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

[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?

Yes, I'd recommend Condorcet for environments where strategic voting  
stays marginal (or is inefficient). I hope most environments meet  
this criterion, especially typical large scale public electuons.

>> 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??

Yes, cycle without strategic voting. I didn't assume the truncation  
to be strategic either.

Frequency of strategic and "natural" cycles depends heavily on the  
environment. I believe strong natural (sincere) cycles are not  
impossible but not very common. In real life I expect sincere cycles  
to be mostly weak (preferences that form the loop are typically weak).

>> - 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.

Ok, A is the left wing, B and C are the right wing, C is not as well  
known as B. C got more first place votes than B, so C can not be very  
unknown.

> C voters definitely hold B as a second choice.

In this case I'd expect many B voters to support C as their second  
choice. C can't be so unknown that B supporters would not be aware of  
C being the second (or actually first) right wing candidate.

> 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.

I assumed that the votes were sincere. Could you describe the sincere  
opinions and strategic votes separately.

I can understand that left wing voters may not be interested in the  
right wing internal battle. I'd however expect some of the "A" voters  
vote "A>B" and some "A>C" (both new opinions would get votes since in  
this scenario C was "more or less extreme than B", not clearly wanted  
or unwanted by left wing).

> 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.

This is complex. I propose to handle one scenario at one time (maybe  
start with one and continue forward if the first one doesn't cover  
all the relevant aspects). And to clearly describe also the sincere  
opinions before any strategies were applied. In real life of course  
there may be many kind of opinions among the voters. In this case I'd  
expect the votes to be less extreme than they are now (now all A and  
B supporters bullet voted and all C supporters gave full rankings).  
But maybe this scenario was intended to be one where the opinions in  
the society are very sharp and uniform among the voters of the  
different groupings (??).

Now I'm a bit confused since in the example the margins strategy now  
occurs in a situation where strategies seem to already have taken  
place. Are we maybe talking about different polls, e.g. one and two  
weeks before the election and strategies that change in time as the  
voters learn the latest sincere opinions and strategic responses to  
the polls (??).

I think the opinion polls should be explicitly mentioned in the  
description of the scenarios since that is the information the voters  
(and strategists) will have (the final outcome of the election is not  
known, just preliminary polls and guesses).

>> - 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?

A and B are only few votes short of being Condorcet winners. C is  
maybe not hopeless but winning is not as easy and probable as for A  
and B. I assumed C to consider C to be "a sure loser" since that made  
the margins strategy work better (no need to try to win).

>> 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.

Show me the plausible real life scenario where this set-up is likely  
to occur and will ruin the credibility of the voting method (not just  
that something is possible since we know that Condorcet always has  
some strategic problems (hopefully marginal)). Then we can consider  
changing margins recommendation to winning votes, or changing  
Condorcet to something else.

>> 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.

They worked still when I sent the mail. It appears that the archives  
are now behind a password. I could repost the old mails but let's see  
first if this only temporary (hope so, the archives are an essential  
part of this list). (old mails available on request too)

> I can tell you the reason why this scenario makes margins generally  
> fail:

"Generally"? Do you mean that this example would turn margins based  
Condorcet unusable in general?

> 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?

It was very "brute force". Any situation where an agreed size group  
of voters (or alternatively any of the groups) could have elected a  
better candidate from their point of view by giving some different  
kind of vote. I thus didn't make any difference between different  
kind of strategies - just counted the cases where a different kind of  
vote (by the whole group) would have been strategically better for  
them (better than a sincere vote).

> 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.

Yes, but FBC identifies of course just one of the strategic voting  
patterns. In my simulation I tried to cover all strategies.

>>> 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.

I'll forward those three mails to your email address. (I hope I  
remember which ones they were - can't double check now from the  
archives)

>> - 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.

I'm not aware of such simple explanation. Minmax is of course quite  
simple, but the explanation above was even simpler. It didn't mention  
min and max and margin (or winning vote) or cycles (=uses non- 
theoretical terminology) and it is very exact and understandable.

> 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.

