Sorry, I missed the 25% preference rule. I'll think a bit more if there are still problems and good examples when the 25% preference rule is applied. BR, Juho > On 11 Nov 2016, at 18:17, Jameson Quinn <jameson.quinn@gmail.com> wrote: > > In the case that Juho discusses, PAR is designed to disqualify/eliminate the minor candidates X, Y, Z, etc. due to the fact that they will have under 25% first preferences. The theory is that any candidate X with over 25% first preferences will be getting enough attention so that voters who don't like X, and who explicitly reject at least one candidate, will take the trouble to explicitly reject X. > > 2016-11-11 11:05 GMT-05:00 Juho Laatu <juho.laatu@gmail.com <mailto:juho.laatu@gmail.com>>: > Negative votes and default votes that are not bottom votes are often problematic. There can be some problems also with rule "default is accept for voters who do explicitly reject some candidates". > > Candidates A and B are considered to be the strongest potential winners. Their first preference support is about 45% and 45%. Candidates from C to Z have much less first preference support. > > It makes sense to A supporters to reject B (hoping that rule 2 will eliminate B, even if B would have more support than A). B supporters will do the same to A. It is thus possible (or even probable in this scenario, if the election is competitive) that the leading candidates will be eliminated. > > Let's assume that there are no obvious compromise candidates that would be preferred over B by A supporters, and vice versa. Some of the other (than A and B) candidates might be rejected too (those that many enough voters bother to reject sincerely). As a result the winner will be someone that could be quite disliked among both A and B supporters. > > A linear opinion space might look like this: D - [C] - [A] - [B] - [E] - F - [G] - ... - X - Y - Z where square brackets point out the eliminated candidates. D and F are maybe the most likely winners, but surprises are possible if many A and B supporters explicitly reject (sincerely but incompletely) only few smaller candidates (e.g. D, C, E, F, G) and thereby give default accept to all the others (e.g. X, Y, Z). If candidate Y has more first preference support than other minor candidates, and some support from X and Z supporters, he/she might win. > > If this is of concern, the easiest fix is of course to use reject as default value in all ballots. > > BR, Juho > > >> On 10 Nov 2016, at 17:39, Jameson Quinn <jameson.quinn@gmail.com <mailto:jameson.quinn@gmail.com>> wrote: >> >> >> >> 2016-11-10 9:04 GMT-05:00 C.Benham <cbenham@adam.com.au <mailto:cbenham@adam.com.au>>: >>> 1. Voters can Prefer, Accept, or Reject each candidate. Default is Accept. >> >> This seems to assume that all the voters are interested in all the candidates and like checking boxes, whereas >> I should think that a lot of voters would be only interested in their favourite and content to keep voting the >> way they did under plurality (and would presumably continue to do so under Approval). >> >> They should be allowed to continue giving the most effective vote possible by simply giving a "Prefer" rating to their >> favourite. In-effect penalising such voters for forgetting to also give "Rejects" to all their non-favourites is unfair >> and dumb. >> >> It will give voters who aren't fans of the new method extra reason to resent it. Suppose that a strong candidate >> from an established party very narrowly loses just because some of his/her supporters forgot to give out "Rejects". >> Don't you think that might fuel a movement to dump the method? >> >> My thinking was that in most real-world situations, you'd only have to check one prefer and one reject to get maximum effectiveness, and it would be obvious which to reject. >> >> But I see your point. So I'm changing the method to: "Default is reject for voters who do not explicitly reject any candidates, or accept for those who do." >> >>> 2.Candidates with a majority of Reject, or with under 25% Prefer, are eliminated, unless that would eliminate all candidates. >> > > > > ---- > Election-Methods mailing list - see http://electorama.com/em <http://electorama.com/em> for list info > >

 1. Voters can Prefer, Accept, or Reject each candidate. Default
 is Accept.

 This seems to assume that all the voters are interested in all the
 candidates and like checking boxes, whereas
 I should think that a lot of voters would be only interested in
 their favourite and content to keep voting the
 way they did under plurality (and would presumably continue to do
 so under Approval).

 They should be allowed to continue giving the most effective vote
 possible by simply giving a "Prefer" rating to their
 favourite.  In-effect penalising such voters for forgetting to
 also give "Rejects"  to all their non-favourites is unfair
 and dumb.

 It will give voters who aren't fans of the new method extra reason
 to resent it.  Suppose that a strong candidate
 from an established party very narrowly loses just because some of
 his/her supporters forgot to give out "Rejects".
 Don't you think that might fuel a movement to dump the method?

