[EM] Yes: FBC must speak of a set of same-preference, same-voting voters

[MIKE OSSIPOFF]

I´ve re-titled the thread, because I´d neglected to write down the subject 
line of the message that I´m replying to.

Markus is right to point out that, as I´ve defined it, FBC has a problem 
when there´s a tie. As Markus pointed out, a single voter can change the 
outcome only by changing a definite win to a tie, or changing a tie to a 
definite win.

FBC, as defined so far,  has a problem with a tie. If the way that you could 
get your best outcome is by breaking a tie, and getting a certain outcome, 
then, if you don´t do so, that same candidate might win the tie anyway, and 
so what you get when you break the tie isn´t better than anything that you 
could get wihtout doing so.  On the other hand, if, by voting someone over 
your favorite, you could make a tie, then you aren´t electing with certainty 
someone who is better than anyone you could otherwise have gotten, since you 
aren´t electing anyone with certainty.

The obvious and easy way out of this is to replace "voter" with "set of 
voters who have the same peferences and vote in the same way".

That fixes the problem. Thanks for pointing the problem out, Markus.

I make that change in both my Certainty FBC and my Nonrandom FBC.

...even though Nonrandom FBC probably doesn´t have that problem. It only 
applies to nonrandom methods, as I´ve defined that term. And it doesn´t 
specify an outcome that can be gotten with certainty, as does Certain FBC. 
For instance, in Plurality, if the greater-evil wins with certainty if you 
don´t vote for the lesser-evil, and you could make a tie between the lesser 
and greater evils  by voting for the lesser-evil, then you can get your best 
outcome only by voting that lesser-evil over your favorite, and so Plurality 
fails FBC in that instance, and therefore fails FBC.

I don´t have my definition of best outcome in front of me right now, but 
what I say in the previous paragraph is probably true.

Anyway, as I said, I´m hereby changing FBC to replace "voter" with "set of 
voters who have the same preferences and vote in the same way".

I define a preference as an instance of preferring one candidate to another.

Markus--

You said:

Dear Kevin,

you wrote (1 March 2005):
>I think, in short, that the "situation" (of odds
>distribution) is not relevant to FBC.

I reply:

Yes, I don´t consider those intermediate lotteries to be outcomes. The 
outcome is the final single winner.

You continued:


As far as I have understood FBC correctly, then it
is about individual voters and not about coalitions
of voters. However, an individual voter usually only
changes the outcome from one decisive situation to an
indecisive situation or from one indecisive situation
to a decisive situation or from one indecisive
situation to another indecisive situation. But an
individual voter usually doesn't change an outcome
from a situation where candidate A wins decisively to
a situation where another candidate B wins decisively.

I reply:

Quite so, and that creates a problem for FBC, at least in my Certain FBC 
version. For that reason I now define FBC to be about a set of voters who 
have the same preferences and vote in the same way,  instead of one 
individual voter. That seems the easiest, simplest way to avoid the problem 
that you have pointed out.

Kevin had said:

>I have to interpret "result" to mean "the candidate
>who actually got the seat,"

I reply:

Yes, that´s how I mean "result".

You (Markus) said:

I see more than one possible interpretation. Examples:

1. Mike uses the resolute model. (The "resolute model"
   says that for every possible profile the winner is
   determined in advance.)

I reply:

As I said, only if you define the resolute model better would I be able to 
say whether or not I  use it. But, as I said, from your definition so far, 
the U.S. uses the resolute model when chosing its president.


You continue:

2. Mike talks about coalitions of like-minded voters
   rather than about single voters.

I reply:

For FBC, Yes. Now I do. But, before, I didn´t.


You continue:

But then the
   question is whether all these like-minded voters
   have to vote in the same manner or whether they
   may vote differently.

I reply:

My FBC improvement, described earlier in this reply, replaces "voter" with 
"set of voters who have the same preferences and vote in the same way".

Kevin wrote:

>Pretending Mike agrees with my interpretation (and that
>he clarifies FBC accordingly), do you think FBC would
>then be unambiguous?

Markus replied:

Your question is quite hypothetic because Mike will
never clarify his definitions.

I reply:

I´ve always answered questions about my definitions. But if you think that 
one of my definitions is vague or ambiguous, then the burden is on you to 
tell me exactly which sentence in that definition is vague or ambiguous, and 
in what way. Or, for any of my criteria, post an example in which that 
criterion is ambiguous about the matter of whether or not some particular 
method passes the criterion.

The problem of FBC when there´s a tie hadn´t occurred to me, but when it was 
pointed out, I changed FBC to get rid of the problem. I´ve been answering 
all the clarification questions, both these questions about FBC, and, in 
general, about any of my criteria. I always answer questions about my 
criteria.

I even always answer Markus´s questions about my critreria. Of course 
sometimes the answer is that I don´t know. That´s the case about whether 
it´s possible to find a PC GSFC failure example, a PC SDSC failure example, 
or whether it´s possible to find a BeatpathWinner FBC failure example.

I also must answer that I don´t know, when Markus asks me if I use the 
resolute model, till Markus gives a better definition of the resolute model.

Another question to which I must answer "I don´t know" is when Markus asks 
me for an instance where SFC gives a different answer than a new criterion 
that Markus has just defined. If Markus doesn´t understand SFC, which was 
defined long ago,and has been much explained, discussed, and used, how can 
he expect me to understand his newly-defined criterion? What that amounts to 
is that Markus is then asking me a question about his criterion, and I must 
answer that I don´t know.

If we want to find out if SFC and Markus-Non-FBC are the same, or if they 
can give different answers, then the best way would be, for several 
particular methods, for Markus to say whether those methods meet 
Markus-Non-FBC.

For instance, the following methods pass SFC:

All wv Condorcet methods, including PC, BeatpathWinner/CSSD, SSD, SD, 
Ranked-Pairs, and Smith//PC.

Markus, do any of those methods fail the criterion that you wrote as your 
possible restatement of SFC?

The following methods fail SFC:

Pluralty, Approval, Margins Condorcet, IRV, Borda, Bucklin, CR...and pretty 
much everything but wv Condorcet.

Markus, do any of the 8 methods listed above pass your criterion that you 
wrote as your possible restatement of SFC?

If neither of us undestand the other´s criterion, then the best way to find 
out if they´re different is for you to answer the above questions.

Mike Ossipoff

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