<html><head><meta http-equiv="Content-Type" content="text/html charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div>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?</div><div><br class=""></div><div>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.</div><div><br class=""><blockquote type="cite" class=""><div class="">On 22 Dec 2016, at 07:14, Michael Ossipoff <<a href="mailto:email9648742@gmail.com" class="">email9648742@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><br class=""><div class="gmail_extra">[Replying farther down] :<br class=""><br class=""></div><div class="gmail_extra"><div class="gmail_quote">On Wed, Dec 21, 2016 at 4:36 AM, Juho Laatu <span dir="ltr" class=""><<a href="mailto:juho.laatu@gmail.com" target="_blank" class="">juho.laatu@gmail.com</a>></span> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><blockquote type="cite" class=""><div class="">On 21 Dec 2016, at 05:21, Michael Ossipoff <<a href="mailto:email9648742@gmail.com" target="_blank" class="">email9648742@gmail.com</a>> wrote:</div></blockquote><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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.</div></div></div></blockquote><div class=""><br class=""></div><div class="">MAM is the ideal, among the methods that look only at pairwise-defeats and their strengths, and that comes from MAM's definition:<br class=""><br class=""></div><div class="">MAM:<br class=""><br class=""></div><div class="">A pairwise defeat is affirmed if it isn't the weakest defeat in a cycle whose other defeats are affirmed.<br class=""><br class=""></div><div class="">A alternative wins if it doesn't have an affirmed defeat.<br class=""><br class=""></div><div class="">[end of MAM definition]<br class=""><br class=""></div><div class="">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).<br class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">I look at the world from a somewhat different angle here. I don't see what the relevance of beatpaths is in real life. </div></div></div></blockquote><div class=""><br class=""></div><div class="">Beatpath, not MAM, is defined in terms of beatpaths.<br class=""><br class=""></div><div class="">But maybe you just mean that a cycle can be called a pair of beatpaths in both directions between 2 candidates.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>Yes, sorry, I intended to talk about paths of pairwise losses in general, not one specific way of dealing with them.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">The "relevance of cycles in real life?<br class=""><br class=""></div><div class="">I'll say it again (but I won't continue to keep saying it):<br class=""><br class=""></div><div class="">A pairwise-defeat is voted public preference.<br class=""><br class=""></div><div class="">A cycle renders meaningless the defeats in the cycle. Therefore cycles have relevance.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""> <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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. </div></div></div></blockquote><div class=""><br class=""></div><div class="">You keep repeating that. And then, of course I keep repeating my answer to it (but I won't continue doing so):<br class=""><br class=""></div><div class="">Sure, likely the Approval winner is better than the winner by a pairwise-count method. <br class=""><br class=""></div><div class="">There are 2 reasons to consider a rank-method:<br class=""><br class=""></div><div class="">1. It's possible for a ranking method to provide a convenient, easy & reliable means for avoiding chicken-dilemma.<br class=""><br class=""></div><div class="">2. Many people have a psychological need for rankings.<br class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class="">3. Finding the CWs, via a poll, can be important, because the CWs is typically the best candidate that people can get?<br class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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".</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">Beatpaths </div></div></div></blockquote><div class=""><br class=""></div><div class="">....by which you mean cycles, because you presumably want to call a cycle a pair of opposite-direction beatpaths between 2 candidates.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>Yes. I note that some of my comments on paths apply to non-cyclic paths too.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">seem to serve the need to linearize the opinions of the group</div></div></div></blockquote><div class=""><br class=""></div><div class="">No. Cycles are relevant if pairwise defeats are of interest. A pairwise defeat is a voted public preference.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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".</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">, or to "break cycles", which I think is not in the requirements list of an election or poll. </div></div></div></blockquote><div class=""><br class=""></div><div class="">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. <br class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">That is more like an aesthetic preference, or a mistaken idea that group opinions should be straightened to linear opinions. </div></div></div></blockquote><div class=""><br class=""></div><div class="">If you say so.<br class=""><br class=""></div><div class=""> <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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). </div></div></div></blockquote><div class=""><br class=""></div><div class="">That would depend on your (often referred to but never stated) opinion about what is the target of the election or the best winner.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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).</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">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!<br class=""><br class=""></div><div class="">Or do we all have to abide by your target and your best winner? :^)<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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.</div><div><br class=""></div><div>(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.)</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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. </div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class="">You have a right to do those things! <br class=""><br class="">Go for it!<br class=""><br class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">Also approval and range are easy to explain from the "possible needs of the society" perspective.