On 10/27/2012 08:39 PM, Michael Ossipoff wrote:
Kristofer:
You complied with two of my requests:
I'd asked for a precise definition of Clone-Independence, and you posted one.,
I'd asked for a failure-example, and you posted one.
But that wasn't all that I'd asked for, was it.
I'd also asked for an explanation of why that critrerion failure is an
acutal problem.
In other words, I'd asked you to show a clone problem for Approval,
Score, ICT or Symmetrical ICT.
You didn't do that.
Of course there isn't a clone problem for those four abovementioned methods.
In your ICT Clone-Independence failure example, half of the A
preferrers, when A2 is introduces as a clone of A, rank A2 in first
place, and demote A to 2nd place. But, you know, they don't have to do
that.
If they want to play it safe, in Approval, Score, ICT or Symmetrical
ICT, those voters can approve or top-rank _both_ A and A2. So doing,
they'd be no worse off than before A2 was introduced. Their
expectation, when approving or top-ranking both A and A2 would be
higher than it was before the introduction of A2. Especially if A2 is
so good that it almost tempts them to not approve or top-rank A. In
fact, it's the raising of their expectation by the introduction of A2
that creates that temptation.
The fact that A2 could be so good as to raise A-preferrers expectation
enough to make optimal a gamble for big improvement, approving or
top-ranking A2 but not A, can hardly be called a problem. As problems
go, it isn't a problem.
The A-preferrers needn't be any worse off than before, because they
can approve or top-rank both A and A2.
So much for ICT's "clone problem".
Let me try that:
"In other words, I'd asked you to show a clone problem for Plurality.
You didn't do that.
Of course there isn't a clone problem for Plurality.
In your Plurality Clone-Independence failure example, half of the A
preferrers, when A2 is introduces [sic] as a clone of A, rank A2 in
first place, and demote A to 2nd place. But you know, they don't have to
do that.
If they want to play it safe, in Plurality, they hold a primary and find
out which A to support. Then they vote only for him."
See how easy it is to say that method X doesn't fail criterion Y if you
apply some procedure external to the method itself to fix the problem?
Of course that external procedure has some risks. The primary might be
gamed or corrupt... or in your counterexample, the A-voters might be
Nader/Gore voters and would prefer Nader to win above Gore, and thus
have to walk the tightrope between certainly getting Gore, or possibly
getting Nader, possibly Bush - and they could get that tightrope walk wrong.
(And if you think "hold a primary" is cheating because it occurs outside
the voting booth, replace it with "then they vote for the candidate with
a last name closest to the start of the alphabet". No action outside the
voting booth required! And similar patches have been used elsewhere,
like SNTV when used in Taiwan, with voters advised to vote for different
candidates depending on the birthday of the voter in question. I think I
prefer actual proportional representation methods to that kind of hack.)
Now, maybe, in this special clone example, with Beatpath, the
A-preferrers have the luxury of being able to sincerely rank A2 over
A, without that being able to make the winner come from outside of
{A,A2}.
But, in typical situations, even including typical u/a elections, TUC
(of which Beatpath is a version) is the method in which you won't know
what to do. You won't know whether to top-rank acceptable candidates.
You'll have mutually-contradictory strategic needs in that regard, as
I've described before.
What's all this about strategy? I don't want to play manual DSV. Isn't
then a method with complex strategy a *benefit?* If you have to be
Kasparov to effectively strategize, and strategy's otherwise a
minefield, not a whole lot of people will. Another barrier to being
strategic means increased chance of honesty.
About Reversal-Symmetry:
You seem to be speaking of it as applying only to ranking methods.
That's ok for right now.
Nope. I have never claimed that Range fails reversal symmetry. But Range
isn't the subject of discussion. ICT is.
If the ranking set is the same, when all the rankiings are reversed,
the reason why those rankings should result in a tie between all the
alternatives is because:
Obviously for every X> Y in that ranking set, thre must be a Y> X as well.
Obviously, in a positional method, for any instance of X being rated
above Y by a certain distance, there must be an instance of Y being
rated over X by the same distance.
So of course there should be a tie between all of the alternatives--if
the method is a positional method or is based entirely on pairwise
order comparisons.
Advocates or usesrs of this criterion, then, seem to be saying that
all methods should be positional methods, or be based entirely on
pairwise order comparisons.
Why?
Sorry, but that requirement needs justifying.
It's an agrees-with-itself criterion. If a method agrees that a
candidate is its choice in an election for best as well as its choice in
an election for worst, something is wrong. It has nothing to do with the
internals of the method. I can get a black box voting method and say,
hey, this thing thinks the same candidate should be elected in a contest
of whom to become president, and whom definitely *not* to become
president (i.e. all ballots reversed).
Using an ambiguous ballot set like I gave is just one (particularly
concise) way of showing reversal symmetry failure. Don't focus on that
particular ballot set, focus on reversal symmetry. If you want a set
that doesn't use that trick, I can give it to you.
Appealing to the internal weights of the method - saying "because method
X favors this particular category in the ballot, it doesn't matter" - is
like IRV advocates claiming that through its elimination logic, it is
obviously fair because it simulates an actual exhaustive runoff, and so
criterion compliance doesn't matter either.
And of course, it would be very easy for me to use the same kind of
argument against Consistency. Something like... "Obviously, in any
positional method, combining two ballot sets where X wins must lead to a
ballot set where X wins. ... It is well known that only positional
systems can pass Consistency ... Advocates or users of this criterion,
then, seem to be saying that all methods should be positional methods
.. Why?"
Does that mean if you disregard reversal symmetry, you also have to
disregard consistency?
Users of Reversal Symmetry don't agree. But they can't legitimately
impose their personal preferences as a requirement for all methods.
Nor can advocates of FBC legitimately impose their personal preferences
in such a manner.
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