[EM] Juho: Symmetrical ITC vs [what?].

[Michael Ossipoff]

I accidentally lost the original subject line. That's ok, because it
doesn't well describe this discussion. So I've substituted a more
descriptive subject-line.

This is part 1 of a 2-part reply.

I'd said:

>> You're the one who wants to use the notion of "the best winner with
>> sincere votes". Odd that you need to ask me to describe your ideal
>> sincere winner. If you want to object that ICT and SITC don't choose
>> the ideal sincere winner well enough, then you're the one who needs
>> to say what you mean by "the best winner with sincere votes".
>
You said:

> Note that my opinion is that different elections may have different criteria. I mentioned one possible criterion of the best winner as an example, but that need not be your target (or not in all elections). You could also in principle declare the operative definition of ICT or SITC as the definition of an ideal winner (with sincere ballots), but I'd have some doubts on the genuineness of that claim since I believe that those methods have some strategy defence flavour embedded in them, and it doesn't sound probable that the strategy defence algorithms and ideal winner definition would coincide. If you pick some other definition of ideal winner, then it is obvious that ICT and SITC sometimes deviate from that ideal.

[endquote]

What did I just say in the passage that you quoted above? I don't
claim to have an ideal sincere winner. As I just finished saying, it
is only you who are making reference to one. Therefore, you, not I,
are the one who needs be specific about what you think the ideal
sincere winner is.

You're speculating that Symmetrical ICT (SITC) won't do well by that
(as yet unknown &/or unspecified ideal sincere winner, because SITC
was chosen for its strategic properties.

But, as I explained before (I shouldn't have to repeat it), SITC
elects the legitimately defined  CW for precisely the same reason as
it passes FBC: It respects the preferences, intent, and wishes of a
voter who ranks 2 or more candidates at top.

I asked you what methods you think choose the ideal sincere winner
better than SITC does. You said that you don't support unimproved
Condorcet. But then, later, maybe in the same post, you cited Dodgson
and Beatpath as methods that you seem to be endorsing or advocating as
methods that do better than SITC, with regard to the ideal sincere
winner.

Dodgson and Beatpath are unimproved Condorcet. For one thing, you said
you don't support unimproved Condorcet. For another thing, unimproved
Condorcet the fails legitimately-defined Condorcet Criterion.   ...The
fail to elect the legitimately-defined CW.

As I said, a CW is widely agreed to be a good choice, and that's no
less true under sincere voting.

Legitimately, SITC's Condorcet efficiency is 100%. That isn't true of
Dodgson and Beatpath.

Candidates who pairbeat all the others tend to do well at social
utility (SU). In fact they tend to be SU maximizers.

And what about when there is no CW? Well, electing the most favorite
of of all the candidates, or of the unbeaten candidates wouldn't be
bad for SU. It certainly sounds like a more obvious good SU choice
than Dodgson or Beatpath's choice, when improved and unimproved
Condorcet have different CWs, or when neither finds a CW.

Therefore, there is no reason to believe or expect that SITC wouldn't
make a good choice under sincere voting. There's good reason to
suggest that Dodgson, Beatpath, and any unimproved Condorcet, doesn't
choose as well as SITC, under sincere voting.

But, as I explained in my previous post, you haven't told us what
exactly you want in the way of an ideal sincere winner, or what method
you think would choose it better than would SITC. (If you're sure you
want to commit yourself to Dodgson or Beatpath, then say so
unambiguously.)

Nor did you answer my question about the chicken dilemma. You say that
people won't favorite-bury, or you think they won't, or you think they
might not...in most societies or in many societies. (I'm more
concerned with how they vote here, however.)  Will they, too, not have
the chicken dilemma, even when using a voting system that is subject
to that problem? Because, otherwise, unimproved Condorcet will give
that problem to voters. That includes Dodgson and Beatpath.

Basically, you haven't answered any of my questions. You're just
repeating statements that I've already answered.

>
>>
>> But, with all sincere ballots, many like the idea of electing the CW:
>> The candidate who pair-beats each of the others, when such a candidate
>> exists. When "CW" is legitimately defined, when equal top and equal
>> bottom ranking are interpreted consistent with the preferences, intent
>> and wishes of people voting in that way, then SITC elects the CW.
>> Beatpath, VoteFair, and all unimproved Condorcet methods fail to elect
>> the legitimately-defined CW.
>>
>> So, there is a popular "ideal sincere winner": the CW.
>
> CW could indeed be part of the definition. All Condorcet methods would be partially ideal (i.e. when there is a sincere CW).

