Pasting from Mike's page:
/Some definitions useful in subsequent criteria definitions:/
A voter votes X over Y if he votes in a way such that if we count only
his ballot, with all the candidates but X & Y deleted from it, X wins.
[end of definition]
Voting a preference for X over Y means voting X over Y. If a voter
prefers X to Y, and votes X over Y, then he's voting a sincere
preference. If he prefers X to Y and votes Y over X, he's falsifying a
preference.
A voter votes sincerely if he doesn't falsify a preference, and
doesn't fail to vote a sincere preference that the balloting rules in
use would have allowed him to vote in addition to the preferences that
he actually did vote.
[end of definition]
Strategy-Free Criterion (SFC):
/Preliminary definition: /A "Condorcet winner" (CW) is a candidate
who, when compared separately to each one of the other candidates, is
preferred to that other candidate by more voters than vice-versa. Note
that this is about sincere preference, which may sometimes be
different than actual voting.
SFC:
If no one falsifies a preference, and there's a CW, and a majority of
all the voters prefer the CW to candidate Y, and vote sincerely, then
Y shouldn't win.
[end of definition]
Michael Ossipoff wrote:
Kevin and Chris posted their criteria that they incorrectly claimed
equivalent to SFC.
These same alternative "SFCs" have been posted to EM before and
thoroughly discussed before.
In fact, we've been all over this subject before.
So why don't you point us to where in the EM archive we can find this
earlier discussion? Are they in your opinion equivalent for
ranked-ballot methods?
Though Chris's and Kevin's criteria clearly are not equivalent to SFC,
maybe someone could write a votes-only cirterion that is. First of
all, what's this obsession about "votes-only"?
Some people worry that criteria that give the appearance that we have to
read voters' minds to see if they are met are not the easiest to check for.
Now, quite aside from that, the efforts to write a votes-only
equivalent criterion seem motivated by a desire to not say things
that happen to be what I want to say. I want SFC to be about the fact
that that majority, because they all prefer the CW to Y, and because
there's no falsification (on a scale sufficient to change the
outcome), can defeat Y by doing nothing other than voting sincerely.
To say it in a way that doesn't say that wouldn't be SFC. If someone
wrote such a criterion, then I'd recognize it as a _test_ for SFC
compliance, but not as SFC. When I say that a method passes or fails
SFC, and someone says "What's that?", then I want to tell them the SFC
described in the paragraph before this one, the one that relates to
the CW, no need for other than sincere voting by the majority and
non-falsified voting by everyone else. If I worded it like Kevin or
Chris, it wouldn't be self-evident why it's desirable to meet that
criterion.
Someone could suggest that I use an alternative as the criterion, and
save my SFC as a justification. No, I want the criterion's value to be
self-evident.
Well its value as something distinct from the Condorcet criterion isn't
self-evident to me. If this CW>Y majority can't elect the CW, why do
they necessarily
care if Y is elected or not?
And the way you've dressed this up, I can't see how it really qualifies
as a "strategy criterion". How are the members of this CW>Y majority
supposed to
know whether or not anyone "falsifies a preference"? And if they do
know what are they supposed to do about it?
From Steve Eppley's MAM page:
/truncation resistance/
<Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm>:
Define the "sincere top set" as the smallest subset
of alternatives such that, for each alternative in the subset,
say x, and
each alternative outside the subset, say y, the number of
voters who
sincerely prefer x over y exceeds the number who sincerely
prefer y
over x. If no voter votes the reverse of any sincere
preference regarding
any pair of alternatives, and more than half of the voters
rank some x in
the sincere top set over some y outside the sincere top set,
then y must
not be elected. (This is a strengthening of a criterion having
the same name
promoted by Mike Ossipoff, whose weaker version applies only when
the sincere top set contains only one alternative, a Condorcet
winner.)
This makes some sense as a strategy criterion, being about deterring a
faction from truncating against the members of the sincere
Smith set. The "weaker version" ascribed to you seems easier to test for.
How does that version differ from your present SFC?
Chris Benham
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