FBC Ambiguity?

[MIKE OSSIPOFF]

Richard wrote:

That is why I am suggesting a simple way to remove the ambiguity: for better
communication of the idea of FBC.

I reply:

Nothing wrong with removing ambiguity. But there's a point at which it's 
necessary to
ask if the likelyhood of the alternative interpretation being taken is 
enough to justify
the added wording. Also, does the ambiguity remain when we apply prevailing 
standards
used in definitions of other critreia?

>Richard continues:
>
>
>A better wording would be:
>
>A method passes FBC if there is no scenario in which, by voting
>another candidate over his or her favorite, a voter could gain an
>outcome he or she prefers to any of the outcomes he or she could
>gain in the same scenario without doing so.

Again, I have nothing against that more explicit wording, though I use my 
briefer
wording when I use FBC. Incidentally, I actually use these criteria, and 
I've helped sink
a few IRV proposals. Of course I have no reason to object if you use that 
scenario-specific
wording.

I'd said:

>
>Ok, so you're interpreting my wording to say that by voting another 
>candidate over
>his favorite, a voter should never gain an outcome that he prefers to every 
>outcome that
>he could get in that or some other election without doing so.

Richard replied:

Well, I'm not *personally* interpreting that way, but that is a good
characterization of the misinterpretation I would like to prevent.

I reply:

As a practical mattter, I haven't found a need to specify the same scenario, 
but that
doesn't mean that someone else shouldn't do so. But it seems to me that it's 
universally
understood in discussions of voting system criteria & examples that 
"outcome" only has meaning  with reference to a particular election, and 
that we aren't talking about outcomes
that could be outcomes of other elections.

Of course what an outcome is, in a candidate election, is a candidate, or a 
tie
between more than 1 candidate. (If the tiebreaker is considered part of the 
event whose
outcome we're talking about, then of course an outcome always means 1 
candidate).
When a criterion speaks of all the candidates, does it always stipulate that 
it's only
talking about all the candidates in that particular election, as opposed to 
those in
other elections, perhaps in other historical periods, other countries, or 
alternative
universes? When a criterion speaks of a majority of the voters, does it 
always stipulate
that it's talking only a majority of the voters participating in that 
election, as opposed to
other elections, perhaps in other historical periods, other countries, etc?

Suppose someone words Condorcet's Criterion to say, in part:

"If there's a candidate who, when compared separately to each one of the 
other
candidates, ..."

Are they talking about each one of the other candidates in previous & future 
elections,
in all countries, and on all planets in all possibility worlds? If so, 
Condorcet's Criterion
has a problem. Maybe you'll say that people should always specify that that 
isn't
what's meant. But do they? So I'm suggesting that prevailing standards  in 
defining
criteria & voting systems confirm my claim that, unless otherwise indicated, 
any outcomes
referred to in a criterion definition are outcomes of the same election.

Again, however, very likely it's desirable to not depend on such 
conventional standards
when writing a definition for mathematicians or logicians.

I've left-in what I'd said about candidate A being the same outcome if he's 
elected in
a different election:

>Actually, an outcome means an outcome of that election. Electing candidate 
>A in
>a different election at some later time isn't the same outcome as electing 
>candidate A
>in today's election. In that future election, the candidates who might win 
>if A doesn't win
>might be different, the social and other conditions in the country might be 
>different,
>and A's own policies might be different. It isn't reasonable to treat 
>"outcome" as meaning
>something other than "outcome of that election".

Richard continued:

I just want the colloquial definition to come across clearly. Hence my
"devil's advocate" role.

I reply:

Of course, that's a necessary role. When writing criteria for mathematicians 
or
logicians, longer wordings are permissible, and even the most unlikely 
misinterpretation
should perhaps be pre-empted by the wording, and maybe then we shouldn't 
rely
on existing conventions about what a word like "outcomes" means in 
definitions.
But you understand that I talk to people who might be convinced by IRVies 
that the
definition of a method or criterion is too complicated.

Now I've posted my Monotonicity definition, with some supporting 
definitions. Today
I corrected a typo in one of those supporting definitions, the definition of 
voting
a candidate higher. It seems to me that my Monotonicity definition applies 
to all
single-winner voting systems, and works as expected with them.

Richard continues:

[regarding my definition of voting Smith over Jones]

Where one might get into trouble is in nonmonotone methods, where
it isn't clear when a voter is "voting one candidate over another".
In such a method, I might contrive a case where my ballot helps my
candidate (when all but the two candidates are eliminated) and another
case where my ballot hurts my candidate (when all but the two candidates
are eliminated). Now, this wouldn't occur in ordinary nonmonotone methods
(such as IRV), because with only two candidates the nonmonotonicity does
not show up. But imagine a severely nonmonotone method, such as one based
on modular arithmetic or some other non-linear function of the number of
votes. While such methods are not practical, they do exist (in the
mathematical sense), and need to be considered (at least if we want our
definition to be complete).

I reply:

Maybe, but such a method could never be considered for actual use. I did 
mention that
the addition that you suggest  below could be helpful if someone comes up 
with a voting
system that requires it. For defining voting Smith over Jones for 
mathematicians or
logicians, I'd include that added wording that you describe.

Richard continues:

By your first definition ("A voter votes A over B if s/he votes in such a
way that one could contrive some configuration of other people's votes such
that, if we delete from the ballots every candidate but A & B, A is
the unique winner if & only if we count that voter's ballot."), my ballot
under this unusual method votes A over B, but it also votes B over A. So
let's tack on your suggested addition: "...and no one can contrive a
configuration of other people's votes such that, if we delete from the
ballots every candidate but A & B, the unique winner is B if & only if we
count that voter's ballot." By the modified definition, my ballot neither
votes A over B nor B over A.

I reply:

Sure, as with your addition to FBC, that addition to the definition of 
voting Smith over
Jones is probably desirable when stating that definition for mathematicians 
or logicians.

If "colloquial" or "informal" means "imprecise", then is the 
English-language FBC
definition still colloquial after your wording is added, to specify that all 
the outcomes
that it refers to are outcomes of the same election? If its meaning is then 
unmistakeable?

Maybe "colloquial" or "informal" should mean suitable for describing a 
voting system
or criterion to a citizen on a streetcorner, but not meeting the necessary 
standards
for a proposed electoral law. Sure, if I were writing an electoral law about 
FBC, I
probably _would_ specify that all the outcomes referred to are outcomes of 
the
same election. If I were writing an electoral law that referred to voting 
Smith over Jones,
I doubt that I'd bother writing it so that it doesn't act unexpectedly when 
a voting system
is nonmonotonic with 2 candidates, since it would never be tested with such 
a voting
system.

By the way, an attorney told me that the best people to write proposed law 
for
voting systems are the people who are familiar with the voting systems, 
whether or
not they're attorneys. Of course, it's important that they avoid ambiguity 
or imprecision,
more carefully than in other discussion, something that they can probably do 
as well
as anyone. Of course they should probably show their final result to an 
attorney before
submitting their initiative language, in case there are some special legal 
meanings that
they don't know about.

If the convention that all the outcomes referred to in a criterion are 
outcomes of the
same election is relied upon in some definitions in journal articles, is it 
still
informal or colloquial?

I don't mean to sound so defensive about those labels, but I'm just trying 
to find out
exactly what they mean.

Mike Ossipoff


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