[EM] Voting-System Choice for Polls (Just one more thing I want to say)

[Juho Laatu]

I wrote lengthy answers below. But it seems that we are already pretty close to consensus. My intention has been all the time to talk about ranked preferences only (and sincere votes). The only remaining obvious difference seemed to be in the question of whether the best sincere winner (according to some appropriate criteria) could be found outside the Smith set. The point is that some candidate outside the Smith set can be few votes short of being a CWs (talking about sincere votes here). And at the same time all members of the Smith set can lose with great margin to one/some of the other candidates. They are thus not even near of being CWs, if measured in strength of losses and needed changes in opinions to become a CWs. My claim thus is that a candidate that would have been a CWs, if few voters more would have voted for him, can not really be a very bad candidate. He could actually be the best candidate to elect. And all this considering only the given pairwise preferences, nothing else (no preference strengths, approvals etc.), both within the method and in any arguments on who the best winner might be. Do we agree or disagree on that?

You may well skip the rest of the mail, or read is as FYI only, if you like, since it doesn't add much to what has already been said.

> On 22 Dec 2016, at 07:14, Michael Ossipoff <email9648742 at gmail.com> wrote:
> 
> 
> [Replying farther down] :
> 
> On Wed, Dec 21, 2016 at 4:36 AM, Juho Laatu <juho.laatu at gmail.com <mailto:juho.laatu at gmail.com>> wrote:
>> On 21 Dec 2016, at 05:21, Michael Ossipoff <email9648742 at gmail.com <mailto:email9648742 at gmail.com>> wrote:
> 
>> Ok, MAM is a quite decent method. If strategic voting is minimal, I guess you pick the method that gives best results with sincere votes. I'm still lacking good understanding of why exactly MAM would produce best winners with sincere votes.
>> 
>> MAM is the ideal, among the methods that look only at pairwise-defeats and their strengths, and that comes from MAM's definition:
>> 
>> MAM:
>> 
>> A pairwise defeat is affirmed if it isn't the weakest defeat in a cycle whose other defeats are affirmed.
>> 
>> A alternative wins if it doesn't have an affirmed defeat.
>> 
>> [end of MAM definition]
>> 
>> It couldn't get any more minimal & ideal than that. MAM (unlike Beatpath, etc.) never unnecessarily disregards a pairwise defeat (by electing someone who has the defeat).
>> 
>> In a method based only on pairwise defeats & their strengths, the only thing that should nullify a defeat would be if that defeat is the weakest in a cycle, and if the other defeats in that cycle aren't nullified in that way.
> 
> I look at the world from a somewhat different angle here. I don't see what the relevance of beatpaths is in real life.
> 
> Beatpath, not MAM, is defined in terms of beatpaths.
> 
> But maybe you just mean that a cycle can be called a pair of beatpaths in both directions between 2 candidates.

Yes, sorry, I intended to talk about paths of pairwise losses in general, not one specific way of dealing with them.

> 
> The "relevance of cycles in real life?
> 
> I'll say it again (but I won't continue to keep saying it):
> 
> A pairwise-defeat is voted public preference.
> 
> A cycle renders meaningless the defeats in the cycle. Therefore cycles have relevance.

I would say that group opinions may be cyclic. Cyclic opinions may be problematic because it is not very easy to identify the winner, but surely all pairwise defeats are meaningful, also those that are part of a cycle. A cycle can be said to be less meaningful to a society than a pairwise opinion since the needs of the society may be more directly related to questions like "is A better than B" than to questions like "is there a chain of positive preferences from A to B". A path would be directly relevant to a society e.g. if there was a plan to first elect B, then agree to change B to X, then to Y, and finally to A. But usually there is no need for such activities. Cycles can be said to be relevant, as you say, even if the society has no direct interest in them.

>   
> I mean that I can not see what difference it makes to the society if there is a chain of defeats with certain strengths, if the target is to elect the best leader or best some other alternative.
> 
> You keep repeating that. And then, of course I keep repeating my answer to it (but I won't continue doing so):
> 
> Sure, likely the Approval winner is better than the winner by a pairwise-count method. 
> 
> There are 2 reasons to consider a rank-method:
> 
> 1. It's possible for a ranking method to provide a convenient, easy & reliable means for avoiding chicken-dilemma.
> 
> 2. Many people have a psychological need for rankings.
> 
> Some people think that they need to elect the CWs, which is easier with a pairwise-count rank method. Some overcompromisers or rival parties would avoid or soften their voting-errors, when voting with rankings.
> 
> 3. Finding the CWs, via a poll, can be important, because the CWs is typically the best candidate that people can get?
> 
> Is there something familiar about this? Oh yes, that's it: This is the same thing that we've both been saying over and over again. But I'm not going to continue doing so.

