[EM] Scoring (was Re: OpenSTV 2.1.0 released)

[Juho Laatu]

On 25.9.2012, at 9.31, Michael Ossipoff wrote:

> Juho:
> 
> Here's the MinMax(margins) chicken dilemma example that I promised, in
> which defection by B voters is successful and rewarded::
> 
> Sincere preferences:
> 
> 75: A>B>>C
> 51: B>A>>C
> 100: C>>(A=B)
> 
> Voted rankings:
> 
> 75: A>B
> 51: B
> 100: C
> 
> Try MinMax(margins) with that example.
> 
> Note that it's a Dodgson example too.
> 
> Note also that the B faction is small in comparison to the other factions.
> 
> Condorcet(wv) reliably rewards defection.
> 
> SITC reliably thwarts and penalizes defection.
> 
> Though MinMax(margins) and Dodgson don't reward defection quite as
> reliably as does wv, (though the example shows that they easily do
> so), they certainly don't reliably thwart and penalize it either.

I think I'll skip the Dodgson part since I have not claimed anything about that method (and that's quite irrelevant too in this context). You may forget Dodgson. I'll comment mainly margins since I prefer margins versions of Condorcet methods to winning votes versions. But I'll address also the winning votes related problems shortly.

> 
> An additional problem of MinMax(margins) and Dodgson:
> 
> It is well established and well-discussed on EM that MinMax(margins)
> has particularly great problem with strategic truncation and offensive
> burial.

And you probably already guessed that I would say that those theoretical vulnerabilities may not be that bad in real elections.

> 
> Those things, even offensive burial, aren't a problem with SITC,
> because the only candidate who can benefit from it is the most
> top-ranked candidate among the unbeaten candidates--or just the most
> top-ranked candidate if there are no unbeaten candidates.

I'm not sure if it is wise to expand this discussion also to SITC. It might however be of interest to me (based of what I have written) to point out that sometimes SITC and electing the ideal sincere winner (your definition) do not coincide.

> 
> Offensive burial can't make anyone else win.


Now to Minmax(margins). I assume that this is a regular public election.

Some reasons why the chicken dilemma might not be a major problem in the given example:

- With these numbers all B supporters will have to implement the strategy to guarantee that B wins. This is very unlikely in real life.

- It is very unlikely that all B supporters use the strategy but none of the A supporters do. A is more popular than B, and therefore A supporters might truncate B with higher probability (due to thinking that B is a weak candidate). If two of the A supporters bullet vote (when all B voters are strategic), C is already tied with B, and according to the given preferences, B supporters would be very unhappy with that. For this reason B supporters should concentrate on making C not win instead of trying to beat A with this very risky strategy.

- The anticipated opinions are likely to change before the election day. If one of the B supporters becomes an A supporter, all candidates are tied. Maybe that single voter didn't like the idea that B supporters would try to steal the victory. This is again one reason why B should try to be friends with A and not try to cheat and steal the victory.

- Opinions are not usually as clean as in this example. There are often also other parties and always some voters whose preferences differ from those three main categories (e.g. A>C>B). This means that it is more difficult to guess how people will vote, to take into account the strategic interests of all voter groups, and to estimate the outcome. There is also always a group of voters who want to vote sincerely. If we assume e.g. +/-5% change of all preference orders, strategic voting gets much more difficult than it is on paper. On paper we can define ourselves how each voter will vote and allow certain interest group to stratgeize with 100% control of the similar minded voters. In real life, if there is one strategy, there may be also other strategies.

Already based on the first bullet point, this strategy seems to be a highly irrational strategy in Minmax(margins). And the other bullet points do not make the life of the strategists any easier. I'd say that you can sleep peacefully and not worry abut the chicken dilemma, at least with this threat scenario. Do you agree?

The winning votes variants are however much more vulnerable to this strategy. There are also strategies where margins are more vulnerble. But I prefer margins based versions of the Codorcet methods, because I find their sincere winner philosophy and also strategic properties better. But I'll try to say some words in favour of the wv versions too in your chicken dilemma scenario.

In your wv example (27: A>B>>C, 24: B>A>>C, 49: C) three strategically truncating B supporters can change the result. That is already a low number that could be well achieved. But there are still many problems on the way of the strategists.

- Also in this scenario it is not probable that only B supporters truncate and A supporters do not. A and B are reasonably close to each others in support. They both may try to beat the other one by collecting more first preference votes. If they both start to truncate, both will lose (to the very disliked C). A and B supporters can also safely vote sincerely, so why would they not do that (and let the more popular of them win). I.e. do they elect mutual destruction or cooperation and victory to one of them. If A and B parties give some recommendations to their voters, it seems that recommendation to vote sincerely would be the correct recommendation.

