[EM] Efforts to improve on CR's strategy

[Bart Ingles]

Ken Johnson wrote:
> >
> Here's an example of the kind of Bad Thing that can happen with
> Approval. There are 3 candidates (A, B, C) and 10 voters. I am using
> signed CR's in the range -1 to 1 (CR>0: approve, CR<0: disapprove).
> Following are the sincere CR's:
>
> 9 voters: A(-1), B(0.1), C(1)
> 1 voter: A(-1), B(1), C(-0.1)
>
> avg CR: A(-1), B(0.19), C(0.89)
>
> approval: A(0), B(10), C(9)
> plurality: A(0), B(1), C(9)

As a near-worst-case example, this outcome isn't bad.  Approval still
manages to pick a winner whose average CR is above the mean for all
candidates.  Can you show me a method where a worse outcome *isn't*
possible?

Actually I consider Approval's worst-case three-candidate example
(assuming rational voters using zero-info strategy) to be something
like:

Sincere preference:
50 voters:  A(1.0), B(.51), C(0)
49 voters:  C(1.0), A(.49), B(0)
1 voter: B(1.0), C(1.0), A(0)

Actual ballots:
50 AB
49 C
1 BC

Election Results:
B=51, A=50, C=50

Avg. SU:
B=.26, A=.75, C=.5

But this still compares well to Condorcet, and especially to IRV (under
IRV a .26 candidate can defeat a near-1.0 candidate).

Bart