Can it be the case that Approval has a better CD strategy than XA ? Not really, because XA voters can always vote approval style by rating only at the extremes of zero and 100%, and in that case XA is reduced to plain Approval. Any strategy available in Approval is also available in XA, which has additional options, more control levers to work with, as it were, if you want to use them. Note that if candidate X is rated 100% on 70 percent of the ballots and rated zero on the other ballots, for example, then the XA score is 70 percent, identical to the Approval score. Also, in the context of cardinal ratings, it makes no difference if X is rated at 100 percent on 70 percent of the ballots or is rated at 70 percent on 100 percent of the ballots. The Cardinal Ratings score is 70 percent. So is the XA score! Contrast this with Bucklin which agrees in the unanimous rating case, but gives a score of 100 percent in the other case. The graphical picture makes this clear: The distribution function F(x) defined as the percentage of ballots on which X is rated above x, stair steps down from the left side to the right side of the square with diagonal corners at (0, 0) and (1, 1). The Bucklin score is determined by where it intersects the vertical line x = 1/2. The XA score is determined by where it crosses the line y = x. The mean Cardinal rating is simply the area between it and the x axis. The XA score favors candidates whose distribution graph is both tall and wide, giving equal importance to both height and width. The further towards the upper right corner of the square along the diagonal given by y = x, the better the point of intersection for the candidate. Once we understand the close relationship of Chiastic Approval with ordinary Approval and Cardinal Ratings, we can justify the following explanation of XA: The purpose of XA is to maximize the effect of voter intent as expressed by their ratings of the candidates. For each candidate, you indicate on your XA ballot what you consider to be an appropriate rating of merit or support on a scale of zero to 100 percent In the XA count, your ballot gives full approval to the candidates that you consider under-rated by the rest of the voters, and no approval to the candidates that you consider over-rated by the rest of the voters. The candidate with the highest (average or total) approval in the XA count is elected. Any suggestions for improvement? Forest

In this graphical framework, you can also think of XA as finding the largest square that fits between the distribution function and the x axis. On Thu, Nov 3, 2016 at 1:00 PM, Forest Simmons <fsimmons@pcc.edu> wrote: > > > For each candidate, you indicate on your XA ballot what you consider to be > an appropriate rating of merit or support on a scale of zero to 100 percent > > In the XA count, your ballot gives full approval to the candidates that > you consider under-rated by the rest of the voters, and no approval to the > candidates that you consider over-rated by the rest of the voters. > > The candidate with the highest (average or total) approval in the XA count > is elected. > > Any suggestions for improvement? > > Sounds like a good explanation to me.

If I may suggest another name for XA, you could call it Capped Approval, for the following reason. A voter *caps* the highest rate at which they are willing to approve candidate X. By rating the candidate at R%, they express that they are willing to contribute a vote to X *only *if less than R% of the electorate is willing to support X at a rate greater than R. So that candidates rating, if it includes the R-voter's ballot, is capped at R. If there are greater than R% of voters who support X at a rate greater than R%, the R-voter's ballot contributes nothing. As an alternative, you could call it Qualified Approval. QA has the alternate interpretation of Quality Assurance. I would be very happy with a method of this type if it could be shown to satisfy at least a weak form of Participation, and Independence from Irrelevant Alternatives. Frango ut patefaciam -- I break so that I may reveal On Thu, Nov 3, 2016 at 9:13 PM, Andy Jennings <elections@jenningsstory.com> wrote: > In this graphical framework, you can also think of XA as finding the > largest square that fits between the distribution function and the x axis. > > > On Thu, Nov 3, 2016 at 1:00 PM, Forest Simmons <fsimmons@pcc.edu> wrote: > >> >> >> For each candidate, you indicate on your XA ballot what you consider to >> be an appropriate rating of merit or support on a scale of zero to 100 >> percent >> >> In the XA count, your ballot gives full approval to the candidates that >> you consider under-rated by the rest of the voters, and no approval to the >> candidates that you consider over-rated by the rest of the voters. >> >> The candidate with the highest (average or total) approval in the XA >> count is elected. >> >> Any suggestions for improvement? >> >> > Sounds like a good explanation to me. > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >

Good suggestions for public names; I prefer Capped Approval to Qualified Approval, since the word "qualify" is a loaded word in the context of elections. Remember when HRC and Bernie Sanders were saying that their opponents were not qualified for the presidency? I'm sure that XA (or CA) satisfies mono-add-plump, since a plump ballot for X cannot reduce the XA score for X, nor can it improve the XA score of any other candidate. On Mon, Nov 7, 2016 at 12:49 PM, Monkey Puzzle <araucaria.araucana@gmail.com > wrote: > If I may suggest another name for XA, you could call it Capped Approval, > for the following reason. > > A voter *caps* the highest rate at which they are willing to approve > candidate X. By rating the candidate at R%, they express that they are > willing to contribute a vote to X *only *if less than R% of the > electorate is willing to support X at a rate greater than R. So that > candidates rating, if it includes the R-voter's ballot, is capped at R. > > If there are greater than R% of voters who support X at a rate greater > than R%, the R-voter's ballot contributes nothing. > > As an alternative, you could call it Qualified Approval. QA has the > alternate interpretation of Quality Assurance. > > I would be very happy with a method of this type if it could be shown to > satisfy at least a weak form of Participation, and Independence from > Irrelevant Alternatives. > > Frango ut patefaciam -- I break so that I may reveal > > On Thu, Nov 3, 2016 at 9:13 PM, Andy Jennings <elections@jenningsstory.com > > wrote: > >> In this graphical framework, you can also think of XA as finding the >> largest square that fits between the distribution function and the x axis. >> >> >> On Thu, Nov 3, 2016 at 1:00 PM, Forest Simmons <fsimmons@pcc.edu> wrote: >> >>> >>> >>> For each candidate, you indicate on your XA ballot what you consider to >>> be an appropriate rating of merit or support on a scale of zero to 100 >>> percent >>> >>> In the XA count, your ballot gives full approval to the candidates that >>> you consider under-rated by the rest of the voters, and no approval to the >>> candidates that you consider over-rated by the rest of the voters. >>> >>> The candidate with the highest (average or total) approval in the XA >>> count is elected. >>> >>> Any suggestions for improvement? >>> >>> >> Sounds like a good explanation to me. >> >> ---- >> Election-Methods mailing list - see http://electorama.com/em for list >> info >> >> >

Thanks for the feedback on mono-add-plump. Thinking about the problem yesterday, I think that XA/CA/ATDT satisfies the same kind of Weak Participation Criterion as Majority Judgment: If candidate A wins under XA with a score of R, adding a ballot supporting A with score >= R and all other candidates with scores < R will not cause A to lose. By definition of XA, no candidate with a score of R minus epsilon can get a higher score if a ballot with a score of R - epsilon or lower is added to to the total, because the new ballot's score caps the total. The middle-score example posted by Jameson last week could not occur under this restriction, I believe. Frango ut patefaciam -- I break so that I may reveal On Tue, Nov 8, 2016 at 12:58 PM, Forest Simmons <fsimmons@pcc.edu> wrote: > Good suggestions for public names; I prefer Capped Approval to Qualified > Approval, since the word "qualify" is a loaded word in the context of > elections. Remember when HRC and Bernie Sanders were saying that their > opponents were not qualified for the presidency? > > I'm sure that XA (or CA) satisfies mono-add-plump, since a plump ballot > for X cannot reduce the XA score for X, nor can it improve the XA score of > any other candidate. > > On Mon, Nov 7, 2016 at 12:49 PM, Monkey Puzzle < > araucaria.araucana@gmail.com> wrote: > >> If I may suggest another name for XA, you could call it Capped Approval, >> for the following reason. >> >> A voter *caps* the highest rate at which they are willing to approve >> candidate X. By rating the candidate at R%, they express that they are >> willing to contribute a vote to X *only *if less than R% of the >> electorate is willing to support X at a rate greater than R. So that >> candidates rating, if it includes the R-voter's ballot, is capped at R. >> >> If there are greater than R% of voters who support X at a rate greater >> than R%, the R-voter's ballot contributes nothing. >> >> As an alternative, you could call it Qualified Approval. QA has the >> alternate interpretation of Quality Assurance. >> >> I would be very happy with a method of this type if it could be shown to >> satisfy at least a weak form of Participation, and Independence from >> Irrelevant Alternatives. >> >> Frango ut patefaciam -- I break so that I may reveal >> >> On Thu, Nov 3, 2016 at 9:13 PM, Andy Jennings < >> elections@jenningsstory.com> wrote: >> >>> In this graphical framework, you can also think of XA as finding the >>> largest square that fits between the distribution function and the x axis. >>> >>> >>> On Thu, Nov 3, 2016 at 1:00 PM, Forest Simmons <fsimmons@pcc.edu> wrote: >>> >>>> >>>> >>>> For each candidate, you indicate on your XA ballot what you consider to >>>> be an appropriate rating of merit or support on a scale of zero to 100 >>>> percent >>>> >>>> In the XA count, your ballot gives full approval to the candidates that >>>> you consider under-rated by the rest of the voters, and no approval to the >>>> candidates that you consider over-rated by the rest of the voters. >>>> >>>> The candidate with the highest (average or total) approval in the XA >>>> count is elected. >>>> >>>> Any suggestions for improvement? >>>> >>>> >>> Sounds like a good explanation to me. >>> >>> ---- >>> Election-Methods mailing list - see http://electorama.com/em for list >>> info >>> >>> >> >