Hello Kevin,
On Apr 16, 2005, at 06:21, Kevin Venzke wrote:
If approval is chosen as the SVM => B should win. If margins is chosen
as the SVM => A should win. If wv is chosen as the SVM => B should win.
Yes. But my point was that you don't seem to offer much guidance as to what an "ideal" winner could or should be.
Ok. I should give rationale for each SVM. I think towards the end of my previous mail I explained my reasoning why minmax(margins) can be seen to be a SVM. Approval is quite natural, the most approved wins. Winning votes I can't explain well enough (quite close to but not enough) to call wv methods SVMs. Same with path based cycle breaking methods. I also somewhere listed "background targets" like intention to elect the most non-hated, most stable, most powerful candidate, one with fanatic supporters etc. And in the end it is a task to all voting method enthusiasts to identify new SVMs and explain why they are SVMs.
I'm not sure you answered my question. I didn't understand why naturalness
suggests suitability as an SVM. All you said relevant to this is that SVMs
are natural by definition. Do you mean that naturalness is all it takes to
be an SVM?
I had difficulties answering your question since the answer seems so "natural" to me. My logic is just based on my way of seeing the world. I guess I believe that those methods that are good, fair etc. are also understandable and therefore what is a SVM must appear natural to people. There may be SVM that nobody has yet found and therefore nobody finds them natural, but when someone identifies them, according to my theory then this method must appear natural to the finder.
What if I invented a method, not natural or intuitive at all, involving
many calculations, which, when fed votes guaranteed to be sincere, produced
a superb winner 100% of the time? Could this be an SVM?
Yes, as long as you are able to bridge the long gap and explain to yourself why the many calculations produce the superb winner.
From this explanation it sounds like you think the only people who canreally revolt are those not matched by the opposition numbers; i.e., the
voters constituting the margin. In other words you suppose that when A
is elected, only 2 B>A voters can cause any trouble, since the other 49
can be restrained by corresponding A>B voters. I think that is a little
silly.
Yes, a bit silly from one viewpoint. That is maybe the most obvious problem of my reasoning. One alternative (maybe more natural) explanation would be to count the total number of people who think that the winner is not the best possible. This explanation actually points out that plurality can be seen as a SVM. (The candidate with most first positions in ranked ballots meets that requirement.)
If one wants to see that "weakest pairwise opposition margin" explanation in a positive light, then one may think that each candidate corresponds to some alternative policy. There are thus as many policies as there were candidates. In this situation one would compare these policies every day in a similar manner as one compared candidates on the election day.
There are thus many potential SVMs and they may provide natural solutions to different election situations. It is up to the electing community to pick the best rationale and corresponding SVM (and practical voting method if the SVM is e.g. too vulnerable to strategies). It may be that sometimes no SVM is identified and one jumps directly to picking the best PVM (to me this approach is not as nice as the first one but certainly very common in real life, and may lead to a stable situation after people "fall in love" with their current "own" voting method).
So, what criterion is not a sincere criterion? Smith?
I think most criteria that people use are sincere and natural in the normal meaning of these words in English. But the definition of "sincere criterion" covers only cases where these criteria are aimed at electing the best winner based on sincere votes. I exclude thus for example those criteria that aim at pointing out which voting methods are strategy resistant.
Smith is a special case to me as I have explained. I believe most people believe that it is intended to pick the best candidate (based on the sincere votes), thus it is in line with that part of the "sincere criterion" definition. But I find it a valid requirement only in 99% of the cases. So I have not included it in the list of my sincere criteria. Sincere in its English meaning => sure Smith is sincere; sincere criterion => good intention in the right direction at least; valid sincere criterion to someone => certainly; valid SC to me => no, at least not for all Condorcet based SVMs since some important ones like minmax(margins) provide good results without respecting Smith.
I say above that sincere criteria have a strategic justification, not
because they "defend the correct winner," but because they relieve supporters
of the "correct winner" of having to vote in specific ways to get what
they want.
Ok. This sounds good.
MinMax(pairwise opposition),
but it has problems: It fails Condorcet, Smith, Majority, Plurality, and Clone-Winner.
"upgrade" to MinMax(wv)
But we still fail Smith, Majority, and Clone-Winner. We could use Schulze(wv)
to fix those.
I should study more to comment. I still find minmax(margins) a nice SVM. As I told, I don't require Smith. Clone problems I should check.
Hmm, I still don't understand this. I can understand if "naturalness" is a
prerequisite to being an SVM. But what does "immunity to munity" have to do
with it?
Well, if by "naturalness" you mean "intuitiveness" or "ease of understanding,"
then I can see that a method could be justified using those reasons.
Yes, this latter comment is in line with my thoughts.
49 A 24 B 27 C>B
True. I guess we are talking about the Smith set.
No, since all three of those candidates are in the Smith set. I'm talking
about the principle which says (among other things) that if there is only
one majority-strength decision, such as B>A, then you can't elect A.
Ok, now I understand which rule we are talking about. I think majority-strength decision could be a requirement in some SVM, but I think there are also SVMs that do not respect this criterion. I guess it depends on what kind of solution the society is looking for.
Ok. My view is that Smith is important for clone reasons. It seems like
a problem that in MinMax methods, votes for similar candidates, by the same
voters, can cause all of those candidates to lose, and cause a candidate to
win who pairwise didn't win any contests.
Interesting comments. Do you refer to the case where e.g. one party members intentionally vote a loop for the candidates of competing party. This is in my mind one of the worst threats against minmax. This is because individual voters can do that quite autonomously (only direction of loop agreed by all) and it doesn't include risks, it just makes the position of the competing party worse. The latter part of your comment is also interesting although I don't agree. I think it is ok to elect e.g. the Condorcet loser if all the other alternatives are even worse (typically a very strongly looped Smith set).
I don't know what you mean by "true clones." A method that chokes on "fake
clones" will also choke on "true clones" since it can't tell the difference.
With true clones I meant situation where one party has set several candidates (that appear next to each others in all votes) and it would have had also the possibility of setting only one candidate. Fake clones would be ones that are always grouped but just by accident.
I hear you saying that you don't know whether clone independence is a
"natural" concept. Am I right? Because whether clone independence is a natural
concept or "sincere criterion" is a matter of opinion, and of no practical
importance.
Clone independence sounds quite natural to me, so it can be used as a sincere criterion. But I'm not ready to say that it should always be respected. Close to but not quite. I'm still checking e.g. if it is like the Smith set that I think is right most of the time but not always.
Clone independence has also some strategic flavour in it since it talks about candidate setting strategies (ability to set multiple candidates without risks) (and not that much about which one of the candidates is the best).
It's not interesting to have a discussion with you about Smith or
clone independence if you're not talking about practical methods that could
actually be used.
I didn't get this. I'm talking about SVMs and PVMs. SVMs describe what we want. PVMs are the ones that can be actually used. I'm hoping that in many cases SVMs (could be PVMs and) and could be used in real elections. To me elections that would focus on electing the best candidate would be a bigger joy to participate than elections that use PVMs that are far from any SVM.
The thing that would change this, is if you want to argue that sometimes
Smith or clone independence causes a worse candidate to be elected. But I
don't think that's what you're saying.
Actually I do. I don't know the clone world well enough to say anything on that but I can make a claim on the Smith set. My claim is that minmax (margins) is a SVM. It may choose a candidate outside the Smith set. And I claim that in line with the "sincere minmax (margins) philosophy" it makes the right choice. And the reasoning is that if the defeats between the Smith set candidates are worse than the defeats of the candidate outside of the Smith set (to the Smith set candidates), then the non Smith set candidate is the least bad of the mentioned candidates. In this case the non Smith set candidate needs least additional votes to become a Condorcet winner.
The claim above thus says that Smith + minmax (margins) sometimes makes worse decisions than minmax (margins).
(Hmm, I feel happy that we got at least one claim that hopefully has a good grip in the sense that it is easy to force people to either agree or disagree with it :-). Too many of my earlier comments were just viewpoints etc.)
Best Regards, Juho
---- Election-methods mailing list - see http://electorama.com/em for list info
