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

[Juho]

 > 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.

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.

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.

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)

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).

Juho


On Jul 27, 2007, at 11:51 , Kevin Venzke wrote:

> Juho,
>
> --- Juho <juho4880 at yahoo.co.uk> a écrit :
>>> It's possible that a coordinated strategy may not be feasible, but
>>> that
>>> is not the heart of the problem in my view.
>>>
>>> Referring again to this scenario:
>>> 49 A
>>> 24 B
>>> 27 C>B
>>>
>>> Under margins the C voters have great favorite betrayal incentive
>>> without
>>> any other faction having to use a coordinated strategy.
>>
>> Sorry about some delay in answering.
>>
>> There certainly are many viewpoints to this scenario. I'll present
>> one. Please point out if I missed some essential things that you
>> thought I should answer.
>>
>> In this example a single C supporter can indeed change the winner (in
>> the case of margins) to B by voting B>C instead of C>B. The strategy
>> is very safe since C supporters can assume that C will not win the
>> race in any case.
>
> Yes the strategy is safe, but it shouldn't be necessary. Why would we
> bother to use a Condorcet method if voters will still need to vote for
> one of the frontrunners?
>
>> The pattern that leads to this strategic option is a loop where
>> - A wins C clearly
>> - C wins B with a small margin (and low number of winning votes)
>> - B wins A with an even smaller margin (but high number of winning
>> votes)
>>
>> How about the weak spots then:
>> - The outcome is not that bad since there is anyway a majority that
>> would elect B instead of A, and C was beaten too badly to even try to
>> win (winning votes actually elect B without requiring strategic  
>> votes)
>
> Exactly. I'm not saying C should win.
>
>> - This scenario assumes a natural loop (not very common, and this
>> type of loop maybe even less common than loops in general)
>
> I don't understand why you say it assumes a "natural loop" or what  
> other
> loops you believe exist if you call this one "natural." I guess you  
> just
> mean that there is a voted cycle without strategic voting (other than
> truncation). In which case I guess you feel that cycles resulting from
> strategic voting (as in offensive strategies) are more common than  
> this??
>
>> - It is difficult to find a real world model that would lead to this
>> kind of votes (what is the reason why voters voted as they did? do
>> you have a story that would explain this election?)
>
> I totally disagree. As for a story, say that A is a left-wing  
> candidate
> and B and C are on the right-wing. C may be more or less extreme  
> than B,
> but is less well-established somehow.
>
> C voters definitely hold B as a second choice. A voters do not give a
> second preference to B because under margins it gives the win to B,  
> and
> under WV it's generally just bad advice to rank the other frontrunner.
> B voters do not list A as a second preference for the same reason. B
> voters do not list C as a second preference for some of these reasons:
> 1. C is not actually their second choice
> 2. If ultimately C>B, the C second preference gives the win to C.
> Condorcet invariably requires that.
> 3. If C is more extreme than B, then if B can't win it wouldn't be
> expected that a lower preference for C might succeed as a  
> compromise vote.
> 4. Under margins (or IRV), the fact that B voters have little  
> reason to
> vote for C means that C voters may realize that they should betray  
> C and
> vote for B anyway.
>
>> - Some of the strategic votes could be natural in the sense that if
>> the numbers above are the outcome of an opinion poll few days before
>> the election, then some C supporters might give up voting C as their
>> first option since C seems to be "a sure loser"
>
> Which... is what we already have. The candidate second in the polls
> deemed a "sure loser" and abandoned to avoid catastrophe? Can't we  
> find
> a better election method than that?
>
>> But of course the fact remains that in this scenario margins are more
>> vulnerable to and encourage strategic voting. The weakest spot of
>> this scenario is that it seems that it is not very likely to occur in
>> real life. Maybe there are some variants with more credible "real
>> life" numbers.
>
> It makes me wonder what scenarios you find to be important, that you
> don't think this scenario is even realistic.
>
>> This problem is margins specific but so far I couldn't find the
>> reasons why this would make margins generally fail (worse and with
>> higher probability than winning votes) in real life (large scale
>> public) elections. I gave some links to the winning votes problems
>> cases. They (for example) seemed more probable in real life to me
>> than this scenario. But I have not done a complete enough analysis to
>> claim that margins would definitely beat winning votes and that the
>> probability of this scenario would be low enough not to be a threat.
>
> Unfortunately your links don't seem to open anymore.
>
> I can tell you the reason why this scenario makes margins generally  
> fail:
> There is just one contest that everybody votes in (A-B), and margins
> trips over the noise of the C voters to elect the loser of this  
> contest.
> Methods should be able to see past the noise. Otherwise voters have to
> guess in advance what information will be "noise" and leave it off. If
> that is acceptable, then why are you even using a Condorcet method.
>
>>>> 2) There are as well cases where winning votes are more  
>>>> vulnerable to
>>>> strategies than margins. So the question is not one-sided.
>>>
>>> However, it is pretty clear that margins has a worse FBC problem  
>>> than
>>> WV does. Simulations have shown this, but it can be argued
>>> logically as
>>> well.
>>
>> May be so. Is there some reason why FBC would be a key criterion in
>> this case? I made some time ago some simulations on margins and
>> winning votes on if some certain random voter group or any of the
>> voter groups could (from their point of view) improve the outcome of
>> the (sincere) election by voting strategically (in whatever way). The
>> simulation gave margins somewhat better results than to winning
>> votes. Maybe the results depend a bit on what one simulates.
>
> What kind of strategy did you implement? What did you consider a  
> "better"
> result?
>
> FBC etc. is important because if voters can't be confident that  
> they can
> safely vote sincerely, then the method is destroying information  
> before
> it collects it.
>
>>> If margins outperforms WV in some respect, I'd like to be able to
>>> state
>>> exactly how.
>>
>> - to me the choices that margins make with sincere votes seem (not
>> necessarily perfect for all needs but) clearly more sensible than the
>> choices of winning votes
>> - some of the scenarios where winning votes have strategic problems
>> appear to be more probable in real life than the problem scenarios of
>> margins (this feeling is however based on only a limited number of
>> cases and not a thorough analysis)
>
> I wish I could open your links for these.
>
>> - margins are easy to explain and understand and justify to the
>> voters/citizens => "least number of additional votes needed to win
>> all the other candidates" (no need to talk about breaking loops and
>> about complex algorithms)
>
> Well, MinMax(wv) is hardly more difficult than this.
>
> Condorcet//Approval is probably easier than either. I would say its  
> FBC
> performance is still poor, but at least it doesn't have the issue of
> electing candidates over whom more than half the voters prefer  
> somebody
> else. It also doesn't elect candidates who have fewer votes than  
> another
> candidate has first-preference votes, as in 7 A>B, 5 B, 8 C.
>
>> Sorry about not providing any more exact answers. The first
>> explanation above is very obvious to me. The second case is just an
>> estimate. The third one is again a fact although "social and
>> psychological" by nature.
>>
>> I've often seen some formal properties of voting methods presented as
>> final proofs of the superiority/inferiority of some particular
>> method. I don't measure the benefits as number of proven theorems.
>> Especially in Condorcet methods the problem cases are typically
>> related to scenarios that are not very common in real life. Therefore
>> I'd like to see the claims linked to real world examples that
>> demonstrate the theoretical scenarios in real life situations and
>> estimate their probability, harmfulness, ease of applying them, risk
>> of backfiring strategies etc.
>
> What three-candidate scenarios involving cycles do you consider  
> realistic?
>
> Kevin Venzke
>
>
>        
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