 2.Candidates with a majority of Reject, or with under 25% Prefer,
 are eliminated, unless that would eliminate all candidates.

 I don't like arbitrary thresholds.  Obviously this causes failure
 of Irrelevant Ballots Independence. But also there is the problem
 that the final exact number of valid ballots can be disputed
 and/or take quite a while to establish.

 Postal votes can take a while to come in, or may be mislaid and
 later found. The validity of certain ballots can be disputed and
 the subject of legal proceedings.  Some people might have
 initially been denied the right to vote, but then succeed in
 having that
 over-turned and are then allowed to vote.

 It is much better if the algorithm just (more-or-less directly)
 compares the candidates with each other rather than measure them
 against
 arbitrary percentage-of-the-votes thresholds.

On 11/11/2016 2:09 AM, Jameson Quinn wrote: > If the number of uncounted ballots is enough to sway the election > using a threshold, it has every chance of being enough to sway the > election without thresholds. Not necessarily. Very close contests are unavoidable, but thresholds add further possible problems. Suppose it is wrongly assumed that the total number of valid ballots is known and the votes are counted and X is declared the apparent winner. Suppose that X is by far the most approved (i.e. most Prefers + Accepts) candidate (and say for good measure the CW) but X only very narrowly makes the 25% threshold of Prefers. Now say that a few extra ballots are discovered, all of which give Accepts to X and Prefers to only nobodies and maybe some Rejects to Y, with the result that X no longer makes the 25% threshold and Y wins. How do you think that will go down? > My thinking was that in most real-world situations, you'd only have to > check one prefer and one reject to get maximum effectiveness, and it > would be obvious which to reject. > > But I see your point. So I'm changing the method to: "Default is > reject for voters who do not explicitly reject any candidates, or > accept for those who do." That is a step in the right direction, but now you have the potential weirdness of blanks meaning different things on different ballots. Suppose on one ballot a single candidate is definitely Preferred and all but one other candidate are definitely left blank. But for the last candidate it is disputed whether it was left blank or was given a Reject. If blanks all mean the same thing, then the dispute only affects that one candidate. But with your proposal it also affects all the candidates left definitely blank. Chris Benham > > > 2016-11-10 9:04 GMT-05:00 C.Benham <cbenham@adam.com.au > <mailto:cbenham@adam.com.au>>: > >> 1. Voters can Prefer, Accept, or Reject each candidate. Default >> is Accept. > > This seems to assume that all the voters are interested in all the > candidates and like checking boxes, whereas > I should think that a lot of voters would be only interested in > their favourite and content to keep voting the > way they did under plurality (and would presumably continue to do > so under Approval). > > They should be allowed to continue giving the most effective vote > possible by simply giving a "Prefer" rating to their > favourite. In-effect penalising such voters for forgetting to > also give "Rejects" to all their non-favourites is unfair > and dumb. > > It will give voters who aren't fans of the new method extra reason > to resent it. Suppose that a strong candidate > from an established party very narrowly loses just because some of > his/her supporters forgot to give out "Rejects". > Don't you think that might fuel a movement to dump the method? > > > My thinking was that in most real-world situations, you'd only have to > check one prefer and one reject to get maximum effectiveness, and it > would be obvious which to reject. > > But I see your point. So I'm changing the method to: "Default is > reject for voters who do not explicitly reject any candidates, or > accept for those who do." > > >> 2.Candidates with a majority of Reject, or with under 25% Prefer, >> are eliminated, unless that would eliminate all candidates. > > I don't like arbitrary thresholds. Obviously this causes failure > of Irrelevant Ballots Independence. But also there is the problem > that the final exact number of valid ballots can be disputed > and/or take quite a while to establish. > > Postal votes can take a while to come in, or may be mislaid and > later found. The validity of certain ballots can be disputed and > the subject of legal proceedings. Some people might have > initially been denied the right to vote, but then succeed in > having that > over-turned and are then allowed to vote. > > It is much better if the algorithm just (more-or-less directly) > compares the candidates with each other rather than measure them > against > arbitrary percentage-of-the-votes thresholds. > > > If the number of uncounted ballots is enough to sway the election > using a threshold, it has every chance of being enough to sway the > election without thresholds. Only under the assumption that all > uncounted ballots are irrelevant does your objection apply > particularly to threshold methods. > > ... > > I'm giving up on the method I'd proposed earlier. It's now called > "CPAR", for Complicated PAR. But I do have a new patch to PAR to make > it pass FBC: > > 1. Voters can Prefer, Accept, or Reject each candidate. Default is > "Accept"; except that for voters who do not explicitly reject any > candidates, default is "Reject". Voters can also mark a global > option that says: "I believe that voters like me should be the > first to compromise." > 2. Candidates with a majority of Reject, or with under 25% Prefer, > are eliminated, unless that would eliminate all candidates. If a > candidate would have been eliminatable considering all the > "prefer" votes they got on "compromise" ballots as "rejects", then > they are considered "eager to compromise" > 3. The winner is the non-eliminated candidate with the highest score. > Candidates score 1 point for each voter who prefers them, and 1 > point for each voter who accepts them and prefers only candidates > who were eliminated or eager to compromise. > > The above method meets FBC, except in vanishingly rare cases where > multiple candidates are simultaneously at a threshold (analogous to > perfect ties). > > No virus found in this message. > Checked by AVG - www.avg.com <http://www.avg.com> > Version: 2016.0.7859 / Virus Database: 4664/13383 - Release Date: 11/10/16 >