...except that unimproved Condorcet doesn't respect voters'
preferences, intent or wishes when choosing its "CW".  SITC does.

>> You see, what you're missing is that the same disregard for voters
>> preference, wishes and intent tha makes unimproved Condorcet fail FBC,
>> also makes it fail the legitmately-defined Condorcet Criterion, and
>> fail to elect the legitimately-defined CW.
>>
>> So, meeting FBC doesn't require some sort of violation of the choice
>> of ideal sincere winner. On the contrary, it comes with the election
>> of the ideal sincere winner, because both gains come from respecting
>> the voters' intent and preference.
>
> Do you mean that the voter should help e.g. by falsifying her sincere preferences by voting some candidates tied at top? :-)

Is that what I said?  If you look at the quoted passage, you'll find
that I said nothing about how the voter should "help".

I refer you to that paragraph written by me, the paragraph that you
quoted directly above. I meant what I said, and nothing else.

And as I explained before, SITC respects equal top ranking voters
preference and intent better than unimproved Condorcet does,
regardless of whether their equal top ranking is sincere or strategic.

>>
>> So that's your best argument: That, because SITC meets FBC, there must
>> be a method (unspecified by you) that does better under sincere
>> voting.
>>
>> The reason why you don't specify a method that does better than SITC
>> under sincere voting is because you don't even know what a method
>> should do under sincere voting. You ask me to describe the ideal
>> sincere winner, because you don't have any idea what the ideal sincere
>> winner should be.
>
> True in some sense. But if you allow me to define the sincere winner for you, and for your >election, you could take my example definition and compare it to SITC.

Right. So you can make irresponsible statements, and never be
contradicted or shown wrong, as long as you don't divulge what it is
that you mean.

> That could be valid for some needs. There is a difference between those two definitions.

What two definitions would those be?

>>> There are different best methods for different needs.
>>
>> Translation: You can't name one.
>
> I already named one (see two lines below).
>
>>
>> You said:
>>
>>> (In my text above I asked you to provide a definition of the best candidate. A simple Condorcet oriented definition could be e.g. "the candidate that requires least additional support/votes to beat any of the other candidates in a pairwise comparison/battle should be elected". This target could be selected because it gives one rational argument why the winner could be able to rule well (= only little bit of additional support needed (if any) to gain majority support for his proposals while in office).)

Ok, you've referred to Dodgson. Earlier in this post, I told why
Dodgeson doesn't do better, and arguably doesn't do as well, as SITC.

Dodgson's CW is illegitimate, for the reasons I've described. The
choice of circular tie solutions is arbitrary, when it comes to "ideal
sincere winner". Ideal sincere winner matters most when there's a CW.
SITC's choice, when there isn't exactly 1 unbeaten candidate, looks at
favoriteness. That's difficult to criticize or argue with, especially
in regards to SU, when there's no CW.

There's no particular reason to believe that Dodgson's circular tie
solution would do especially well by SU, under sincere voting.

Is that the best argument you have? Some sort of arbitrary quibble
between circular tie solutions?

>> [endquote]
>>
>> That sounds like Dodgson. Sure, it can be justified as you say.
>
> That was supposed to be equal to Minmax(margins).

Well, it sounds more like Dodgson. But that's ok, because what I said
applies to MinMax(margins) as well.

MinMax(margins) looks at the biggest defeat. Dodgson looks at the
number of pairwise preferences that would have to be changed in order
to make your candidate the CW. Those are two different considerations.
You explicitly referred to the one that is Dodgson.

But, as I said, it doesn't matter, because what I said applies just as
well to MinMax(margins).


>>
>> You want to elect the best winner under sincere voting. Is that what
>> you claim is the best winner under sincere voting (ideal sincere
>> winner)?
>
> That could be the definition for some needs.

Ok, so you say that Dodgson is sometimes the best--except that now
maybe it's MinMax(margins) instead.

Then you need next to show that Dodgson (or is it MinMax(margins)?) is
indeed better than SITC, with regard to ideal sincere winner, "for
some needs". Then you need to show that those needs are socially
important and frequently needed.

>>
>> You described a circular tie solution, for when there's no CW. And
>> presumably the CW that you'd choose would be the traditional (as
>> opposed to legitimate) one.
>
> That definition covers also the CW (= no additional support needed).

