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

[Juho]

I was a bit puzzled when answering this mail. Our terminologies did  
not yet quite match. There is also still some confusion with what the  
sincere votes were in your original example (49 A, 24 B, 27 C>B) (see  
below). And I'm still wondering if you felt that D was the rightful  
winner in the basic example where sincere opinions were 1000 A>B,  
1000 C>D, 1 D>B (or 1000 A>B>C=D, 1000 C>D>A=B, 1 D>B>A=B). The rest  
of the reactions/comments are embedded below in the mail.

Juho


On Jul 31, 2007, at 7:36 , Kevin Venzke wrote:

> Juho,
>
> --- Juho <juho4880 at yahoo.co.uk> a écrit :
>> 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.
>
> But you haven't come any closer to explaining what the problem is.
> You seem to basically admit it is just an aesthetic issue.
>
>> 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.
>
> This is why I keep pointing out that this is a Condorcet method and  
> we're
> trying to find the best compromise. I really think you are overly
> impressed with first preferences, and that is why I keep bringing  
> up IRV.
> C>D voters are not going to thank you for preventing D from winning,
> unless C wins instead.

I don't think I have any interest in the first preferences here. I'm  
basically interested only in the pairwise matrix that is neutral to  
where the preferences come from. I didn't understand why IRV is  
relevant here - I think the C>D voters are not going to thank me for  
changing the voter from X to Y in any system if they prefer X to Y.

In the latter example I changed a two way AB tie to a four way tie  
(either by adding the last vote in wv or by changing the method from  
margins to wv).

If people think in the margins way I might get more thanks than  
blames. But if people feel that wv is the natural measure of  
preference then the situation is more neutral. Based on this am I  
right to assume that already in the first example (1000 A>B, 1000  
C>D, 1 D>B) you found D to be the natural and correct winner  
(assuming sincere votes)?

((Now btw you used a "first place argument" :-).))

>
>>> 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.
>
> I didn't say we would add approval. However I believe these is an  
> implicit
> sense of approval in casting an explicit vote for a candidate.
>
> I do not regard the cast votes A>B>C=D and A>B as meaning the same
> thing. If you ruin the election when the vote is A>B>C=D then I don't
> mind as much.

The vote counting algorithm treats A>B>C=D and A>B in the same way.  
Voters should be made aware that there is no difference between these  
two voting styles.

>
>> One solution would be to make it mandatory to rank all the
>> candidates. (This would also solve the margins vs. winning votes
>> debate :-).)
>
> I hope this is a joke. That would practically make "betray or risk  
> being
> betrayed" a checkbox on the ballot.

Yes, this was a joke as indicated, but I don't think it would somehow  
make the method unusable.

(I'm not sure but your comment sounds to me a bit like the old  
argument that use of wv makes Condorcet acceptable while margins keep  
it unacceptable. My point has been that we should cover all arguments  
in both directions, and that it is not clear to me why this single  
argument would be more important and a bigger threat than the others.)

>
>>> 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.)
>
> Well, I don't know what to say here. I did much better than simply  
> assert
> that 51-49 is stronger than 49-0. I pointed out that if the method is
> equipped to ignore noise then you don't have to rely on the "not
> catastrophic = OK" doctrine so much.

What's the "not catastrophic = OK" doctrine? What is considered noise?

>
>>> 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.
>
> This is very irritating. How am I assuming there's an approval cutoff?
> I'm trying to point out that no one in the scenario cares about this
> issue since everybody is too busy trying to elect the best  
> candidate they
> can.
>
> Here is a question for you: If this faction really doesn't want their
> second choice to win (since it goes against their unanimous  
> preference for
> their first choice), why do they even vote for him?

You are again using the "first choice" argumentation. I'm not. Maybe  
your thinking based on the wv philosophy (and mine is one step closer  
to the margins) and that is why the terminology looks a bit  
different. Lets be explicit in the wordings to understand what we mean.

I'm just saying that from the rankings point of view 100% of the C>D  
voters ranked C above D. They want C to win D but they want D to win  
the others. (And as should already be clear I don't assume that the  
votes carry a message that the candidates that are marked in the  
ballot are somehow "approved".)

>
>>> 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.
>
> I don't know what you think "compromise" means. AEHJ are not  
> compromises
> at all; they are the first preferences of each large faction.

Ok, now I understand a bit where you see me promoting the first  
choices. But still I say I have no interest in putting some specific  
weight on the first preferences. It just happens to be so that if a  
voter marks some candidate at the #1 position, then that candidate  
gets lots of points in the matrix (=preferred to all others).

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.

>
>>> 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.
>
> This situation doesn't encourage strategic voting under WV. Did you  
> not
> notice it only takes *six* out of 35 to make the strategy backfire?  
> It is
> not reasonable at all for C voters to think this is a reliable  
> strategy.

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.

>
>> 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.
>
> Incidentally, I don't see it as likely that one party will nominate  
> two
> candidates, exactly because of the defection and betrayal  
> incentives that
> exist. If there are two candidates of the same ideology, I think it is
> likely that one is better established than the other, and the  
> supporters
> of the better established candidate are in a much better position to
> force the other candidate's supporters to aid them.

