[EM] How close can we get to the IIAC

[Markus Schulze]

Hallo,

> Here's a method I proposed a while back that is monotone,
> clone free, always elects a candidate from the uncovered
> set, and is independent from candidates that beat the
> winner, i.e. if a candidate that pairwise beats the
> winner is removed, the winner still wins:
>
> 1. List the candidates in order of decreasing approval.
>
> 2. If the approval winner A is uncovered, then A wins.
>
> 3. Otherwise, let C1 be the first candidate is the list
> that covers A. If C1 is uncovered, then C1 wins.
>
> 4. Else let C2 be the first candidate in the list that
> covers C1. If C2 is uncovered, then C2 wins.
>
> etc.

Situation 1:

Suppose the order of decreasing approval is CDAB.

A beats B
B beats C
C beats D
D beats A
A beats C
B beats D

uncovered set: A, B, D.

The winner is D.

*********

Situation 2:

Suppose some voters rank D higher so that D beats B.

Suppose the order of decreasing approval is still CDAB.

A beats B
B beats C
C beats D
D beats A
A beats C
D beats B

uncovered set: A, C, D.

Now, the winner is C.

So, monotonicity is violated.

Markus Schulze