This is sound criticism of the utility provided by margins with  
sincere votes (I assume these words were intended to be, although you  
didn't explicitly say so). One can discuss if a 51-49 win is stronger  
than e.g. a 49-39 win. I wouldn't however jump all the way to winning  
votes to tune the comparison strengths of margins since in my opinion  
winning votes may (at least in extreme situations) elect much  
stranger winners (e.g. in 100 A>B>C, 100 D>E>F, 1 F>B).

Note also that one can measure majority in many different ways, e.g.  
comparing votes that took position, with respect to number of votes,  
number of citizens etc.

> 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.

This sounds a bit artificial to me. I mean, the chosen words sound  
dramatic but A is two votes short of being the Condorcet winner =>  
not a catastrophic choice. Also C and B have their problems (and  
corresponding more or less convincing explanations of them). Only 8  
voters would have interest to change A (if elected) to C while 7  
would oppose that change (and 5 would be neutral).

I think it is quite possible to have different targets for different  
elections. Sometimes the society should elect a compromise candidate  
that generates as little negative feelings as possible. sometimes  
some other criteria could be used. But margins is a pretty good  
generic criterion that can be used in many cases and may be optimal  
in some.

>> 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?

First of all, my experience suggests me that most problematic  
scenarios can be covered with examples that have only three  
candidates. That means that typically studying the three-candidate  
scenarios is enough. Not always though => e.g. the strategy of  
generating cycles that include candidates of a competing party leads  
to study scenarios with more than three candidates. But three is  
enough in most cases.

Starting from natural loops with sincere votes, I expect cycles to be  
quite possible. In most cases the preferences are weak and therefore  
reliable estimates on what strategies to apply are difficult to make  
based of polls that are made before the election (due to inaccuracy  
in the polls, due to changing opinions etc.).

It is possible to have also stronger loops with sincere votes when  
e.g. the themes chosen by the candidates for their campaigns happen  
to address different voter groups in some suitable cyclic way (I have  
written on this list about these cases - can forward the mail if  
needed).

How about the artificial loops (as a result of strategic voting  
intending to generate loops (or maybe in some cases also  
unintentionally generating them)). These are quite possible in  
theory. In practice they are limited by the available information and  
its reliability (unreliable polls leading to risks and uncertainly).  
They are also limited by the heterogeneity of the voters. It is hard  
to find uniform groups, interested in similar goals, willing to take  
part in strategic plotting, and capable of carrying the strategy  
through.

I often refer to public large scale elections as the default case  
when discussing the voting method related strategies. This scenario  
provides additional protection against strategic voting (and also  
artificial cycles). This includes issues like inability to hide the  
strategy, irritation of voters when some candidates try to use  
strategies (they might decide to vote differently), and difficulty of  
controlling and instructing large masses of voters.

I also note that there may be quite significant differences between  
different societies. In some countries it is for example today quite  
normal to receive guidance on strategic voting. Voters may feel that  
this is normal, not something negative, or just part of the game. In  
some other societies people would be seriously upset if some  
candidates/parties would even propose them to take part in a (dubious  
clandestine) plan whose aim is to falsify the results of the election  
(and thereby ruin the society). In all countries there is probably a  
portion of people who will vote sincerely since they believe that is  
the right thing to do. It is also typical that some individual voters  
and/or societies favour individual independent decision making  
instead of following the pack and recommendations of others (like  
"party strategy officials").

In summary both natural and artificial cycles are possible. I expect  
the real life cycles to be typically considerably weaker in strength  
than the extreme/theoretical examples that we often use when  
discussing about different strategies (like the one you used above,  
and the 100/100/1 example I used). The weakness of the cycles  
typically makes use of strategies more difficult and more risky.

In addition it is always nice to have a real life explanation to some  
given voting behaviour, just to make it possible to estimate which  
cases are the ones that we should be worried about and which ones are  
just theoretical extreme cases that will practically never occur in  
real life (e.g. in large public elections with individual decision  
making). All cycles are thus not equal.

Juho

> Kevin Venzke
>
>
>        
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