On Tue, May 27, 2003 at 06:31:22PM -0400, Nathanael Nerode wrote:
> > Do all these perverse cases also require less than 2Q votes to
> > be cast?
> Sadly, no. They do require less than Q votes to be cast with A above
> the default, and nearly all of the other votes to be cast with A equal
> to the default.
You can have 2Q-3 votes that have explicit ranks for all options, viz:
Q-1 ABD
Q-2 BDA
A beats B, Q-1:Q-@, A beats D, Q-1:Q-2; B beats D, 2Q-3:0.
(Any more than that, and you've either got A beats D by >=Q:<blah>, and
it makes quorum, or D beats A Q-1:>=Q-1, and A doesn't make it's majority
requirement)
You can have an additional 2Q-4 votes if your votes are of the form:
Q-1 ABD
Q-2 DAB
2Q-4 B
(A beats B, 2Q-3:2Q-4; A beats D, Q-1:Q-2; B beats D, 3Q-5:Q-2). If you have
any more votes:
where A > D, then A will make quorum
where D > A, then A won't make its majority requirement
where B > A, then A won't be the Condorcet winner
you can vote A=D > B without contravening those rules, though, for something
like:
Q-1 ABD
Q-2 DAB
X B
Y (A=D)B
with A beats B, 2Q-3+Y:X; A beats D, Q-1:Q-2; B beats D, Q-1+X:Q-2+Y, which
is satisfied as long as:
X > Y
Y > X-2Q+3
In the last election, we had 303 votes that expressed full preferences,
which is much greater than 2Q-3 (85); and we had precisely three votes
of the form "X=D, X,D > Y".
> They also require an electorate with strongly divided,
> balanced views on at least two options, and another option which lots of
> people rank equal to the default (which gets kicked out).
Fundamentally, what it requires is for very few people to express
full preferences. There're only two reasons for this: one is that most
people don't understand the issue, which isn't what happens in Debian;
and the other is that they see some benefit in voting against their
true preferences.
And for large X and Y, the above example is very unstable; and I don't
believe it could realistically be used as a strategy.
> So, in this situation, how would you feel if only Q-1 developers voted
> for C, but lots of other people voted C at equal rank to D?
Tough luck. It's not remotely difficult to get Q developers to rank an
option higher than "further discussion".
Cheers,
aj
--
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
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