[EM] FBC ambiguity

[MIKE OSSIPOFF]

I'd said:

>Still, I'll say that my official version of my definition of voting Smith 
>over Jones is the
>one that adds that it must _not_ be possible to contrive a configuration of 
>the
>other people's ballots such that, if we delete everyone but Smith & Jones 
>from the
>ballots, then Jones wins if & only if we count that voter's ballot.

Richard replied:

If you add this second condition, and it *is* possible, for each possible
ballot, to contrive a configuration of the other ballots that converts
the winner to Jones, then there is no such thing as a "Smith over Jones"
ballot...

I reply:

Are we talking about a voting system in which it isn't possible to write an 
example
in which someone can vote one candidate over another, by my definition that 
I
adopted above?

Then no one could gain by voting someone over their favorite, since no one 
could
vote anyone over their favorite (or over anyone else either).

I guess, then, that I'd have to say that that, by the above-quoted 
definition, that
method passes FBC. Maybe that would be a fault of FBC, to the extent that 
such
a method is important, but maybe it's ok. After all, my goal with FBC is 
that no one
should ever have strategic need to vote someone over their favorite. If 
we're using
a method in which it's impossible to vote anyone over anyone, then my goal 
is
satisfied. A person can only vote in a way that could, with just 2 
candidates left on
the ballots, make Smith beat Jones, or could make Jones beat Smith. I 
wouldn't call
that dumping Smith or Jones, and so that method doesn't sound bad in that 
regard.
Of course it would have considerable other problems, as you said.

It seems to pass FBC fair & square, but does so at the cost of taking away 
the
possibility of voting anyone over anyone.

But if you're just talking about a special example that can be written in 
which no
voter can vote anyone over anyone, then that isn't a problem, since all we 
have to
do is write a different example by which we _can_ test the method by FBC.

Richard continued:

Then it is impossible to test this sort of method for FBC, using
this definition.

I reply:

But FBC's wording, mostly for the purpose of brevity, says "By voting 
another candidate
over his/her favorite, a voter should never gain an outcome that s/he 
prefers to every
outcome that s/he could get in that election without doing so."

No one can gain a better outcome by voting someone over his favorite, 
because no
one can vote anyone over anyone.

Richard continued:

You could say that voting Smith over Jones means that,
if every candidate but Smith and Jones is removed from the election,
and if this ballot is the only ballot that is counted, then Smith will win.

I reply:

I'd considered that, but resisted it. Is it absolutely necessary? Is it 
necessary to
avoid the possibility, with a method like you describe, of voting Smith over 
Jones &
Jones over Smith? Or the possibility of FBC not being violated by a method 
in which
it's impossible to vote anyone over anyone?

But that definition that speaks of only counting that one ballot--that 
should be listed
as one definition of FBC. It might be interesting to take a poll, on which
Condorcet Criterion definition, and which Monotonicity Criterion definition, 
and which
FBC definition, and which definition of voting Smith over Jones, should be 
official on EM. I wouldn't argue with the results. I suggest
separate categories for English & Mathematical definitions, so as not to pit 
them
against eachother, since neither could replace the other.

I can't say for sure that the 1-ballot definition isn't better than the 
ballot-configuration
definition, of FBC. But it's more likely to make people balk when we speak 
of only
counting one ballot.

Incidentallly, I don't personally think that CC means much by itself, which 
is why I
use criteria that offer more and are more difficult to meet.

You know that CC has several different definitions that give different 
results. I've
counted 4 CC definitions. I like mine best, but you could say that I'm 
biased.

Mike Ossipoff


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