Are you recommending a two-party system or two-candidate elections?  
That would make the Condorcet strategies disappear :-). The one  
candidate per party idea could be extended to having one candidate  
for the left wing parties and one for the right wing parties.

If this would be the preferred mode of operation, then the "tree  
voting" style where candidates are organised in a tree like  
structure. See e.g. my mails on tree structures at March 11th 2007.  
That is one strong but a bit limiting way of getting rid of the cycle  
based strategies.

>
>>> 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.
>
> If you want to argue that WV is more seriously vulnerable to offensive
> strategies than margins, I don't think you will succeed, but I'm not
> going to get into it unless there's some really good argument.

I tried to point out that there are problems in both directions, and  
that winning votes have some problems also with the sincere votes,  
and that margins may be more natural measure than winning votes, and  
that strategies are not very probable in Condorcet in general, and  
that when summing all this up margins may well be the better method  
of these two. We didn't touch the vulnerability of margins much. The  
strength of those vulnerabilities should of course also be estimated  
to make the calculation/estimation complete.

>
>>> 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.
>
> Well I can help you out. A and B factions truncated because they were
> the frontrunners. C voters didn't truncate because they didn't expect
> C to win, and therefore needed a second preference as a compromise.

Ok, this is a clear explanation but I have some questions still.

- 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.

- Why is B considered a frontrunner with less first place support  
than C had?

- Why did A supporters decide to truncate? Being one of the  
frontrunners is not yet a good enough reason.

- Why did B supporters decide to truncate? Is this a winning votes  
counter strategy?

>
>
>>> 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.
>
> Just a note. There is no need to assume some C voters will truncate,
> unless you are trying to trick yourself into thinking this is a real
> election or something. C voters didn't truncate because they knew C  
> was
> not a frontrunner. In real life, some C voters would truncate, sure.
> But "I had to assume that some C supporters will truncate since some
> B voters did so too" is ridiculous logic.

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.)

>
>> 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.
>
> This paragraph makes a lot of sense.
>
>> 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.
>
> It might be unrealistic that these are sincere, but it's not  
> unrealistic
> that so few A voters would vote for their main opposition.

Do you mean that voting "A>B>C" would be giving support to B and that  
A supporters should by default vote "A" (if B is considered "main  
opposition")? My basic thinking is that vote "A>B>C" differs from  
vote "A" only in that the voter takes position on if B is better than  
C. (Without strategic considerations) this should have no impact on  
how much the voter prefers A over B and C.

>
>> 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)
>
> So you say a scenario becomes more realistic when information is very
> poor? Or it becomes realistic when all three candidates have a  
> chance of
> winning?

None of these. My intention is to say that a large population is  
likely to have more than three types of sincere opinions (with three  
candidates). A strong bias in the opinions (from random distribution)  
also needs to be explained to make the scenario credible.

>
> I'm not sure you understand my point with this scenario. If the C  
> voters
> vote sincerely in this scenario, then A wins and the C voters wish  
> they
> had betrayed their candidate (who wasn't expected to win anyway). If
> we give people incentive to betray candidates who aren't frontrunners,
> what do we even need a better election method for?

Ok, after the election some group notes that they could have  
falsified the result to something better from their point of view by  
voting strategically. That is not yet a serious problem. What happens  
at the election day is more serious. I tried to demonstrate that with  
good probability there are no easy strategic options available, and  
that in a large population that probability decreases. I'm trying to  
find such sincere opinions where the basic scenario that you  
presented could be realistic in normal large scale elections (and  
then analyse that case, to see the probabilities, the damage level,  
ease of applying the strategy, risk of getting worse results than  
planned etc.).

In the modified scenario that I presented the success of the strategy  
was one vote away but still the strategic plan appeared to be less  
than clear due to the numerous uncertainties with controlling the  
strategy, changes in the opinions before the election day, reactions  
to the strategic voting plans (counter strategies, reduced support to  
the plotters) etc.

>
>> 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).
>
> Not sure what you're getting at here since the strategic voting in  
> this
> scenario is just favorite betrayal by supporters of weak candidates;
> this strategy is practically never risky if you know who the  
> frontrunners
> are.
>
> Not to mention that using the strategy here actually improves the  
> result.
> If you want voters to be sincere, don't force them to strategize.
>
> I see it as crucial that we not give voters reasons to stick to voting
> for frontrunners.

My ideal outcome of these studies would be to find out that Condorcet  
methods are not too vulnerable to strategic voting and as a result  
all voters could safely vote sincerely. The conclusions may be  
different in different societies depending e.g. on the level of  
interest in strategic voting. If the voters are forced to strategic  
(or counter strategic) votes, that is already a problem to me. A good  
method should allow sincere voting. Also electing some other  
candidate than the best one (with sincere votes) is a problem that  
should be avoided. I'm thus more interested in sincere voting than  
allowing strategies and counter strategies to take place.

The last paragraph talked about Condorcet in general, not about this  
particular example.

>
> Kevin Venzke
>
>
>        
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