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

[Juho]

On Aug 5, 2007, at 23:09 , Kevin Venzke wrote:

> 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.

Correct, C>D voters want C to win the others. I didn't understand  
your last sentence (in winning votes?).

>>> 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.

Ok, this was for the benefit of the C>D voters. Were there some  
consequences?

>>>> 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.

Excuse to what?

>> 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.

Would that be an issue if the votes would have been interpreted to be  
sincere?

My current understanding is that with sincere votes your ideal  
winning candidate is the one that winning votes elect (or something  
close to that). My ideal selection is closer to margins. Ok to have  
different opinions here (and maybe different functions for different  
elections).

>> (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.

In winning votes D won while margins tossed a coin between A and C.  
In wv the last voter could pick any of the candidates. The C>D  
voters' coin toss preference depends on their utilities (that are not  
known) as you say. Tossing a coin between all the candidates (the  
last voter picking any candidate is about a coin toss) would most  
probably give lower average utility sum than picking the winner among  
A and B.

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

No idea.

>>>> 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.

Ok, talking about the feelings, not about the algorithm. I don't know  
how we should interpret first and other preferences in the sincere  
votes/utilities. Do you maybe think that people generally have a  
bigger utility difference between the first and second preferences  
than between second and third, or what? If we want to discuss these  
things we should probably concretely present the sincere opinions as  
utility values to set a solid basis for the discussions (=> e.g.  
A=100, B=80, C=70 instead of A>B>C) (I note that you used "B>>>C>A"  
notation later).

>> (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."

What then, "justified precaution" or "necessary precaution" or "just  
regular voting behaviour with this method"?

> 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).

Ok, you assume wide use of strategic voting (= not ranking /  
betraying 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.

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).

>>>> - 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.

Yes, I used term "frontrunner" in the sense that voters used that  
information to make decisions on how to vote (a bit like in Approval  
where knowing he frontrunners is important when deciding how to  
vote). That was thus information collected from polls etc., not from  
the outcome of the election. Maybe the two phases (sincere opinions  
and actual votes) can be used to model the strategic thinking process.

>> 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.

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.

>>>> - 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.

I believe this depends a lot on the society in question. Certainly  
there will always be some voters trying to be strategical, even if  
that would not be strategically efficient.

>> 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 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).

(If needed the strategy descriptions may include elements that give  
power to experts that determine the best strategy.)

> 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 I'm thinking here is if Condorcet will require all voters to  
consider and maybe use strategic voting or if it would be ok to just  
vote sincerely. Of course this depends on how well the election day  
opinions can be estimated, the tradition of the society etc.

>> 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"?

Quite the same thing that was discussed above. If there are two  
equally strong candidates within one party then the voters may be  
tempted not to approve the other candidate in order to make their  
preferred candidate the winner.

> 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.

This is not good news for the voting methods. If the elections only  
have two major candidates and some candidates that are too weak to be  
elected the method could almost as well be plurality. I however  
expect the voters to be a bit more dynamic so that there will be  
changes in opinions after the candidates have been nominated, and  
therefore exact planning is not possible.

(In a two-party country the election set-up may be more straight  
forward and the outcome easier to estimate than in a multiparty  
country. I have followed e.g. some two-round elections where the  
opinions have changed considerably during the long election process.)

>> 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.

I expect the people to be just regular people with some interest in  
strategies and relatively strong competitive instincts. But I'm  
hoping that in many societies (that of course consist of people) that  
are not too strategy oriented, and in elections where the set-up is  
not very clear (= there are multiple candidates that could win and  
the opinions are changing all the time) Condorcet strategies would  
not be worth playing with, and as a result the strongest trend would  
be to simply vote sincerely.

Note that strategic voting is not something that would be controlled  
in some systematic way even today. For example in plurality elections  
many people vote sincerely the weak candidates that have no chance of  
winning although they have been told that they are in a way wasting  
their vote. I don't claim that these sincere, strategy-unaware etc.  
voters would change the system, but if we are lucky the strategic  
votes could be just waste of time. Possibly in some cases we could  
also prove that some strategies that were applied actually worked  
against the interests of the strategic voters.

>> (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.

But is is also not always clear that order reversals would pay off.  
The opinion polls are always outdated, there may be several of them  
etc. There could also be many different recommendations for strategic  
voting (just like in this list concerning many voting methods  
although people here are expected to be some sort of experts of this  
area :-)).

(But I'm thus hoping all this would be noise and regular citizens  
could in most cases simply vote sincerely without that causing them  
any fears and nightmares.)

> 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.

 From some point (not proven) at least Condorcet can be said to  
improve Plurality by allowing (in general, in most cases,...) to  
sincerely express their preferences.

>> - - - - -
>>
>> 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.

Maybe word "centre" was too strong. I only derived from your words  
the assumption that A supporters found B to be better than C. There  
was thus one linear preference axis where B was somewhere between A  
and C. I thought there were not many voters whose sincere preference  
would have been A>C>B.

>> 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.

This would be another example where the sincere opinions could have  
been:
49 A>B>C
  3 B>A>C
  2 B>C>A
46 C>B>A

I don't quite understand the "49 A>B". I think that would be a third  
example where actual votes could be e.g.:
25 A
24 A>B
  5 B
46 C>B
And the sincere opinions could be the same as in the previous example  
few lines above.

> 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.

I may analyse this later.

>> 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 didn't fully follow this. In this case C was the rightful winner  
(based on the sincere opinions), and B supporters could then change  
the result. The C strategies came only after this (and therefore  
maybe are less damaging).

> 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.

No, I'm preparing for concluding A, B, C or D but would be happier  
(than with many other conclusions) if the conclusion would turn out  
to be one particular conclusion out of the possible conclusions.

> 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.

I have tried to go through these examples and study how safe and how  
efficient these strategies are. I have leaned towards real life  
examples since often the strategies are less efficient and less  
secure in those cases.

As already stated few times I'm interested in studying the border  
line where strategy free Condorcet elections turn into elections with  
widespread strategic voting. There are some strategies that may be  
always applied (btw I have mentioned before the strategy of  
generating an artificial loop between three candidates of a competing  
party).

> 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?

Sure there are also cases where truncation hurts the voter (e.g. the  
case where two Republicans truncate each others and the Democrat wins).

Your words "voting for candidates they are trying to defeat" sound a  
bit as if the voters were thinking of being in an Approval election  
(where mentioning B means full support to B) or something similar.  
Isn't in natural in a society that is used to ranking based elections  
to vote A>B>C even if the voter would strongly dislike the idea of B  
winning A?

> 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.

Do I read this right. "Condorcet with widespread truncation is better  
than Approval, and Condorcet can't do better than this"?

Juho

>
> Kevin Venzke
>
>
>        
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