In my Tideman bad-example, I neglected to say how many voters there are. Say there are 12 voters. Then D's defeat by A is unanimous. B's defeat by D is with an 83.3% majority. C isn't majority-defeated, only having 1 vote against it in a defeat. So Tideman's method, at least as defined in the _Journal of Economic Perspectives_ article, as I interpret the article, does violate GMC. It also violates Beat-Path GMC: In C's only defeat, C is only beaten with 1 vote against. That means that there can be no beat-path to C that's stronger than 1. Now, say C beats A with 7 votes-against, instead of 5. (Or with 11, for that matter). Now there's a majority beat-path from C to B, but not from B to C. B is disqualified by Beat-Path GMC. But Tideman electes B, which is disqualified by both versions of GMC. Mike Ossipoff
