[EM] Another method idea

[Daniel Bishop]

Forest Simmons wrote:

> Ballots are ordinal rankings or cardinal ratings.
>
> Any candidate with more than average first place rankings or ratings 
> gets a point.  Any candidate with fewer than average last place (or 
> truncated) rankings or ratings gets a point or an additional point.
>
> The candidate with the most points wins.
>
> In case of ties, all but the tied candidates are stricken from the 
> ballots, and the method is repeated.
>
> If the method gets stuck on a set, then the tie is broken by random 
> ballot restricted to members of the tied set.
>
> Call this method "The first and last place point system."

Consider the set of candidates {A, B, C} and ballots

3: A>B>C
2: B>C>A

If I understand your method correctly, the relevant math is:

First-place votes:

A: 3 (above average)
B: 2 (above average)
C: 0 (below average)
Average: 5/3=1.666...

Last-place votes:

A: 2 (above average)
B: 0 (below average)
C: 3 (above average)
Average: 5/3=1.666...

Points:

A: 1
B: 2
C: 0

So B is elected.  But A has an absolute majority of first-choice votes!