I’ve been working on a further generalization of generalized cumulative voting and in the process confirmed that rational STAR voting and rational CB voting are sometimes less honest than rational SV voting (i.e. min-max). The following is an example:
Utilities: A B C D
Rational zero-information SV vote: A B C D
Rational zero-information STAR or CB vote: A B C D
The SV vote is identical to the honest vote (in which B’s score is rounded to 0) and closer than STAR/CB to the utilities fitted to the range. If we increase A’s utility, the rational STAR and CB votes will eventually become honest (i.e. min B), but not until it reaches 14 (in the case of CB) or 17 (in the case of STAR). The cause of this dishonesty is of course that, whereas in SV the question is, is increasing my influence by 1 point in the event of a BC tie (i.e. whether B or C survives being within my control) or BD tie worth decreasing my influence by 1 point in the event of a BA tie? Of course not. But in STAR (and to a lesser extent CB), that tie may occur in, for example, the runoff, where there’s no difference between 5 and 1 and 5 and 0 and all the difference in the world between 1 and 0 and 0 and 0.
Combine that with the fact that, even when STAR and CB are more honest than SV, they’re not much more honest (in fact, rational voting in both STAR and CB approaches min-max as MAX approaches infinity, the only difference being that CB’s approach is slower). For example, the STAR ballot A B C D is necessarily irrational, regardless of the voter’s preferences.
So what remains of the argument for STAR/CB once the resistance-to-strategy myth is dispelled? Resistance to irrelevant alternatives, I suppose, only irrelevance is a self-fulfilling prophecy in these systems. The final two are often part of a top cycle, in which it’s not clear that the rightful winner is even part of the cycle, much less one of those two. The Condorcet winner should obviously always win when there is one, but I’ve seen no evidence that any candidates other than Condorcet losers and candidates outside the Mutual Majority set can be safely eliminated. That’s the virtue of Tom’s method. It has all the benefits of normalization without the risks attendant to automatic elimination.