[EM] Lottery methods. wv between all possible lotteries? New methods.

[MIKE OSSIPOFF]

Lottery, defined by Jobst recently,  is an aesthetically appealing method. 
Simple, neat, & natural. It´s regrettable that it does  poorly in terms of 
defensive strategy need, due to ignoring the strength of defeats. One would 
hope that there´s a situation where it could be recommended, such as a 
situation where people don´t care about optimizing their outcome, and some 
aesthetic consideration is more important than social utility. Otherwise, if 
voters don´t 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 Forest´s example, that method 
didn´t 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 wouldn´t do very well by my standards. That´s 
because so very few methods can match Condorcet(wv), Approval, and CR in 
that regard. But there´s always the hope that there´s a lottery-method, a 
semi-random method, that will approach the strategy-freeness of 
Random-Ballot (RB), without RB´s possibility of electing a really despised 
alternative, and without RB´s 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 there´s something desirable to be found in 
such a method.

Thanks for explaining Sprucing-Up, though there´ve been a few different 
definitions of a covering set posted.

I don´t 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 CSSD´s outcome when CSSD is used within the Dutta set?

Most of the things that I´ve 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 it´s 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 don´t yet know what they are: Spruced up methods, and Condorcet lotteries. 
Well, you´ve recently answered a question that someone else asked about 
Sprucing Up,  but several definitions of a covering set have been posted.

I´m interested in those new methods, the Lottery methods and Spruced-Up 
methods, in case they can improve on enhanced wv. Nothing has yet, but 
there´s 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 I´ve defined elsewhere on EM).

I´m 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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