Adam Tarr wrote: > > Bart Ingles wrote: > > > Adam Tarr wrote: > > > Specifically, there is the remarkable fact that a voter in a > > winning > > > votes-based Condorcet voting system can NEVER be hurt by fully > > expressing > > > their preferences. There are cases where fully voting your > > preferences can > > > fail to help you, but it can never actually hurt you. > > > > Never is a strong word. > > True, and I lack a rigorous proof, but every empirical example I have > seen supports this. Your example is no different... > > > How about the following: > > > > (projected vote percentages shown; assumed accurate to within +/- 5 > > percentage points) > > > > 45% A B C > > 5% B A C > > 5% B C A > > 45% C B A > > There's no sense in talking about uncertainty and ties; it only > confuses the issue.
Sorry to spoil your clarity. Having never seen an election where the exact vote count is known in advance (except possibly in a couple of counties in Florida), I would say that uncertainty IS important. Also, my example wasn't really intended to show a tie, so much as it was to show no clear winner before the election. In the above example the probability of either A or C winning an A/C pairing is 0.5, therefore those candidates' voters are better off truncating whenever their perceived utility for B is less than 0.5. Similarly, if the probabilities for A and C in an A/C pairing were 70/30, then the A voters would want to truncate whenever their utility for B was < 0.7, and the C voters would want to truncate whenever their perceived utility for B was < 0.3. Obviously, when the election is complete and the votes are counted, you can say that the losing voters would have been better off ranking fully. I don't think this would translate to 'regret', though, since truncation was the best strategy available at the time of the election. > In winning votes methods, truncation for the ABC voters makes no > difference (i.e. does not hurt them, even if it fails to help them). > In margins methods, truncating can prove costly for an ABC voter. > This is neither here nor there for the purposes of my analysis; I can > show you a counter-example where truncation can help in margins cases. > > The point is, nowhere here do we get any suggestion that a voter in a > winning votes method can be helped by truncation. My initial > contention still stands. > > > But then I don't see truncation as necessarily a bad thing. If > > truncation can defeat a "hated middle" candidate, it addresses my > > main misgiving about the Condorcet methods. > > Much in the same way that we can't differentiate between the > indifferent voter and the lazy voter, we cannot distinguish between > the "respected (if unglamorous) compromise middle" and the "hated (yet > still) compromise middle". Smart CBA voters in an approval election > will still approve B, to defeat A, anyway. Substitute "low utility Condorcet winner" for "hated middle" if you like. The approval CBA voters who approve B are only smart if they are relatively certain that A would win otherwise, or if they have an extremely high opinion of B. > What method would actually > prevent B from winning when the voters act in a logical manner? Even > plurality and IRV encourage CBA voters to dump C for B if they have > perfect information. "Perfect information" being the key phrase here. If perfect information were available it wouldn't matter what we used. Bart ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
