[EM] Typo in Condorcet's Criterion definition

[Michael Ossipoff]

The Condorcet's Criterion definition that I posted today doesn't make any
sense, due to a typo.

Where I said, "rank X over Y", I should have said "prefer X to Y".

Of course, likewise, "rank Y over X" should be replaced with "prefer Y to
X".

So, the correct definition is:

A definition of Condorcet's Criterion:

X is collectively preferred to Y if the number of voters who prefer X to Y
is greater than the number of voters who prefer Y to X.

The "Condorcet candidate" is a candidate who is collectively preferred to
each one of the other candidates.

If there is a Condorcet candidate, and if everyone votes sincerely, then
the Condorcet candidate should win.

[end of definiition of Condorcet's Criterion]

As I said, I've previously posted a precise definition of sincere voting,
which I'll re-post upon request.

But, if you don't ask for the definition, then rest assured that the
precise definition is consistent with the usual
conversational meaning of that term, with which you're familiar.

My system of criterial has been criticized for its use of the word
"prefer". I've been asked for  definition of it.

My answer:

Take any reasonable dictionary definition, or your own conversational
meaning, as the definiiton of "prefer".

For the purpose of my critreria, that word's definition doesn't matter.

That's because my definition of sincere voting uses "prefer", and specifies
a particular manner of marking a ballot, if the voter prefers a certain way.

 So, saying, in the premise of a criterion, that voters have certain
preferences among the candidates, and that those voters vote sincerely,
therefore stipulatres, in that criterion-premise, a particular manner in
which those voters mark their ballots.

Because the definition of "prefer" doesn't matter, it could (for example)
just as well be replaced by Lewis Carroll's nonsense verb "outgribe",
without changing the meaning of my critreria that use the word "prefer".

Now that I've already said so much, I might as well include my
criterion-system's definition of sincere voting:

A voter votes sincerely iff, on her ballot, s/he doesn't contradict any of
her preferences, or fail to vote a preference of hirs that the balloting
system
in use would have allowed hir to vote in addition to the preferences that
s/he actually does vote.

[end of definition of sincere voting]

To vote a preference for X over Y means voting X over Y, when preferring X
to Y.

To contadict a preference means voting Y over X, when preferring X to Y.

I've previously posted two precise and usable definitions of voting X over
Y. For the purposes here, either will do. I'll re-post them upon request.
However, if you don't ask for the precise definitions, rest assured that
they're consistent with what you mean by "vote X over Y".

Why this system of critreria? Because it's the way to define some criteria
(such as Condorcet's Criterion) in a way that applies neatly and seamlesslly
to all methods.

For that reason, some of my critreria refer to preferences. They've been
called "preference criteria". But sometimes I've used criteria that are
not preference criteria. Not all critereia need that kind of definition in
order to be universally seamlessly applicable.

There has been much sputtering and anger about preference criteria. But, as
I said, they're the only way to specify certain requirements (such as what
we mean by Condorcet's Criterion) in a way that is seamlessly and neatly
applicable to all methods.

My definitions of sincere voting, contradicting a preference, voting a
preference, and voting X over Y, are supporting definitions, for
the system of preference criteria.

Mike Ossipoff
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