- You assumed for simplicity that all C supporters will truncate. I guess you meant that they could as well rank A and B. It makes sense to C supporters to not truncate since the polls show that the A/B group may win, and C supporters can decide which one of them wins. If all C supporters (or almost all) use rankings and give equal support to A and B, B's strategy does not work. If majority of C supporters prefer A to B, B's strategy gets more difficult. (If C supporters clearly prefer B to A, B wins without any strategy.)

I guess that's enough on the winning votes. They are much more risky than margins in this chicken case, and strategies could sometimes work. But it seems that sincere voting would make more sense to the A and B parties since they have to cooperate in order to not let the unliked C side win.

I note that winning votes based versions of the methods make poor choices also with sincere votes. Your chicken scenario is close to the old wv problem case where B wins with sincere votes 49: A>B, 2: B>C, 49: C. I guess most people think that B shouldn't be that close to winning if almost all voters think either A>B or C. That strange approach to truncated opinions makes wv also weaker than margins in the chicken case.

> 
> I'll try to answer (only) the parts of this posting that I didn't
> answer in part 1 of my reply:
> 
>> I don't think the following four questions that you gave as a response are ones that I left unanswered, but new questions or new formulations. I'l check them anyway.
>> 
>>> 1. What makes you think that MinMax(margins), Dodgson, or Beatpath
>>> won't have a chicken dilemma?
>> 
>> I already said that I do believe that basic Condorcet methods are not very prone to this problem. I >know that you disagree. Maybe you'll find one day a proof that will convince me.
> 
> Above, in this reply, I've posted an example in which defection by the
> B voters is rewarded. The A voters, expecting likely defection by the
> B voters can co-operate, by ranking B, because at least one faction
> must co-operate in order to defeat C. But, if they do, they'll lose to
> B, because they've been had by the B voters.
> 
> That's the chicken dilemma, and it's fully there, with MinMax(margins)
> and Dodgson.

I don't think the margins case was a major problem for Minmax(margins).

> 
> As for Beatpath, Beatpath's failure was shown in my posting with my
> old 27,24,49 example. It's easier to show Beatpath failing, having the
> chicken dilemma. But, as you can see from the example shown above in
> this post, MinMax(margins) and Dodgson fail quite easily too.

All wv based versions are more vulnerable to this attack (including Beatpath(wv) and Minmax(wv)).

> 
> 
>>> Must I do that, to show you their
>>> chicken dilemma? Request it and I will.
> (I showed an example, in this posting, in which MinMax(margins) has
> that problem.
> 
>> 
>> No need since I don't expect that to change my opinions. It could be a wasted effort. I'm >interested if there is something really convincing, but maybe better leave this topic this time, with >the assumption that I would not believe it anyway.
> 
> If an example of it happening doesn't convince Juho, then nothing
> will. That's ok.
> 
> You said:
> 
> Many Condorcet strategies are difficult to identify, to use, to
> coordinate, and often they may also backfire.
> 
> [endquote]
> 
> Sure. As I said, in Condorcet, even in a u/a election, you won't know
> what to do. For example, in a u/a election:
> 
> Approval: Approve the acceptables and none of the unacceptables.
> 
> Score: Top rate the acceptables and bottom rate the unacceptables.
> 
> SITC: Top rank the acceptables, and don't rank anyone else.
> 
> Unimproved Condorcet (Including MinMax(margins), Dodgson, Beatpath,
> etc.): You still have the same need to top rank the acceptables, and
> for the same reason. But, with Unimproved Condorcet,
> that can, as you said, backfire, because top ranking someone (you
> don't know which one) could cause your last choice to win. In
> Unimproved Condorcet, you won't know what to do, even in a u/a
> election.
> 
> But suppose there is one Democrat, and some Republicans. There are
> also some progressives whom you prefer to the Democrat. You believe
> (you've always heard it in the media, which you completely believe)
> that the Democrat and the Republicans are the only candidates who can
> win. You feel that the Republican is unacceptable, and that the
> Democrat is acceptable, and that it is all-important to ensure that
> the Republican doesn't win.
> 
> What do you do? Your optimum strategy is to rank the Democrat _alone_
> in 1st place. Now, if there are several Democrats, then you have a
> problem. You then have a dilemma that you wouldn't have in Approval,
> Score, or SITC. You must try to guess which Democrat(s) to top rank,
> but you know that one of them (you don't know which) could, by being
> top-ranked, change the win from a Democrat to a Republican.  That's a
> dilemma that you wouldn't have in Approval, Score, or SITC.

There was a lot of stuff in the preceding lines. Maybe you will repeat the claim/message/question if there was a key message that you want me to comment.

