[EM] Symmetrical ICT can work as intended, and meet Later-No-Help.

[Michael Ossipoff]

On Fri, Oct 12, 2012 at 9:09 PM, Jameson Quinn <jameson.quinn at gmail.com> wrote:
>
>
> 2012/10/12 Michael Ossipoff <email9648742 at gmail.com>
>>
>> It's easily fixed.
>>
>> To the definition, after the line
>>
>> X beats Y iff (X>Y) + (X=Y)B > (Y>X) + (X=Y)T...
>>
>> insert:
>>
>> ...except that two candidates can't beat eachother. If the above line
>> would have two candidates beat eachother, then one of them beats the
>> other. The one that beats the other is the one who is ranked over the
>> other on more ballots than vice-versa.
>>
>
> So the only way this is different from Condorcet...

It doesn't differ from Condorcet. It is a Condorcet method. ...an
improved one. Hence the name "Improved Condorcet".

Improved Condorcet (including ICT, Symmetrical ICT as I now define it,
and the previous Symmetrical ICT that didn't work) differs from
unimproved Condorcet in regards to the two terms, in the above-quoted
beat-condition, that are not present in unimproved Condorcet.

ICT and Symmetrical ICT differ in that ICT doesn't use the "+(X=Y)B" term.

To say it in a different way, Improved Condorcet differs from
unimproved Condorcet by respecting the preferences, intent and wishes
of an equal-top or equal-bottom ranking voter. I've justified that
statement here at EM, but upon request I'll repeat the justification.

> is if two candidates don't
> beat each other in either direction?

Not at all. See above, for the difference between improved and
unimproved Condorcet..

But the difference between Symmetrical ICT as I define it now, and the
previous Symmetrical ICT that didn't work, is in regards to situations
where the above-quoted beat-condition says that X and Y both beat
eachother. The previous Symmetrical ICT recorded them both as beaten
thereby. Symmetrical ICT as I define it now doesn't label both
candidates as beaten due to that beat-condition saying that they both
beat eachother. Symmetrical ICT as I define it now has an
exception-clause that follows that beat-condition. That clause
specifies that two candidates can't beat eachother, and specifies
which candidate beats the other when the beat-condition statement says
that they both beat the other.

By the way, I'm going to have to withdraw my claim that Symmetrical
ICT as I now define it meets Later-No-Help. Because you can't make two
unranked candidates beat eachother, I don't suppose LNHe is still
complied with. But it's really as good as if it were.

Though it doesn't strictly meet the letter of LNHe:

When you don't rank two unacceptable candidates, you're still doing
everything that you can to ensure that one of them will be beaten.If
you rank one of them, you're only doing all that you can to ensure
that a particular _one_ of them is beaten--the one that you didn't
rank. But you're doing more to ensure that, if one of them is beaten,
it will be the unranked one.  ...and maybe the unranked one is the one
who has more 1st rankings than do the acceptable candidates. That's
why I withdraw the claim that Symmetrical ICT meets LNHe.

But that involves information that you can't really know, and so
strategic ranking of unacceptables won't be called-for.

And, for one thing this isn't associated with a psychologically
entrenched strategy-tendency like lesser-evil giveaway. For another
thing, we're only talking about bottom-end strategy, which is much
less important.

But, in that regard, Symmetrical ICT guarantees something that
unimproved Condorcet doesn't guarantee:

By not ranking some two candidates, you're doing everything you can to
ensure that one of those two will be beaten. In spite of LNHe-failure,
there's really no need to rank unacceptable candidates in a u/e
election.

In contrast, unimproved Condorcet's u/a strategy calls for ranking the
unacceptable candidates in reverse order of winnability, because
otherwise you're not contributing to any of them being beaten by other
unacceprables.

Because that isn't needed in Symmetrical ICT, Symmetrical ICT has
effectively as simple a u/a strategy as do Approval and Score. More
so, really, because chicken dilemma is automatically avoided.

But the important difference between improved and unimproved Condorcet
is Improved Condorcet's FBC compliance and unimproved Condorcet's FBC
failure.

That's the most important property-gain with Improved Condorcet, in
comparison to unimproved Condorcet.

But ICT and Symmetrical ICT also automatically avoid the chicken
dilemma nuisance. Because the chicken dilemma can keep you from
supporting your 2nd choice, it's a nuisance that is more important
than LNHe.

As I've said, the chicken dilemma nuisance, though not an actual
problem, is the nearest thing to a problem that Approval and Score
have. Any rank method that doesn't get rid of the chicken dilemma
doesn't improve significantly on Approval and Score. Therefore,
there's no reason to bother wih any rank method that doesn't get rid
of the chicken dilemma...and meet FBC.

Summarizing the differences between Symmetrical ICT and unimproved Condorcet?:

FBC, chicken dilemma, and the matter of whether or not you need to
rank the unacceptable candidates in reverse order of winnabililty, as
opposed to just not ranking any of them.

(I"d like to clarify that, from now on, when I say "Symmetrical ICT",
I'm referring to Symmetrical ICT as I define it now.

I've recently asked the advocates of unimproved Condorcet (such as
Beatpath, Ranked-Pairs, River, Goldfish, Kemeny, VoteFair, etc.) what
advantages or desirable properties unimproved Condorcet has, that
outweigh its disadvantages in comparison to ICT and Symmetrical ICT.

I've also asked advocates of unimproved Condorcet what advantages or
desirable properties it has that outweigh its disadvantages in
comparison with Approval and Score.

Of course the Condorcet Criterion is an answer to the latter question.
But Condorcet Criterion compliance only means something if the worst
strategy-needs are avoided, as they are in ICT and Symmetrical ICT. I
suggest that unimproved Condorcet can't claim the Condorcet Criterion
as an advantage, because unimproved Condorcet often won't have the
benefit of the Condorcet Criterion, because many people will need to
do other than rank sincerely.

Approval's and Score's advantages in comparison to unimproved Condorcet are:

FBC
LNHe
And, because of those, Approval and Score have the simplest and
easiest u/a strategy:

In Approval, rank the acceptable candidates, and none of the
unacceptable candidates.

In Score, top-rate the acceptables and bottom-rate the unacceptables.

Mike Ossipoff