Lottery, defined by Jobst recently, is an aesthetically appealing method. Simple, neat, & natural. Itīs regrettable that it does poorly in terms of defensive strategy need, due to ignoring the strength of defeats. One would hope that thereīs a situation where it could be recommended, such as a situation where people donīt care about optimizing their outcome, and some aesthetic consideration is more important than social utility. Otherwise, if voters donīt care about optimizing their outcome, then CR seems best, due to its good social utility. In public political elections, voters care very much about optimizing their outcome, and routinely falsify their favorite in a probably miss-informed attempt to do so.
With 3 candidates, Lottery is reminiscent of the proposal to solve circular ties by Random-Candidate. Likewise, Forest mentioned a similarity to Spruced-Up Random-Candidate.
Forest suggested a variation that does a Condorcet count based on inferred rankings of lotteries and candidates, but, in Forestīs example, that method didnīt do as well as Condorcet(wv), though the wv version did better than the margins version.
But what Forest described used only the lotteries that elected one candidate with 100% probability, and those that chose between 2 candidates fifty-fifty. What about finding the lottery that would win against all of the other possible lotteries in CSSD/BeatpathWinner or RP?
Of course, most likely it wouldnīt do very well by my standards. Thatīs because so very few methods can match Condorcet(wv), Approval, and CR in that regard. But thereīs always the hope that thereīs a lottery-method, a semi-random method, that will approach the strategy-freeness of Random-Ballot (RB), without RBīs possibility of electing a really despised alternative, and without RBīs low social utility (SU).
Someone in Australia was looking for such a method, with a specific ambitious goal, till someone else told him that it had been proved that that goal is unattainable. But maybe thereīs something desirable to be found in such a method.
Thanks for explaining Sprucing-Up, though thereīve been a few different definitions of a covering set posted.
I donīt understand the importance of the Dutta set. The appeal and importance of the Smith and Schwartz sets are obvious, but what makes 2-defeat beatpaths special?
Can the Dutta set exclude a member of the initial Schwartz set? Might that not mess up CSSDīs outcome when CSSD is used within the Dutta set?
Most of the things that Iīve wanted to find out about voting systems have been found out. I wanted to find out if the strongest majority defensive strategy criterion is attainable, and found that itīs attainable, but at a probably unacceprable price in indecisiveness. AERLO & ATLO solve some strategy problems that others have mentioned, which, though not serious, had concerned me some. Cardinal Pairwise probably solves those problems too. Then there are other Condorcet enhancements that offer even more strategy freedom, at the cost of more complexity, and without all the reliability that one might want, some involving automated strategy that looks for certain signs of offensive order-reversal.
The enhancements for Condorcet are a bit like hang-on pollution-control devices for intrinsically dirty engines, but they make significant improvement on Condorcet(wv), a method which is good enough without improvemement.
During the time that I was away from EM, some new methods were defined, and I donīt yet know what they are: Spruced up methods, and Condorcet lotteries. Well, youīve recently answered a question that someone else asked about Sprucing Up, but several definitions of a covering set have been posted.
Iīm interested in those new methods, the Lottery methods and Spruced-Up methods, in case they can improve on enhanced wv. Nothing has yet, but thereīs always a chance. Do any of those methods significantly ease the need for strategy? Or, in particular, the need for defensive strategy? I define defensive strategy as strategy intended to protect the win of a CW or to protect majority rule (which Iīve defined elsewhere on EM).
Iīm mostly interested in methods that can be proposed to the public, especially as an initial voting system reform proposal. That means methods definable in a few short paragraphs. But after Condorcet has been enacted, if people later want further improvement, and are by then used to Condorcet, they might accept something more complicated that brings the improvement that they then want.
Mike Ossipoff
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