In my previous mail I tried to emphasize that whatever I said about Smith set and also paths had nothing to do with approval or range style argumentation, and nothing to do with strategic voting. My target was to discuss who is the best winner with sincere votes, taking only pairwise preferences (in the matrix, and optionally also those of individual voters) into account (i.e. no approval considerations etc.). And the key claim was that (depending on what kind of criteria the society has) the best winner could be sometimes found outside the Smith set. This is related to the claim that the winner may be identified also by other means than "breaking cycles".

>  
> Beatpaths
> 
> ....by which you mean cycles, because you presumably want to call a cycle a pair of opposite-direction beatpaths between 2 candidates.

Yes. I note that some of my comments on paths apply to non-cyclic paths too.

>  
> seem to serve the need to linearize the opinions of the group
> 
> No. Cycles are relevant if pairwise defeats are of interest. A pairwise defeat is a voted public preference.

With "linearization" I mean the activity of "breaking cycles" so that some preferences are "ignored" in order to make one of the candidates "winner without losses". The target seems to be to make group opinions look like individual voter opinions, that we can expect to be always linear. My preference is to accept the fact that group opinions may sometimes be cyclic (nothing wrong with that), and be able to identify the best winner despite of then. That process may not need any "breaking of cycles" / "linearization".

>  
> , or to "break cycles", which I think is not in the requirements list of an election or poll.
> 
> Nonsense. Defeats in a cycle aren't saying anything about public wishes. Should an election or poll reflect public wishes? :^) There are voting systems that look only at pairwise preferences. MAM is one of them. MAM, for example, has many desirable properties. 
> 
> But I have no idea what your "reqirements list is (or what is the "best winner" that you keep talking about). But that's ok. It's your business. Far be it for me to tell you what your "requirements list" or "best winner" should be.
> 
> Quite possibly your requirements list and your best winner aren't gotten by pairwise-count methods. Fine. You've still got Approval, Score, and Bucklin, all good methods.

Let's talk about pairwise preferences only. If some community needs an election method, I might ask them what kind of a candidate they want to win. They might say that they want a good compromise candidate, or one that is not controversial, one that has only weak opposition, or one that voters would not like to change to numerous other candidates. I exclude opinions like "widely approved" here since we are talking about preferences only. After hearing those requirements of the society I might be able to point out which election method would do what they want it to do. I wold probably tell them what method seems to be the best with sincere votes, but I would address also possibility of strategic voting and possible need to use some other method than the one that provides best results with sincere votes.

>  
> That is more like an aesthetic preference, or a mistaken idea that group opinions should be straightened to linear opinions.
> 
> If you say so.
> 
>  
> I agree that MAM could be seen as aesthetically beautiful, but I thus fail to see the connection to the targets of the election / poll (to find the best winner with sincere votes).
> 
> That would depend on your (often referred to but never stated) opinion about what is the target of the election or the best winner.

See above. In principle I let the society tell me what kind of winner they want, and then try to pick the best method for them (covering both sincere votes and possibility of strategic voting). We can also discuss which method is best with sincere votes. A good discussion would include a description of what makes a good candidate (or multiple alternative descriptions).

> 
> You (presumably) know what your target for the election/poll is, and what your best winner would be. By all means feel free to implement your opinions, when you choose a voting system!
> 
> Or do we all have to abide by your target and your best winner? :^)

In principle I leave it up to the society to tell what they want. But I can give some examples. The simplest to explain is minmax(margins). One definition of it says that (assuming sincere votes) it elects the candidate that needs least number of additional votes to become a CWs. That criterion can be considered to be a valid definition of "best winner" by some society. The society might think that this winner is strong and good leader since he needs only a minimal amount of additional support to make decisions (maybe to thwart the proposals of the former competitors) when in office. This is certainly not the only way to define which candidate is the ideal winner to a society, and there may be additional criteria, but this is one possible target that is easy to meet with one particular method.

(I find it more difficult to create this kind of (real life related) explanations (on who is the best winner) for methods that are based on paths and breaking cycles.)

