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

[Juho Laatu]

> On 21 Dec 2016, at 05:21, Michael Ossipoff <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. 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. Beatpaths seem to serve the need to linearize the opinions of the group, or to "break cycles", which I think is not in the requirements list of an election or poll. That is more like an aesthetic preference, or a mistaken idea that group opinions should be straightened to linear opinions. 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). 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. Also approval and range are easy to explain from the "possible needs of the society" perspective.

> 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, not about which method is best with sincere votes. Not to be counted in favour of MAM in this branch of discussion.

>> 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. And I claim that under these assumptions some methods can easily justify selecting the winner also outside the Smith set.

>> 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. And the CWs could be also outside of the Smith set as a result of strategic voting.

> 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 they truncate for non-strategic reasons, we must assume that their preferences are flat with the rest of the candidates. It is not possible to tell which voters did that on purpose and which ones by mistake or laziness.

> 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. 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. 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. 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 :-).

> 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, and where things are either black or white, and where people hate to give up that way of thinking, and where people therefore will use also more civilised methods like ranked methods as if there were only black and white candidates (not meaning race here). :-)

> 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.

BR, Juho


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