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 ---- Election-methods mailing list - see http://electorama.com/em for list info