> 
>  
> In comparison for example the target of minmax is much clearer - elect a candidate that people will not oppose too much while he is in office, measured as strength of interest to change him to one of the competitors in opposition.
> 
> MinMax has, for years, been widely-regarded as not doing as well as MAM, in a number of ways. But if you like it better, then use it next time you do a poll, or advocate it for electing officeholders where you live.
> 
> You have a right to do those things!  
> 
> Go for it!
> 
>  
> Also approval and range are easy to explain from the "possible needs of the society" perspective.
> 
> So very true.
> 
>  
> 
>> Additionally, MAM has excellent burial-deterrence & thwarting. That's why I use MAM, in Pairwise-Winner(MAM,  Smith,MMPO).  ...for MAM's burial-deterrence. But MMPO, & not MAM, is chicken-dilemma defection-proof, which is why I like to combine both of their strategic advantages, in
>> P(MAM,  Smith,MMPO), for polls with possibly offensive-strategic voters.
> 
> This is about strategic voting
> 
> 
> Are you sure?  :^)

Words like "burial" seem to refer to strategic voting scenarios, not to performance with sincere votes.

> 
>  
> , not about which method is best with sincere votes.
> 
> I said that P(MAM,   Smith,MMPO) is for electorates in which offensive strategy would be particularly likely, unless deterred or at least thwarted.
> 
> Have we established that yet?

I tried to focus on performance with sincere votes. Performance with strategies is another interesting area of discussion, but I tried to keep the discussion simple and avoid strategic considerations at this point since it seems we did not find common language on the sincere side yet, and the points I wanted to make dealt with performance with sincere votes (= who is the best winner with sincere votes).

> 
> MAM is also very good with sincere voting. MAM is a component of 
> P(MAM,  Smith,MMPO).
>  
> Not to be counted in favour of MAM in this branch of discussion.
> 
> That MAM is good with sincere votes is to be counted in MAM's favor.

Yes. As I said, so far I have seen some elegance / aesthetics in MAM, but I'm not able to translate that to an explanation why MAM would pick the best winner for _some_ society with sincere votes.

One viewpoint to path and cycle breaking based methods is that they provide us with a complete linear order, or at least parts of such ordering, allowing us to visualize the candidates so that there is one candidate at the top, then members of the Smith set, and then the rest. Some of the preferences would be discarded and thrown aside. My point here is that this image might be easy to sell to the public, claiming that the best candidate won. But I still have difficulties explaining to myself why forcing natural cyclic group opinions to a more linear looking graph would be needed to identify the best winner. My example of sometimes finding the best winner outside the Smith set is intended to demonstrate that sometimes a linear ordering like visualization might not make sense at all.

> 
> 
> [Replying farther down] :
>  
> 
>>> I can't say why it's important to guarantee that the winner is in the voted Smith-set, other than that it confers compliance with various criteria, including Mutual-Majority.
>> 
>> That's a good answer since there are situations where one can justify electing from a Smith set that consists of very similar minded clones. The top cycle can be sincere or strategic. The same matrix can however probably be also a result of sincere votes where the Smith set candidates are not clones but a much more competitive group. In such cases it could make sense to elect outside the Smith set. One key point here is that information in the matrix is limited, and it is impossible to say if there are clones, and which preferences are strong and which ones weak.
>> 
>> But, with pairwise-count methods, the number of people voting a preference stands-in as an indication of its importance, imperfect though that may be.
>> 
>> It's important to find out the CWs, because that's the best that anyone can expect to get. Truncation-proof MAM & MMPO still elect the CWs when someone truncates it. MAM's deterrence of burial, improves the likelihood of electing the CWs if there is one--& there usually is one.
> 
> Yes. I think in this discussion we focus solely on methods where CWs is considered to be the ideal winner, and preference is measured solely as pairwise comparisons, that in most methods are derived from the pairwise matrix.
> 
> That's because, as I've already said many, many times, this thread originated about polls that I conduct with the purpose of finding the CWs.

Ok, approvals are out.

> 
>  
> And I claim that under these assumptions some methods can easily justify selecting the winner also outside the Smith set.
> 
> ...because that will make the method more likely to choose the CWs when there is one?  :^)

That example assumed that there is no CWs.

> 
> But, as I said, I cordially invite you to use the methods of your choice, for polls, and for your proposals for how to elect officeholders where you reside.
> 
> [Replying farther down] :
>  
> 
>>> But, because one member of the voted Smith set will be the CWs, if truncation or burial is being attempted against it (neuter gender because I'm talking about poll-alternatives) then that means that disqualifying non-members of the voted Smith-set narrows the field in a way favorable to the CWs.
>> 
>> It is not possible to tell if there was a CWs.
>> 
>> True, but if there is one, then it will win even if there's a truncation-caused cycle.
> 
> Also some other member of the Smith set might win.
> 
> No kidding? 
> 
> More likely with some methods than others. Choose the manner of selecting from the Smith set accordingly.
> 
> But, primarily, do what you want.
>  
> And the CWs could be also outside of the Smith set as a result of strategic voting.
> 
> No. 
> 
> Truncation or burial against the CWs will result in a top-cycle that includes the CWs.

