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 ---- Election-methods mailing list - see http://electorama.com/em for list info