</div></div></div></blockquote><div class=""><br class=""></div><div class="">So very true.<br class=""><br class=""> <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class="">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<br class=""></div><div class="">P(MAM, Smith,MMPO), for polls with possibly offensive-strategic voters.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">This is about strategic voting</div></div></div></blockquote><div class=""><br class=""><br class=""></div><div class="">Are you sure? :^)<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>Words like "burial" seem to refer to strategic voting scenarios, not to performance with sincere votes.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""> <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">, not about which method is best with sincere votes. </div></div></div></blockquote><div class=""><br class=""></div><div class="">I said that P(MAM, Smith,MMPO) is for electorates in which offensive strategy would be particularly likely, unless deterred or at least thwarted.<br class=""><br class=""></div><div class="">Have we established that yet?<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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).</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">MAM is also very good with sincere voting. MAM is a component of <br class=""></div><div class="">P(MAM, Smith,MMPO).<br class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">Not to be counted in favour of MAM in this branch of discussion.</div></div></div></blockquote><div class=""><br class=""></div><div class="">That MAM is good with sincere votes is to be counted in MAM's favor.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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.</div><div><br class=""></div><div>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.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""><br class=""></div><div class="">[Replying farther down] :<br class=""> <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class="">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.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">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.</div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">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. </div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>Ok, approvals are out.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">And I claim that under these assumptions some methods can easily justify selecting the winner also outside the Smith set.</div></div></div></blockquote><div class=""><br class=""></div><div class="">...because that will make the method more likely to choose the CWs when there is one? :^)<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>That example assumed that there is no CWs.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class="">[Replying farther down] :<br class=""> <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class="">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.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">It is not possible to tell if there was a CWs. </div></div></div></blockquote><div class=""><br class=""></div><div class="">True, but if there is one, then it will win even if there's a truncation-caused cycle.</div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">Also some other member of the Smith set might win. </div></div></div></blockquote><div class=""><br class=""></div><div class="">No kidding? <br class=""></div><div class=""><br class=""></div><div class="">More likely with some methods than others. Choose the manner of selecting from the Smith set accordingly.<br class=""><br class=""></div><div class="">But, primarily, do what <u class="">you</u> want.<br class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">And the CWs could be also outside of the Smith set as a result of strategic voting.</div></div></div></blockquote><div class=""><br class=""></div><div class="">No. <br class=""><br class="">Truncation or burial against the CWs will result in a top-cycle that includes the CWs.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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).</div><div><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class="">Truncation-proofness is important, even in a sincere electorate, because truncation can be non-strategic (lazy, hurried, principled, etc.).<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">Here my medicine would be to educate voters to cast fuller votes (to rank at least the potential winners).</div></div></div></blockquote><div class=""><br class=""></div><div class="">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."<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class=""> If they truncate for non-strategic reasons, we must assume that their preferences are flat with the rest of the candidates.</div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>I wanted to say that the method must treat other truncations the same way it treats "sincere truncations".</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class=""> It is not possible to tell which voters did that on purpose and which ones by mistake or laziness.</div></div></div></blockquote><div class=""><br class=""></div><div class="">Quite.<br class=""><br class=""> <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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.</div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">I wouldn't assume anything on the probability of finding the best winner within or outside the Smith set. </div></div></div></blockquote><div class=""><br class=""></div><div class="">Suit yourself. <br class=""><br class="">In all of our EM polls, Approval, Score elected Condorcet's CWv.<br class=""></div><div class=""><br class=""></div><div class="">[Replying farther down] :<br class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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).</div><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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.</div></div></div></blockquote><div class=""><br class=""></div><div class="">Maybe, but, by pairwise-count standards, electing from the Smith set keeps the winner among the pairwise publicly-favored candidates.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">I don't understand your definition of "pairwise publicly-favored candidates". Why can't candidates outside the Smith set be such candidates? </div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">I claim that with some pairwise preference based criteria of best winner, the best winner could be outside of the Smith set.