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

[Kevin Venzke]

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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