> 
>> The details have been debated in the EM list.
> 
> But the specifics of the above-described situation haven't been
> discussed. u/a elections have been little discussed here, other than
> by me. Of course yes, unimproved Condorcet's FBC failure is well known
> and well-discussed at EM.
> 
>> 
>>> Sometimes you seem to say that you're just speaking in general, about
>>> most societies, or many societies. Sometimes, though, you make
>>> assertions about what won't happen here.
>> 
>> I started with general claims but I commented also the U.S. related stuff since that seems to be >on your agenda.
> 
> That's right, you did. You sometimes do, but then, at other times, you
> insist that you're only speaking generally, about most societies, or
> about a matter of "maybe".
> 
>>> 3. What is your best argument to support your belief that Dodgson,
>>> MinMax(margins) or Beatpath would do better at choosing the ideal
>>> sincere winner, if voting were sincere, than SITC would do?
>> 
>> I don't claim that. I left the selection of the sincere winner criterion open.
> 
> Of course that means that you can't use it. You can only speculate. Of
> course that's what you've been doing.
> 
> You said:
> 
> As already noted, methods that are strongly strategy defence related
> may not be exactly built to reflect targets that have been set for
> selecting the winner based on sincere votes.
> 
> [endquote]
> 
> You're repeating, again, something that I've answered--the first time
> you said it, and also in each repetition.

What else should I do than repeat my position if you seem to assume that I said something else? :-) Ok, maybe I'll assume next time that the comment was just a rhetoric one to demonstrate disagreement. :-)

> 
> Choosing well under sincere voting, and not causing favorite-burial
> incentive aren't mutually incompatible, because they both result from
> respecting the voters' preferences, intent and wishes.
> 
> Aside from that, I don't know if you're aware that you're talking pure
> speculation, about how (you believe) maybe there could be a problem,
> unspecified by you.
> 
> 
>> 
>>> 4. Tell the requirements that describe the ideal sincere winner.
>> 
>> I repeat, I left the selection of the sincere winner criterion flexible and open.
> 
> Thereby, you left yourself with only some pure speculation.
> 
> 
> 
>> I presented one >example definition that could be used somewhere.
> 
> I answered about Dodgson and MinMax(margins).
> 
>> 
>> If you want some more generic comments, I might say that a good ideal sincere winner definition >is supposed to tell what kind of properties the society wants the winner to have. It does not care >about strategic vulnerabilities and does not defend against them.
> 
> Is that right. Funny, but this society's mass media regularly claim
> that favorite-burial strategy is needed "So that you won't waste your
> vote, you must vote pragmatically." Nearly all of the voters obey
> those instructions.
> 
> Oh, but that's right: You were only referring to most societies, or
> many societies.
> 
> I guess you're talking about how a society _should_ be. This "ideal
> single-winner definition"--where would it be useful? La La Land?
> 
> You said "supposed to". Supposed by whom? You?

I correct the words to "an ideal sincere winner definition tells...". The meaning stays the same.

> 
> You're vaguely referring to some supposed ideal or standard, without
> saying whose ideal or standard you think it is.
> 
> You said:
> 
> You could want the winner to be a person that is accepted by all,
> supported by majority, one that has strong support of some major
> party, one that has wide geographical support, support in all age
> groups, one that is not hated by any state, or whatever that makes the
> winner good. Once you know what you want, you can pick a practical
> election method that elects such a candidate (or is close enough),
> maybe tries to defend against strategies, is simple enough to use etc.
> 
> [endquote]
> 
> Or you could just seek to carry out what the voters themselves choose,
> instead of your antidemocratic, autocratic Soviet-like
> social-engineering goals.
> 
> While you're at it, it would be nice if the voting system doesn't
> discourage sincere voting, at least not to an easily-avoidable
> reasonable degree (No favorite-burial incentive. If it's a rank
> method, no chicken dilemma).
> 
>>> Certainly SITC is a different method from Dodgson or MinMax(margins).
>>> It wasn't clear that that's what you meant. But, if that's what you
>>> meant, then you're right about that.
>>> 
>>> So what?
>> 
>> That was part of my basic claim that best winner criteria and methods that aim at being strategy >proof are different.
> 
> Your completely unsupported claim about that.
> 
> You said:
> 
> You seem to be close to saying that SITC is not only a relatively
> strategy resistant method but also (close to) your definition of an
> ideal winner with sincere votes.
> 
> [endquote]
> 
> I said that the CW is a widely-accepted notion of the ideal sincere
> winner. But change that to legitimately-defined CW.
> 
> But the more your voting system forces drastic departure from sincere
> voting, the less sincere voting you're going to get.
> 
>> 
>>> You mean the status against opposition in office of the candidate
>>> whose largest margin against him, in favor of another candidate, is
>>> the least. And being the most favorite, having the largest faction,
>>> doesn't confer any status against opposition in office? :-)
>> 
>> Yes, the "least additional support/votes required" criterion (as a definition of good sincere winner) >points in that direction.
> 
> You're telling us your own personal opinion about what would (maybe)
> be the ideal sincere winner (in the event of a circular tie).
> 
> You keep saying it, but that isn't the same as supporting it.
> 
> I'm not going to keep on repeating my answers to that.