You seem to refer to a successful burial of one candidate. Let's say there are three parties of about equal size, L, C and R. One of the C (centre) candidates is a CWs. Both L and R supporters consider other parties to be in their bottom-set, and they follow the strategy that you presented, and bury C candidates under either L or R candidates. It is quite possible that there will be a Smith set that consists of L and R candidates, and CWs is not in this set (since up to 66% of the voters may have buried it).

>  
> 
>> Truncation-proofness is important, even in a sincere electorate, because truncation can be non-strategic (lazy, hurried, principled, etc.).
> 
> Here my medicine would be to educate voters to cast fuller votes (to rank at least the potential winners).
> 
> If you mean "Try to rank down to the CWs", then that's valid strategy for trying to get the best you can (if that's your goal). You could also say "Rank the best candidates.", or "Rank only your strong top-set."

My general guidance would be to rank at least all those candidates that are considered potential winners. I would not call this a strategy but just a warning against casting a weak vote that would not take position on which one of the (maybe two) strongest candidates should win.

>  
> If they truncate for non-strategic reasons, we must assume that their preferences are flat with the rest of the candidates.
> 
> No. Maybe they're in a hurry. Maybe they don't want to bother or take the time, even though they have lower preferences too.
> 
> But there's no point in assuming what you said, because your "If" is, itself, an unsupported assumption. You don't know that they truncated for nonstrategic reasons.

I wanted to say that the method must treat other truncations the same way it treats "sincere truncations".

> 
>  
> It is not possible to tell which voters did that on purpose and which ones by mistake or laziness.
> 
> Quite.
> 
>  
> 
>> The top loop can be sincere as well (or a result of various good and bad strategies). And the best sincere winner might be also outside the Smith set.
>> 
>> Certainly, because it would be possible for the alternative satisfactory to the most people to be outside the Smith set. But probably it will usually be the CWs, or in the sincere Smith set if there isn't a CWs.
> 
> I wouldn't assume anything on the probability of finding the best winner within or outside the Smith set.
> 
> Suit yourself. 
> 
> In all of our EM polls, Approval, Score elected Condorcet's CWv.
> 
> [Replying farther down] :
>  
> With sincere votes that depends on what our criteria for the best winner are (when there is no CWs). With all kind of strategic and lazy votes, the location of the best winner is even more difficult to guess (it is e.g. possible that multiple groups try to bury the CWs).
> 
>>> Note that electing outside the Smith set may sometimes also help us, e.g. by making strategic plans void by not electing the (possibly strongly top-looped) favourite of the strategists.
>>> 
>>> Maybe, but, by pairwise-count standards, electing from the Smith set keeps the winner among the pairwise publicly-favored candidates.
>> 
>> I don't understand your definition of "pairwise publicly-favored candidates". Why can't candidates outside the Smith set be such candidates?
>> 
>> Because, pairwise is what the Smith set is about. Something outside the Smith set might be more approved than the Smith set members, but it won't be pairwise publicly preferred to them.
> 
> I claim that with some pairwise preference based criteria of best winner, the best winner could be outside of the Smith set.
> 
> Yes, evidently some pairwise preference based criteria that aren't about pairwise defeats or their strength. Fine. You have a right to value whatever standards you want to, and use whatever polling methods you want to.

I did not assume any other criteria.

