[EM] Range versus Condorcet

[Greg Nisbet]

--- En date de?: Mer 15.10.08, Greg Nisbet <gregory.nisbet at gmail.com> a
?crit?:
> On the topic of whether there is a method that
> satisfies both
> Condorcet and FBC.

There is not. I believe I have demonstrated this in the past, by modifying
a Woodall proof that shows Condorcet to be incompatible with LNHarm.

> http://osdir.com/ml/politics.election-methods/2002-11/msg00020.html
> claims
> that any majority method will violate FBC.
Note the term *strong* FBC. When FBC is mentioned usually only the weak
form is discussed because the strong form is almost impossible to satisfy.

=what is strong FBC, no incentive to make equal either? Which methods do
satisfy strong FBC? I saw this article about a variant of ER-Bucklin that
appear to satisfy it, but I couldn't follow it.

> Think of it this
> way, any
> majority method without equal rankings will always
> encourage betrayal so
> that a compromise candidate will get the majoirty thereby
> sparing you
> potenial loss.

Yes.

> Anything with equal rankings cannot be a
> majority method b/c
> simultaneous majorities will form and only one will win,
> hence allowing a
> candidate with a "majority" to in fact lose.
This is avoided by defining the majority criterion to refer to strict
first preferences.

=There are three possible ways to handle "indecisive" voters like this.
1) Ignore them entirely for the purposes of majority
2) Give 1/n to each n candidates that share the first position
3) Do not have them count for any particular candidate, but still count them
in the sense that the total against which majority is tested is incremented.

Example

3: A>C
2: B>C
16: A=B>C

Under definition 1 A has a majority 3/5
Under definition 2 A has a majoirty 3 + 8 = 11/21
Under definition 3 A does not have a majority 3/21
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20081015/44536003/attachment-0002.htm>