[EM] SFC and "margins vs. winning votes"

[Russ Paielli]

On March 1, 2005, Mike Ossipoff wrote:

Here´s the actual definition of SFC:

SFC:

If no one falsifies a preference, and if a majority prefer the CW to 
candidate Y, and vote sincerely, then Y shouldn´t win.

[end of SFC definition]

Here's my comment:

Mike considers this criterion critical and uses it as evidence that 
certain Condorcet variations are less vulnerable to insincere strategy 
when they base defeat strength on "winning votes" rather than "margins."

Forget for now all the disputes about Mike's definition of preferences. 
Even if Mike's definition of preferences is clear and unambiguous (and I 
realize that's a big "if"), what is the significance of SFC?

Well, since Mike feels that he can write his own version of the 
Condorcet criterion, I'll write my own version of SFC, and I'll call it 
the margins SFC:

If no one falsifies a preference, and if the margin of the victory of 
the CW over candidate Y is larger than any other margin of victory, then 
Y shouldn't win.

[end of margins SFC definition]

Does it now appear that margins is less vulnerable to strategy than 
winning votes?

When you get right down to the basics, Mike's SFC is simply an arbitrary 
criterion that happens to favor winning votes, but an equally arbitrary 
criterion can be written to favor margins. Hence, Mike's SFC criterion 
is completely irrelevant to the debate over winning votes vs. margins. 
In fact, it's completely irrelevant, period. And so is its generalized 
version, GSFC, of course. They're both really just pedantic tricks.

I realize that "margins vs. winning votes" is an old topic here, but I 
would just like to add my two cents worth. And I thank Chris Benham for 
recently citing Blake Cretney's article, which I found very enlightening.

If you argue for wv, you are claiming that a 51-49 victory is "stronger" 
than a 49-0 victory. Common sense tells us that's nonsense. Some of us 
still have common sense.

Just for fun, let's frame this in terms of Mike's definitions of 
preferences and sincere voting. I don't feel like searching for it now, 
but Mike recently wrote something to the effect that a sincere vote is 
one in which the voter does not falsify any preferences and votes every 
preference that the particular method allows.

That means that a "sincere" vote cannot be truncated unless the voter 
truly rates all the unranked candidates *exactly* equal. Well, what does 
that mean? As I tried to explain previously, it requires a model of 
voter preferences, though Mike doesn't seem to understand that. What do 
I mean by a "model" of voter preferences?

The very concept of preferences implies that the voter either explicitly 
or implicitly rates the candidates on a one-dimensional scale. Suppose I 
claim that the scale is continuous rather than discrete. Well, it's as 
good a model as any. That means that the voter's ratings of the 
candidates fall essentially randomly on a continuous real-valued scale. 
It also means the the probability of two candidates being rated exactly 
equal is zero.

If the probability of exactly equal ratings is zero, that means that 
Mike's definition of a "sincere" vote has zero probability of being 
truncated. It also means that no equal rankings will occur. And what 
does that all mean? Your jumping the gun! Yes, that's right! It means 
that winning votes and margins are equivalent, given that continuous 
model of voter preferences.

As Blake pointed out, we can think of truncated votes as more or less 
equivalent to the same votes completed with random rankings. In that 
case, any margin of victory translates to a majority victory.

Yes, Mike, I plan to revise my webpage on this topic ASAP.

--Russ