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

[Juho]

On Jul 29, 2007, at 2:51 , Kevin Venzke wrote:

> Juho,
>
> Thanks for forwarding your old messages. I will comment on these  
> first.
>
> In the first two posts you discuss scenarios where equally-sized  
> factions
> vote according to a mentality of "never mind the candidates of other
> parties except that they are worse than the candidates of my own  
> party."
> You note that under WV a single additional voter has at least some  
> way of
> voting that can change the winner into any candidate. You ask for an
> explanation of the WV philosophy that all the candidates are  
> roughly equal
> prior to the single voter.
>
> The first scenario is 1000 A>B, 1000 C>D. In MinMax(WV) it is a  
> four-way
> tie; in MinMax(m) it is an AC tie. If a D>B vote is added, under WV  
> this
> becomes a D win. Under margins it is still an AC tie. Note that D  
> does not
> win under either if the vote is just for D.
>
> I don't see first of all why this is very interesting. Not only is  
> this
> not a realistic scenario, but your argument here is just that the  
> behavior
> doesn't seem reasonable to you.

I agree that this example is not realistic since it is too extreme to  
ever happen in real life. But I don't agree with the word "just". I  
mean that voters/citizens would probably be quite unhappy with their  
election method if this happened in real life. This example is  
intended to demonstrate that winning votes seems to put too little  
weight on some very clear opinions expressed by the voters. In an  
election with many candidates and many parties the voters may be  
happy to rank only the best candidates from their point of view and  
truncate many that they consider less good. Some of these truncated  
candidates might be potential winners, and something close to the  
described scenario might happen. This is not a strategy related  
problem but a problem of possibly making unwanted decisions already  
with sincere votes. I wouldn't say that is less important than the  
problems with strategic voting.

Here's another version of the example - longer, but now the numbers  
could be from real life. There seems to be a consensus (within both  
of the two parties, "AB" and "CD") that A is better than B and C is  
better than D. Some voters (32%) truncate the candidates of the other  
party but all rank their own candidates. One additional vote (e.g.  
B>D) can lift B and/or D to the same level with A and C. The point is  
that this threat exists also when votes are more balanced than in the  
first (extreme but easy to catch) scenario. This may quite well  
happen in real life elections.

10 A>B
12 A>B>C
9  A>B>D
6  B>A
8  B>A>C
5  B>A>D
10 C>D
12 C>D>A
9  C>D>B
6  D>C
8  D>C>A
5  D>C>B

> For an explanation I can see a couple. One is based on the concept of
> approval. This is Condorcet and we are looking for a compromise  
> candidate.
> The candidates who received the most votes (of any type) are D and  
> B. By
> this concept one of these two should win.

Yes, approval could be added. But that'd be another voting method.  
Voters should be informed about that. They could btw still vote  
A>B>C=D instead of A>B>truncate and spoil the election.

One solution would be to make it mandatory to rank all the  
candidates. (This would also solve the margins vs. winning votes  
debate :-).)

> The other principle is that of unambiguous defeats, where more than  
> half of
>
> the voters voted some way on a given issue. D is the only candidate  
> not on
> the losing end of one of these.

Sounds like a "very strong majority requirement". Preference 51-49  
(out of the citizens that voted) is considered stronger than  
preference 49-0. (Note that also margins could be criticized of  
saying that 3-0 is a stronger preference than 51-49 (it depends on  
interpretation if this is considered bad or not), but I think the  
problems of winning votes are worse here.)

> In practical terms I can't see how the C voters could feel cheated  
> that D
> wins. If the C voters had not voted for D, then C would still lose  
> due to
> the pairwise loss to B.

I think you are assuming the approval cutoff to be present in the  
votes at the end of the listed candidates here. A more straight  
forward (and a more "ranking oriented") interpretation might be that  
they unanimously said that C is better than D.

> In the second scenario you suppose equally-sized factions voting  
> A>B>C>D,
> E>F>G, H>I, J. (Again, this is not a realistic scenario.) Under WV  
> a single
>
> additional voter has at least some way to vote that can turn any  
> one of
> these candidates into the winner. You say:
>
> "The question thus is if it is acceptable that winning votes  
> doesn't put
> any weight on the unanimous opinion on the order of candidates set  
> by the
> voters of each party to the candidates of that party."
>
> This is a Condorcet method. We're looking for a compromise choice, not
> selecting a representative of voters belonging to one party. When  
> people
> want to attach weight to many voters' first preferences then they  
> use IRV.

I don't see the link to IRV. The first preferences were not the  
deciding element here but truncation.

It is characteristic to Condrocet methods to elect a good compromise  
candidate. In this case I think A, E, H an J would maybe have been  
better compromises than the others.

> In the third post you bring up the scenario 20 A, 15 ABC, 10 ACB,  
> 35 BC,
> 20 CB and note that the latter faction can use order reversal to  
> steal the
> win.
>
> The order reversal here backfires and elects A if the 35 BC voters  
> don't
> vote for C. If even 6 BC voters truncate, it backfires. As I discussed
> earlier, I don't see why B voters would vote for C anyway. (Nor why A
> voters vote for B or C, but that does not seem to be essential to the
> scenario.)

Yes but the point of the example is that in this type of (realistic!)  
situations margins doesn't encourage strategic voting but winning  
votes does. With winning votes the use of the (working) strategy  
might lead to a counter strategy that may well further lead to a  
"catastrophe" and elect A.

To me the easiest explanation to why B supporters voted C and the  
other way around was that they were the two candidates of one party  
(e.g. Republicans). They are both average Republicans (not extremists  
in any direction). B is just a bit more competent for the job than C.  
This applies to A voters (Democrats) too.