Your specification doesn't define "CW", but I'm assuming that you're
using the traditional, illegitimate, definition.
I'm referring to your circular-tie solution specification that amounts
to Dodgson.

>>
>> For another thing, everyone agrees that the election of the CW under
>> sincere voting is a lot more important than how you choose when there
>> _is_ no CW. So the circular-tie-breaker isn't so important.
>
> Maybe that is your definition.

That isn't a definition. And no, it isn't only my statement. It's
widely agreed that choice under sincere voting matters a lot more when
there's a CW.

You said:

Maybe you mean that all candidates are equally good if there is a top loop.

[endquote]

If I'd meant that I'd have said it. I meant what I said.

But yes, if there's a top-cycle, the choice, under sincere voting, is
less important, as compared to when there's a candidate who pairbeats
each of the others.


You said:

In that case the ideal method would be one that picks a random
candidate if there is no CW.

[endquote]

Go for it. Propose such a method. But I didn't say that would be the
ideal method. I merely said that, under sincere voting, the choice
doesn't matter as much when there's no CW.


You asked:

 (Or do you want to limit the lottery to a smaller set of candidates?)

[endquote]

If you're asking about SITC's rules, here they are:

1. If exactly one candidate is unbeaten, then s/he wins.

2. If everyone or no one is unbeaten, then the winner is the candidate
top-ranked on the most ballots;

3. If some but not all, candidates are unbeaten, then the winner is
the unbeaten candidate who is top-ranked on the most ballots.

I've defined SITC's definition of "beats" for you, in a previous reply.

You'd said:

>>> A method that has been modified to cope with strategies does not elect the ideal sincere winner > always.
>>

I'd replied:

>> Does any method? You don't know, because you don't know what an ideal
>> sincere winner would be.
>

You now reply:

> Take my example definition above.

So you're now saying that Dodgson (the method you specified there)
always chooses the ideal sincere winner.

For one thing, I claim that Dodgson is based on an illegitimate
definition of "CW".

For another thing, there's no particular reason to believe that
Dodgson's circular tie solution is necessarily the ideal sincere
winner, under sincere voting.

As I said, circular tie solutions are quite arbitrary under sincere
voting. There's no reason to believe that Dodgson's circular tie
solution does particularly well by SU. There's no reason to expect it
to do as well as SITC's solution when there isn't exactly 1 unbeaten
candidate.


>>> See my first comments above. Their deviation from the ideal should become visible after one defines the ideal sincere winner.
>>
>> Ok, let's define the ideal sincere winner as the legitimately-defined
>> CW.
>
> This would be another partial definition.

And, by it, Dodgson and Beatpath choose the ideal sincere winner less
often than does SITC.

>>>
>>>> Because I don't know what method you're referring to, of course
>>>> there's no way to answer your expression of belief.
>>>
>>> I referred to basic Condorcet methods. (Ranked Pairs, MInmax,...)
>>
>> And remember that unimproved Condorcet also has the chicken dilemma.
>> You said that you don't think that people would favorite-bury. I've
>> answered that amply, but do you also believe that there will be no
>> chicken dilemma?
>
> Condorcet methods are not very prone to that.

That's where you're wrong. Look at the chicken dilemma examples.
Unimproved Condorcet methods have the chicken dilemma as much as
Approval has it. That's why I say that they don't improve
significantly on Approval. The chicken dilemma is the nearest thing to
a "problem" that Approval has (though it isn't really a problem).But,
though it isn't really a problem, you don't significantly improve on
Approval unless you get rid of it.


>
>> Because, if the chicken dilemma will happen, then it
>> will happen in unimproved Condorcet, because unimproved Condorcet has
>> the chicken dilemma. SITC doesn't have the chicken dilemma.
>>
>> Your talk of sincere voting loses even what relevance it had before,
>> when I remind you that unimproved Condorcet has the chicken dilemma.
>
> What claim are you referring to and what is the problem with it?

The text from me that you quoted made no reference to a claim.

But you'd claimed that favorite-burial won't be a problem (but, when
pressed, you become entirely vague about where it won't be a problem).
 So I asked you if you think that the chicken dilemma, too, won't be a
problem in most societies or in many societies, or wherever you're
referring to.

Someone claimed that unimproved Condorcet is better than Approval, by
the chicken dilemma, because if A and B voters rank sincerely, the
larger faction will win. But Approval can accomplish something
similar, if both factions rate eachother's candidate at .99 max.

No, unimproved Condorcet fully has the chicken dilemma.

(to be continued)

Mike Ossipoff