Folks,
I've been busy for several days due to a family medical crisis, so I've been unable to reply to the many interesting messages that have been posted. However, I would like to present some general ideas I've been thinking about. Some of them may be obvious, and most if not all are probably unoriginal, but I would like to lay them out anyway just for the record if nothing else. They will give you a clue as to what guides my thinking, and perhaps they will provide some insight. Please tell me if you disagree with anything.
We've been discussing the integration of Condorcet and Approval methods. As most of you know, Concdorcet is an ordinal (ranking) method, and Approval is the simplest form of a cardinal (rating) method.
Ordinal methods allow the voter to express the relative preferences among the candidates, but cardinal methods allow the voter to express an "absolute" rating of the candidates. I put "absolute" in quotes because it is probably too strong a word. The key is that they are "less relative." Cardinal ratings allow the voter to express a rating of the candidates relative, not to each other, but to the "expected value" of the outcome of the election itself.
Ordinal and cardinal methods complement each other -- or so it seems to me. Given that, I conclude that an "ideal" election, if one exists, method must incorporate both ordinal *and* cardinal information.
Pure Condorcet is ordinal only, and its main deficiency is the possibility of cycles that must be resolved by deciding which votes to ignore. That can get complicated, which is a serious problem for public acceptability. The complexity itself is not the fundamental problem, however. The fundamental problem is that ordinal-only methods simply do not obtain cardinal information from the voters.
A pure cardinal rating system, on the other hand, allows the voters to rate the candidates on a continuous scale. An actual continuous scale is not practical, of course, but it can be approximated by a high enough discretization, say 0-100.
The practical problem with Cardinal Ratings, as I perceive it at least, is that it just doesn't "seem" right for public elections. I simply cannot imagine a major public election in which I am allowed to "rate" each candidate on a scale of 0-100 or even 0-10. Well, I can imagine it, but I think I can safely say that it won't happen.
The other problem with a cardinal rating system is that it provides more "resolution" than is strategically necessary. A wise voter will realize that, in a "large" election at least, the best "strategy" is to give each candidate either the maximum or minimum rating. This is comparable to "bang-bang" control, in which an actuator must be either completely on or completely off for best efficiency (most home heating systems, for example). The intermediate gradations may appeal to naive voters, but they don't add much, if any, real value.
In other words, Approval Voting is arguably as good as any cardinal rating system. If that is true, then any cardinal rating system other than Approval is unnecessarily complicated. Hence, an "ideal" election method that incorporates both ordinal and cardinal information should use Approval as the cardinal information. This rules out any "graded" system that has the voters "grading" the candidates on a scale of, say, A-F (as in school report cards).
OK, where do we stand at this point? I claim that an "ideal" election method must integrate both ordinal and cardinal information, and the cardinal information should be simple approval (yes/no for each candidate).
I think that's enough for now, so I will continue later.
--Russ ---- Election-methods mailing list - see http://electorama.com/em for list info