There is no need to answer my comments unless I write explicit questions (or if you have something that you want to say yourself).

> I refer you to
> my previous replies, where I've answered that statement of yours many
> times--each time, in various ways.
> 
> You said:
> 
> I don't know what "most favorite" and "largest faction" exactly mean
> 
> [endquote]
> 
> That's funny, because I just finished defining them, in the post to
> which you're replying.
> 
> "Most favorite" was a brief wording for "Voted in 1st place by the
> most people". First place is the most favored place. So I was
> referring to the candidate most favored with 1st place ranking.
> 
> The "largest faction"?  Maybe I'd better define two words for you:
> "Faction" and "Largest".
> 
> A "faction" refers to a set of people (voters in these discussions)
> who share some preferences or wishes, and co-operate toward achieving
> what they want. In voting system discussion, we're referring to a
> faction of voters who have sufficient preferences or goals in common
> that they support and vote for the same candidate as favorite, or at
> least for many of the same set of candidates.
> 
> In particular, in the examples that I've been posting, I made it clear
> that the A faction prefers candidate A as 1st choice, and that the B
> faction prefers candidate B as 1st choice, and that the C faction
> prefers candidate C as 1st choice. That defines the factions, in that
> usage. Factions defined by whom they most want to elect.
> 
> "Large". The large-ness of a faction refers to the number of voters in
> that faction. No, contrary to what you thought, it has nothing to do
> with the body-size of the individual persons.
> 
> The "-est" in "Largest": That means "more large than the others."
> 
> Let me know if you still don't understand what a faction is, or what
> "largest faction" means.
> 
> At least I should give you credit for making a statement that isn't a
> repetition. But you should have checked a dictionary.
> 
> About the repetition: I'm not going to keep on answering statements
> that you keep repeating. I've done that enough. More than enough.

Yes. Better not comment all my sentences. Answers to direct questions are welcome. (Sorry, that was repetition. :-) )

> 
>> 1, but I think they are not addressed by the "least additional support/votes required" criterion.
> 
> ...required to make the candidate CW.
> 
> That isn't a criterion. It's the definition of Dodgson.

??

> 
> You may personally like Dodgson (though like to mistakenly call it
> "MinMax(margins)), but merely stating its definition doesn't establish
> it as the standard by which to evaluate method when there's a natural
> circular tie under sincere voting. You're only expressing an opinion.
> 
> You're welcome to your opinion. You haven't told why anyone else should agree.
> 
> Why should the candidate who could most easily be made into CW by
> adding (or subtracting, or disregarding, or reversing) the fewest
> pairwise votes be the ideal sincere winner in a natural circular tie?

Sorry, repetition coming :-). The society is free to pick whatever best winner criterion it wants. (I hope you meant regular "votes" since "pairwise votes" looks like a new term and new potential source of confusion. :-) )

Juho


> Because you think so? That isn't enough.
> 
> When you rank someone in 1st place, or when you rank a set of
> candidates in 1st place, it's because you want to help them win
> instead of the ones you didn't rank in 1st place. The candidate who
> has been so voted by the most people has strong claim to be the
> rightful winner when there is no one unbeaten, or no one uniquely
> unbeaten.
> 
> No, I'm not advocating Plurality--largely because of its strategy
> problems. But as a Condorcet completion, the favoriteness standard (a
> short name for what I described in the paragraph before this one)
> doesn't bring Plurality's problems, and has a valid claim to
> rightness. Certainly such a candidate, after being elected, has
> undeniable strong authority against opposition in office
> 
> But I've said that before too. I'll repeat that I'm not going to keep
> repeating the answers to your repeated remarks.
> 
> You said:
> 
> It is characteristic to Condorcet methods (like Minmax(margins)) that
> they can sometimes elect compromise candidates that have limited first
> preference support.
> 
> [endquote]
> 
> Don't worry about that. That's for the voters to choose, for
> themselves. If you don't like a compromise, then I advise you not to
> support him, even as a compromise. You don't like the alternative?
> Well, you do have a problem, don't you. But don't blame it on the
> voting system.
> 
> There are a number of justifications for electing CWs. They tend to
> have good social utility. They're the candidate who would be elected
> in repeated elections, eventually arrived at, when everyone find out
> eachother's preferences. They're, therefore, the natural strategic
> choice. Oops, there's that word that you don't like.
> 
> I only advocate SITC for informational polling. I don't recommend
> anything other than Approval and Score for official public elections.
> 
> But, if we had to have a rank method, SITC would be the best choice.
> If you want to propose some rank method, for any purpose, then I
> suggest that SITC would be better. I've amply told why.
> 
> Mike Ossipoff