[EM] Independence from Clones, and Condorcet//FPP criterion failures

[Michael Ossipoff]

Kristofer:

You said:


On to some criterion failures:

If there is no truncation or no equal-rank, then (I've been told) ICT is
equal to Condorcet//FPP. Hence, finding an example where Condorcet//FPP
fails independence from clones with no equal-rank or truncation suffices:

[endquote]

Correct.

You said:

	70: A > B > C
	68: B > C > A
	66: C > A > B

	There's no CW, so A wins.

	Now clone A into A1 and A2:

	35: A1 > A2 > B > C
	35: A2 > A1 > B > C
	68: B > C > A1 > A2
	66: C > A2 > A1 > B

	Now B wins. Cloning A made A lose (or B win).

[endquote]

Approval and ICT don't have Plurality's split-vote problem. The
A-preferrers can equal-top-rank A and A2. I assume that you're adding
a new candidate, A2, who is a clone of A.

If they top-rank both A and A2, then there won't be a split vote. A
and A2 will still have higher top-count than the other candidates.

If this A2 that you've added is so much better than A, as judged by
the A voters, that they decide to top-rank A2, but no longer top-rank
A, how bad is that really? You've offered them something better, more
optimistic, and it trying for it has changed their perceived optimal
strategy.

Remember, you were asked to show an improvement by traditional
unimproved Condorcet (TUC) methods, such as Beatpath, that is so
important that it outweighs the loss of FBC and CD compliance (for
comparison to ICT), or FBC, CD and zero-info LNHe (for comparison to
Symmetrical ICT), or FBC, LNHe, Participation, Consistency and IIAC
(for comparison to Approval and Score).

So that's the best that you can do?

That means that this clone problem that you speak of must be so bad
that it's more important than failure of FBC and CD, or FBC, CD and
zero-info LNHe, or FBC, CD, LNHe, Participation, Consistency and IIAC.

Purpose and advantage of ICT's top-count:

Because, when that Condorcet completion is applied, the method only
looks at top-count, then effectively, in the A,B,C chicken dilemma
example that I've spoken of, the A voters are withdrawing their
support for B. That deters chicken-dilemma defection by B-preferrers.

In order for for the B voters to be confident in the safe success of
burial, or of chicken-dilemma defection, they must know that B has the
largest top-count (whether or not it's because A and C have been
cloned, with their supporters choosing to split the top-count vote).

If cloning A and C, with suitable voting decisions by their
preferrers, could spoil ICT's chicken-dilemma deterrence, remember
that Beatpath doesn't have any defection-resistance to begin with.
Beatpath, like the other TUC proposals, fails CD.

Let's clarify that Approval, Score, ICT and Symmetrical ICT don't have
Plurality's split-vote problem. If a clone of candidate A is added,
A2, then the A preferrers can approve or top-rank both A and A2 if
they want to. Of course maybe they'll find A2 to be so much better
than A, that they'll no longer approve or top-rank A.

In Beatpath, if A2 is added as a clone of A, and the A preferrers
decide to rank A2 in 1st place and A in 2nd place, are you saying that
that can't change the winner from A to someone other than A or A2,
because of how the clone-set definition says other people must vote
for A and A2?

If so, that's nice, but, regrettably, in real life, you won't know if
candidates are clones. Beatpath, and the other TUC proposals, are a
strategic mess, as I've described, even in a u/a election.

Isn't it more than a little irresponsible, to propose a method whose
optimal strategy wouldn't be known, even in a u/a election?

And some other failures while I'm at it:

You said:


Reversal symmetry:
	1: A>B>C
	1: C>B>A
	1: B>A>C
	1: C>A>B

	There's no CW and reversing every ballot leads to the same ballot set.
Hence, the outcome must be A=B=C (since the method can't distinguish
between this set and its reverse), but C has a Plurality count of 2 and
thus wins.

[endquote]

Remember, we're looking for a problem that outweighs the TUC
disadvantages that I listed above. Do you really consider that one a
serious problem?

Sure, as with other popular criteria, it would make sense to comply
with it. But, as you know, a method can't comply with every criterion,
and so one must choose, based on which seems more important.

Reversal Symmetry comes under the heading of an embarrassment
criterion, a consistency criterion about a method contradicting
itself. Certainly TUC violates enough of those. (...such as
Participation, Consistency and IIAC).

TUC advocates forgive failure of FBC, CD, LNHe, 0-info LNHe,
Participation, Consistency and IIAC, but they draw the line at
Mono-Add-Plump and Plurality (complied with by Approval, Score, ICT
and Symmetrical ICT, along with TUC), and Reversal Symmetry and Clone
Independence (at least if their favorite TUC version passes them).
Could it be that we're being a bit self-servingly selective?

You continued:

Condorcet loser, majority loser, mutual majority, Smith, Schwartz,
Landau, others?:

[endquote]

The Condorcet Criterion, Condorcet Loser, MMC, Smith, and Schwartz
lose their meaning and value when voters experience the
preference-distorting strategy needs of methods that fail FBC and CD


	2: A>B>C>D
	2: B>C>A>D
	3: D>C>A>B


You said:

Independence from Smith-dominated alternatives:

[endquote]

So, because traditional unimproved Condorcet (and Condorcet methods in
general) fail IIAC, you fall back on weakenings of IIAC. And if your
method fails IIAC, but meets a weakening of it, then you can say,
"_This_ is the one that's important."

If such criteria are important to you, then I recommend Approval and Score.

You said:

Mono-add-top, Participation:
	
[endquote]

Beatpath and other proposed traditional unimproved Condorcet (TUC)
versions likewise fail Mono-Add-Top and Participation.

Because TUC fails Participation, there's no reason to even evaluate it
by the stronger Mono-Add-Top. TUC fails even the easier-to-meet
Partilcipation.

As I've said,  I don't propose any rank method for official public
elections. For that, I recommend only Approval and Score.

Approval and Score meet Mono-Add-Top, Participation, Consistency, FBC,
LNHe, and IIAC.

TUC fails all of those criteria.

Symmetrical ICT meets FBC, CD, and 0-info LNHe.

Beatpath and other TUC proposals fail all of those.

And if Reversal Symmetry were generalized to methods other than rank
methods (so that it would apply to such methods), as it could be, then
Approval and Score would meet it too.

And didn't someone suggest a criterion called "0-info Sincerity"?

I assume that it says that optimal strategy in a 0-info election
should be sincere.

Approval passes it, but TUC fails it.

...unless it's one of those criteria written to lexicographically
apply only to rank methods.

Mike Ossipoff