</div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>I did not assume any other criteria.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">In polling, my purpose is finding the CWs (there usually is one). <br class=""><br class=""></div><div class="">But you're free to have entirely different goals & purposes. Go for it!<br class=""></div><div class=""><br class=""></div><div class="">[Replyng farther down] :<br class=""> <br class=""></div><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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.</div><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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.</div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class="">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).<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">Yes, pairwise preferences and CWs are the norm in this discussion. See above.</div><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class="">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.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">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)</div></div></div></blockquote><div class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">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. </div></div></div></blockquote><div class=""><br class=""></div><div class="">You could do whatever you want to. whatever you think is best. <br class=""><br class=""></div><div class="">Not everyone would agree with you about the merits of margins. But don't worry about that. Do it the way that <u class="">you</u> want to.<br class=""><br class=""></div><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">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).</div><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">Many voters would vote sincerely since that's what they believe is the right thing to do. </div></div></div></blockquote><div class=""><br class=""></div><div class="">Voting in way that's more likely to elect someone who won't hurt a lot of people is hardly unethical.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">But a society where nobody cheats is highly ethical :-).</div></div></div></blockquote><div class=""><br class=""></div><div class="">Offensive strategy isn't cheating. It complies fully with the voting-rules.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>Ok, maybe word "cheat" should be defined that way and some other word should be used instead of it.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">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.<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>Approval et. are out of scope here, as we both agree. :-)</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""> <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class="">Burying someone in your strong bottom-set doesn't need good predictive information.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">This sounds like you are talking about a society that has been living too long under a two-party rule</div></div></div></blockquote><div class=""><br class=""></div><div class="">1. The Democrats & Repugnicans aren't two parties. They're one party with two right wings.<br class=""></div><div class=""><br class="">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".<br class=""><br class=""></div><div class="">Better idea: Just be glad if you have legitimate democracy.<br class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">, and where things are either black or white, </div></div></div></blockquote><div class=""><br class=""></div><div class="">You haven't a clue what you're talking about. I reside here. You don't. <br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>Ok, maybe black and black. :-)</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">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 :^)<br class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">and where people hate to give up that way of thinking</div></div></div></blockquote><div class=""><br class=""></div><div class="">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. <br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">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?<br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>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.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class="">, and where people therefore will use also more civilised methods like ranked methods as if there were only black and white candidates <br class=""></div></div></div></blockquote><div class=""><br class=""></div><div class="">It's ridiculous to say that ranked methods are "more civilized". <br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>I should have said "methods that allow also more expressive votes".</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class="">"...as if..." ?<br class=""></div><div class=""><br class="">It really couldn't be any more starkly "black & white" than it is. <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class=""></div><span class=""><div class=""><br class=""></div><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class="">Strategy can't do any significant harm if the CWs is in your strong bottom-set.<br class=""></div></div></div></div></div></blockquote><div class=""><br class=""></div></span><div class="">True for any method when the sincere winner is in the bottom-set.</div></div></div></blockquote><div class=""><br class=""></div><div class="">Quite.<br class=""><br class=""></div><div class="">But, as I've said, I doubt that the CWs would be a bottom-set candidate for the 99%. <br class=""></div></div></div></div></div></blockquote><div><br class=""></div><div>Good news :-). That might mean that the bottom-set burial behaviour is not common (at least when there is a CWs).</div><div><br class=""></div><div>BR, Juho</div><div><br class=""></div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><div class=""><br class=""></div><div class="">As I said, in Internet polls, the CWv is usually someone like Jill or Bernie, or Nader.<br class=""><br class=""></div><div class="">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.<br class=""><br class=""></div><div class=""><br class=""></div><div class="">Michael Ossipoff <br class=""></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class=""><div class=""><br class=""></div><div class="">BR, Juho</div><div class=""><br class=""></div><div class=""><br class=""></div></div></div><br class="">----<br class="">
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