> Your fourth post brings up the scenario 45 AB, 5 BA, 15 B, 5 BC, 30  
> CB and
> seems to argue that order reversal by the A faction can be  
> countered under
> margins mostly by B voters getting irritated enough to vote for C even
> though they weren't going to. You seem to envision that the threat  
> of C
> actually winning such an election would result in A voters not  
> risking the
> strategy. I don't have much to say about this scenario.
>
> I see your fifth post as similar, arguing that offensive strategy  
> is not
> likely to be feasible under margins.

The main (or at least one) point of these postings has been to  
demonstrate that winning votes are not a trick that cures all the  
problems of margins but that winning votes has problems of its own  
that may well be worse than the problems of margins.

> You say the point of your sixth post is that you describe a scenario
> where "strongish natural cycles" could be possible. Your scenario
> involves each third of the electorate voting A>B>C, B>C>A, C>A>B, with
> this vote reflecting their sincere preferences. That's fine, but I  
> don't
> see why such a cycle is more plausible than a cycle that arises solely
> because of truncation (which was the case in my scenario).

This example (March 23, 2005 8:29:18 GMT+02:00, "Re: majority rule,  
mutinous pirates, and voter strategy") was just part of a discussion  
on if "strongish natural cycles" are possible in the first place (not  
intended to discuss margins vs. winning votes).

In your example (see below) I couldn't find a plausible (real life)  
explanation to why some groups truncated so strongly while one group  
didn't truncate at all.

Juho

> --- Juho <juho4880 at yahoo.co.uk> a écrit :
>>> --- 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.
>>>>
>>>> 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.
>
> You say this a lot, but usually you are dismissing claims that  
> margins is
> unusually vulnerable to order reversal (causing weak candidates to
> defeat series contenders).
>
> In this case you seem to be saying that you hope the C voters *don't*
> realize how to salvage their vote, so that a candidate can win that  
> more
> than half of the voters didn't want.
>
>>>> - 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).
>
> I still don't understand what you refer to when you say that the cycle
> in my scenario (49 A, 24 B, 27 C>B) is "maybe even less common than  
> loops
> in general." What is an example of a type of loop that you think would
> be 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.
>>
>> 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.
>
> I hope this is just a summary and not an argument. I am not going  
> to try
> to argue that a candidate who is "less well-established somehow" is
> necessarily "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.
>
> I explained later in that post why, if it is possible that C could
> receive more first preferences than B, it is harmful for B voters to
> give a second preference to C.
>
>>> 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.
>
> For the sake of discussion you may assume that these are the sincere
> preferences:
> 49: A>B>C
> 24: mix of B>A>C and B>C>A
> 27: C>B>A
>
>> 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).
>
> Why don't you pretend they are there? It shouldn't make a scenario
> substantially more plausible by adding noise to it.
>
> Plus, we're talking about a scenario where A wins under margins. Yes,
> if the A voters give lower preferences to B, they can make themselves
> lose. That doesn't mitigate the problem.
>
>>> 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 (??).
>
> No, it was intended to be a scenario where all the noise has been  
> removed.
>
>> 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).
>
> The polls say the race is between A and B, and that the strength of  
> the
> C faction is substantial. (Under margins, the C faction is  
> potentially a
> spoiler candidate. So even a candidate of substantial strength  
> could be
> mostly abandoned in the actual vote.)
>
>>>> - 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).
>
> C probably is a sure loser. That doesn't mean voting for him should  
> spoil
> the result. Compare this to plurality voting.
>
>>>> 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.
>
> As far as I can tell, I did this. Even if you don't like my numbers, I
> gave the scenario.
>
>>> 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?
>
> No, this is a response to your saying this:
> "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."
>
> This problem does not occur under winning votes at all, and I was
> specifying what exactly "this problem" is.
>
> I am not sure whether margins is usable in general. But in this  
> scenario,
> and any along the same principle, I feel margins has missed the  
> point of
> holding the election by failing to identify which contests were  
> important.
>
>>> 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.
>
> I don't know what to say about this at the moment. I attach less  
> importance
> to strategies that involve ranking disliked candidates high which are
> effective only given very good information.
>
>>>> - 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).
>
> And this is basically the same scenario as in the other posts. You  
> don't
> even argue why it is a problem.
>
> Yes, one can discuss if 51-49 is stronger than 49-39, but there are
> practical implications to one's decision. I want the election  
> method to
> notice what contests the election was probably about; for that it is
> better to look at who brought in the most numbers.
>
>> 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.
>
> Yes, but this decision shouldn't be made arbitrarily. For instance, it
> might be a better measure of the importance of a contest to see the
> number of people that "took position." But this would have the side- 
> effect
> that a voter is better off not voting in a contest they expect to  
> lose.
> Additionally this measure can't reflect the certainty with which a
> candidate is defeated when they lose to a full majority.
>
>>> 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).
>
> The chosen words are a wording of the plurality criterion. The  
> issue is
> that there is no plausible reason why A is a better winner than C.
> Head-to-head, A loses. In a plurality vote, A loses. The only reason A
> wins here is because margins thinks it is more important that B does
> not win. Which candidate looks more like a consensus choice than B?
>
> Your "not a catastrophic choice" standard is not very persuasive to  
> me.
> I do not think that in a close contest it is OK for anybody to win.
>
>>> 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.
>
> I agree. In fact when you present scenarios where the exact same  
> faction
> seems to be offering multiple candidates, I find this unrealistic.
>
>> 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.
>
> Ok, I've read all this, and I still feel that I didn't get an answer.
> Do you have a three-candidate election, that you feel is realistic,  
> where
> everyone votes sincerely (except possibly for truncation), and  
> where you
> feel the WV outcome is problematic? If you don't, that's fine.
>
> Kevin Venzke
>
>
>        
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