At 03:06 PM 4/24/2010, [email protected] wrote:
Markus pointed out that Bucklin fails mono add top. Now I see why. If x is
ranked second on all of the ballots except the new one, and some
other candidate
y has exactly 50% first place support, then one ballot of the form x>y will
change the Bucklin winner from x to y, because now the collapse to second rank
is unnecessary..
What is meant here? I don't think it's correct as stated. Let's see:
50: y > x
50: z > x, x wins in second round.
add
1: x>y, x still wins.
I think this is meant:
50: y > > x
50: z > > x (this was a legal Bucklin vote, ranks could be left
blank. That's part of why I claim that a Bucklin ballot is a range ballot)
x wins in the third round, with 100% of the vote.
add
01: x > y
Still doesn't work.... Forest what do you have in mind? If the
collapse to second rank is made unnecessary by the casting of an x>y
vote, that means that the y vote is not counted, only the vote for x,
so if this terminates the election, it must be for x. Not for y as you stated.
So we let's state a special version of participation that Bucklin satisfies:
If x wins Bucklin by collapse to level k, then adding a new ballot
cannot switch
the winner from x to y unless y is ranked above level k or x is ranked below
level k.
In other words, the new winner has to be ranked relatively high to k or else x
has to be ranked relatively low to k in order to change the winner.
This seems like a reasonable Participation criterion. It should be enough to
overcome the No Show phobia.
I don't think that bizarre election criteria failures, even if
possible, will deter voting at all. Absolutely, voters in Bucklin
will truncate when they prefer their favorite with sufficient
strength. That's why the ballots work as range ballots! (I.e., they
are strategically optimal, in ordinary circumstances, if voted
according to sincere utility differences.)
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