[EM] Sincere methods

[Juho Laatu]

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 can
> really 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