# [EM] Craig's posts

Markus Schulze schulze at sol.physik.tu-berlin.de
Fri Sep 7 16:09:48 PDT 2001

```Dear Rob,

you wrote (7 Sep 2001):
> I believe it's similar to IRV, except that every candidate with a
> lower-than-average first-place vote count is eliminated, so one step
> sometimes eliminates more than one candidate.  For example:
>
> 45:A>B>C
> 22:B>C>A
> 33:C>B>A
>
> IRV picks C after eliminating B, but Craig's IFPP eliminates both B
> and C in the first step (neither has the quota of 100/3=33.33 votes)
> and elects A.  Note that B is the Condorcet winner!  I find IFPP to
> be well short of ideal, although Craig claims that it's monotonic at
> least.

Your example also demonstrates that Craig's IFPP violates the majority
criterion for solid coalitions, the reversal symmetry criterion and the
independence from clones criterion.

IFPP also violates the participation criterion. If 5 BCA voters hadn't
gone to the polls, then C would have been elected. Thus these 5 BCA
voters changed the winner from C to A.

IFPP also violates the consistency criterion.
Example:

Situation 1:

45: A>B>C
35: B>C>A
14: C>B>A
6: C>A>B

The winner is A.

Situation 2:

45: A>B>C
33: B>C>A
22: C>B>A

The winner is A.

Situation 1+2:

90: A>B>C
68: B>C>A
36: C>B>A
6: C>A>B

The winner is B.

Craig claims that IFPP was monotonic. But in so far as he hasn't
yet defined IFPP for more than 3 candidates, this claim is quite
arbitrary.

Markus Schulze

```