The inspiration for Yes/NoCandidateProxy, SODA, MAS, SARA, etc. was fundamentally this: Approval voters tend to have a top set that they definitely approve, and a bottom set that they definitely disapprove. The question is what to do with the rest, the "indefinite set" between Top and Bottom. As Michael has pointed out there are various strategies that work in various contexts, and the current USA context would not require anything sophisticated. Here's a strategy that I have been thinking about that could be automated as a DSV system, but is simple enough that it could be recommended for use by the man (or woman) behind the plough (as Charles Dodgson put it). The context is an Approval election with partial but not too reliable information about winning probabilities. 1. Approve all candidates that you definitely approve, i.e. all candidates in your "top set." 2. Leave unapproved all of the candidates in your "bottom set." 3. Approve p percent of the remaining indefinite set, where p is given by the formula (1 + pB - pT)/2 , where pB is your subjective estimate of the pobability that someone from your bottom set will be elected, and pT is the probability that someone from your Top set will be elected. So if pB=pT, the formula recommends that you approve half of the remaining candidates. If pB>pT you will approve more than half of the remaining candidates. If pB<pT you will approve fewer than half of the remaining candidates. If pB=0, and pT = 1,then it recommends that you approve none of the remaining candidates If pB=1 and pT=0, it recommends that you approve all of the remaining candidates. This formula follows from the "approve above expected merit" method in the context where the candidates in the indefinite category are distributed uniformly between zero and one in merit. But it is so robust that it should give good results even if that assumption is only approximately true. One can always follow one's gut feeling when in doubt. If the method recommends that you approve seven candidates and you are feeling doubtfull about the worst of the seven, then by all means (and medians) leave that one unapproved. Other guidlines that involve a sense of who the CWs is, or which candidate are below the merit midrange can help inform borderline cases. Of course, if you have enough information to know that the distribution of merit among the indefinite candidates is no where near uniform, then you have enough information to use a better decision method, like approve above expected merit. Thanks, Forest

, Yes, for drawing the Approval cutoff in the uncertain zone, this is a good way to estimate where the expected winner-merit is, using only an estimate of the relative win-probabilities of the definite top-set & the definite bottom-set. And the only distribution-assumption is within the uncertain region, instead of a global distribution assumption. The estimate about the relative win-probabilites of the definite top & bottom sets makes it unnecessary to make estimates about wider-scale distribution, and is arguably a more reliable thing to estimate. But of course, as you know, if these are official public elections, then we're talking about elections in a better future, like what I call "the Green scenario", not the questionably-valid current political system, in which it's in the 99%'s interest to use the completely easy & simple strategy of approving only their top-set, the progressive candidates, in an Approval election. Michael Ossipoff On Wed, Nov 2, 2016 at 6:35 PM, Forest Simmons <fsimmons@pcc.edu> wrote: > The inspiration for Yes/NoCandidateProxy, SODA, MAS, SARA, etc. was > fundamentally this: > > Approval voters tend to have a top set that they definitely approve, and a > bottom set that they definitely disapprove. The question is what to do > with the rest, the "indefinite set" between Top and Bottom. > > As Michael has pointed out there are various strategies that work in > various contexts, and the current USA context would not require anything > sophisticated. > > Here's a strategy that I have been thinking about that could be automated > as a DSV system, but is simple enough that it could be recommended for use > by the man (or woman) behind the plough (as Charles Dodgson put it). > > The context is an Approval election with partial but not too reliable > information about winning probabilities. > > 1. Approve all candidates that you definitely approve, i.e. all > candidates in your "top set." > > 2. Leave unapproved all of the candidates in your "bottom set." > > 3. Approve p percent of the remaining indefinite set, where p is given by > the formula (1 + pB - pT)/2 , where pB is your subjective estimate of the > pobability that someone from your bottom set will be elected, and pT is the > probability that someone from your Top set will be elected. > > So if pB=pT, the formula recommends that you approve half of the remaining > candidates. If pB>pT you will approve more than half of the remaining > candidates. If pB<pT you will approve fewer than half of the remaining > candidates. If pB=0, and pT = 1,then it recommends that you approve none of > the remaining candidates If pB=1 and pT=0, it recommends that you approve > all of the remaining candidates. > > This formula follows from the "approve above expected merit" method in the > context where the candidates in the indefinite category are distributed > uniformly between zero and one in merit. But it is so robust that it > should give good results even if that assumption is only approximately > true. > > One can always follow one's gut feeling when in doubt. If the method > recommends that you approve seven candidates and you are feeling doubtful > about the worst of the seven, then by all means (and medians) leave that > one unapproved. > > Other guidlines that involve a sense of who the CWs is, or which candidate > are below the merit midrange can help inform borderline cases. > > Of course, if you have enough information to know that the distribution of > merit among the indefinite candidates is no where near uniform, then you > have enough information to use a better decision method, like approve above > expected merit. > > Thanks, > > Forest > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >