The election method of course has to  
> elect a good candidate also in this case. I will not talk about this  
> line further now since the actual votes hat were used above don't  
> look like a typical set of sincere opinions.)
> 
> (Now my feeling is that you were quite happy with voters regularly  
> applying the defensive strategies (truncation). I'd be happier to  
> conclude that such voting patterns are generally not needed. Real  
> life elections are not as extreme and clear, and controlling  
> strategic voting is difficult, opinion polls may vary etc. etc. DOes  
> this make Condorcet methods strategy free in practice or should we  
> prepare for wide spread strategic voting? Is Condorcet better than  
> other methods if strategic voting is widespread?)

I don't know what to say about what you're "happier to conclude," whether
that means you've already decided what you're going to conclude or are
perhaps asking for help in concluding something.

I believe that people will use strategies that are mostly safe, even with
low quality information. All you can do about that is design methods 
that don't have those strategies.

You ask "should we prepare for widespread strategic voting" in Condorcet.
If you're referring to truncation then I'd say yes, it's almost funny to
ask. People will truncate where they feel they can until you prove to
them it can never hurt them. You may even have to prove that it may often
be useful. Otherwise why should they bother taking the risk of voting
for candidates they are trying to defeat?

You ask whether Condorcet is better than other methods if strategic voting
is widespread. If people don't feel compelled to use favorite betrayal
strategy, and don't use offensive strategies that can backfire, then I
imagine it would be better than e.g. Approval.

Kevin Venzke


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