> 
> In polling, my purpose is finding the CWs (there usually is one). 
> 
> But you're free to have entirely different goals & purposes. Go for it!
> 
> [Replyng farther down] :
>  
>  
> No references to approval or range style thinking needed. The simplest example is minmax (seen as a definition of the ideal winner). See comments above.
> 
>> I mean situations where the leading candidate outside the Smith set could lose by one vote to all the Smith set members. Losing only marginally to many candidates could be a better result than losing a lot to fewer candidates.
>> 
>> Sure, that could be argued on ethical grounds. But pairwise defeats are what's important if you want to avoid an angry majority who prefer someone else to the winner.
>> 
>> And the CWs is important to find, in polls, because it's the best that anyone can get (unless they're a good offensive strategist, in an election or poll using a method vulnerable to that strategy).
> 
> Yes, pairwise preferences and CWs are the norm in this discussion. See above.
> 
>>> Of course, in an election, when Approval elects the candidate approved, considered satisfactory by the most people, is probably more important than electing the CWs or from the sincere Smith-set.
>> 
>> Also pairwise comparisons can sometimes lead to situations where best candidate (based on those pairwise comparisons) is found outside the Smith set. (see the marginal loss example above)
>> 
>> Yes. looking at the strength of pairwise oppositions instead of at pairwise defeats. But the pairwise defeats have great importance in regards to finding the best that we can get.
> 
> The simplest is pairwise margins. You could elect the candidate whose worst pairwise margin is least bad, and that candidate could be outside of the Smith set.
> 
> You could do whatever you want to. whatever you think is best. 
> 
> Not everyone would agree with you about the merits of margins. But don't worry about that. Do it the way that you want to.
> 
>  
> Note that I see minmax not only as one of the methods but also as one possible definition of ideal winner with sincere votes (for some society with some set of needs).
> 
>> Many voters would vote sincerely since that's what they believe is the right thing to do.
>> 
>> Voting in way that's more likely to elect someone who won't hurt a lot of people is hardly unethical.
> 
> But a society where nobody cheats is highly ethical :-).
> 
> Offensive strategy isn't cheating. It complies fully with the voting-rules.

Ok, maybe word "cheat" should be defined that way and some other word should be used instead of it.

> 
> All that you've been saying here suggests that you'd be happier with Approval, Score, or Bucklin.  As I said, they're fine methods.

Approval et. are out of scope here, as we both agree. :-)

>  
> 
>> Burying someone in your strong bottom-set doesn't need good predictive information.
> 
> This sounds like you are talking about a society that has been living too long under a two-party rule
> 
> 1. The Democrats & Repugnicans aren't two parties. They're one party with two right wings.
> 
> 2. Parties don't rule in a democracy. The public rule, by electing whom they want to. Of course we don't have democracy. If that's what you meant, then you're quite right. But still, the Democrats & Repubnicans don't "rule". They're pseudodemocratic charade-theater. If you want to find out who rules, then search Google for "Who Rules America, by G. William Domhoff".
> 
> Better idea: Just be glad if you have legitimate democracy.
>  
> , and where things are either black or white,
> 
> You haven't a clue what you're talking about. I reside here. You don't. 

Ok, maybe black and black. :-)

> 
> Progressives vs Repubugnocrats? It doesn't get any more stark "black or white" than that. But you can't be expected to know that.So maybe you shouldn't be telling me about how it really is  :^)
>  
> and where people hate to give up that way of thinking
> 
> You're completely unclear regarding what "way of thinking" you're talking about. The stark difference between progressive candidates, vs Repugnocratic candidates has nothing to do with "way of thinking". It's simple plain fact. But, again, you can't be expected to know that. 

I don't want to make exact claims of any specific society. I just note that people might sometimes visualize the world in a "full spectrum of positive alternatives" way too.

> 
> Maybe you need to not be explaining to me about the country in which I reside. Does it occur to you that that's more than a little pretentious, presumptuous & egotistical on your part?

I don't want to be any more specific than that it appears that there is some criticism in the air, including the two-party dominance related aspects.

> 
>  
> , and where people therefore will use also more civilised methods like ranked methods as if there were only black and white candidates 
> 
> It's ridiculous to say that ranked methods are "more civilized". 

I should have said "methods that allow also more expressive votes".

> 
> As for the candidates here, the Repugnocrats are remarkably consistently uniform in regards to moral character & honesty. The distinction between the progressives & the Repugnocrats is remarkably sharp and ...well...distinct.
> 
> "...as if..." ?
> 
> It really couldn't be any more starkly "black & white" than it is.  
> 
>> Strategy can't do any significant harm if the CWs is in your strong bottom-set.
> 
> True for any method when the sincere winner is in the bottom-set.
> 
> Quite.
> 
> But, as I've said, I doubt that the CWs would be a bottom-set candidate for the 99%. 

Good news :-). That might mean that the bottom-set burial behaviour is not common (at least when there is a CWs).

BR, Juho


> 
> As I said, in Internet polls, the CWv is usually someone like Jill or Bernie, or Nader.
> 
> Now, I'd say that we've both said what we have to say on this matter. I say that, because we've been saying the same things over & over again.
> 
> 
> Michael Ossipoff 
> 
> BR, Juho
> 
> 
> 
> ----
> Election-Methods mailing list - see http://electorama.com/em <http://electorama.com/em> for list info
> 
> 

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