Here's one example that is quite different from the previous one, but still somehow in line with my "crusade against negative votes and default better than bottom votes" :-) . First preferences are 35:A, 35:B, 30:C. Preference orders are mixed. Opinion space is thus not linear. Most A, B and C supporters reject their competitors in the hope of disqualifying them based on rule 2. There are more bullet voters among A and B supporters than among C supporters. Candidate C maybe recommended his/her supporters to explicitly reject A and B. As a result A and B will get more rejects (>50%) than C (<50%). Candidate C wins although he/she had less first preference support than A and B, it is not centrist (sincere Condorcet winner), most reject votes are strategic (not sincere), and C was the most strategic candidate. The 25% prefer elimination limit is quite high. If there are no "near clones" that many voters prefer as equal best candidates, we may typically have max three candidates left after the disqualification round (unless all were disqualified and as a result none). At least 20 of the A supporters and at least 20 of the B supporters reject other candidates (quite possible). Less than 50 of the A and B supporters (combined) reject C (quite possible). All C supporters reject other candidates (not probable but we could be quite close to that, and some additional rejects by A and B supporters would fill that gap). It seems that general rejection of competitors is a good strategy, and with three candidates of about equal strength, the number of strategic reject votes might easily determine the winner (instead of the number of positive sincere votes). Any misses this time? :-) BR, Juho Definition of PAR: Voters can Prefer, Accept, or Reject each candidate. Default is "Reject" for voters who do not explicitly reject any candidates, and "Accept" otherwise. Candidates with a majority of Reject, or with under 25% Prefer, are disqualified, unless that would disqualify all candidates. Each voter gives 1 point to each non-eliminated candidate they prefer; and any voter who gave no such points (because their preferred candidates were all eliminated) gives 1 point to each non-eliminated candidate they accept. The winner is the candidate with the most points. > On 11 Nov 2016, at 18:28, Juho Laatu <juho.laatu@gmail.com> wrote: > > Sorry, I missed the 25% preference rule. I'll think a bit more if there are still problems and good examples when the 25% preference rule is applied. > > BR, Juho > > >> On 11 Nov 2016, at 18:17, Jameson Quinn <jameson.quinn@gmail.com <mailto:jameson.quinn@gmail.com>> wrote: >> >> In the case that Juho discusses, PAR is designed to disqualify/eliminate the minor candidates X, Y, Z, etc. due to the fact that they will have under 25% first preferences. The theory is that any candidate X with over 25% first preferences will be getting enough attention so that voters who don't like X, and who explicitly reject at least one candidate, will take the trouble to explicitly reject X. >> >> 2016-11-11 11:05 GMT-05:00 Juho Laatu <juho.laatu@gmail.com <mailto:juho.laatu@gmail.com>>: >> Negative votes and default votes that are not bottom votes are often problematic. There can be some problems also with rule "default is accept for voters who do explicitly reject some candidates". >> >> Candidates A and B are considered to be the strongest potential winners. Their first preference support is about 45% and 45%. Candidates from C to Z have much less first preference support. >> >> It makes sense to A supporters to reject B (hoping that rule 2 will eliminate B, even if B would have more support than A). B supporters will do the same to A. It is thus possible (or even probable in this scenario, if the election is competitive) that the leading candidates will be eliminated. >> >> Let's assume that there are no obvious compromise candidates that would be preferred over B by A supporters, and vice versa. Some of the other (than A and B) candidates might be rejected too (those that many enough voters bother to reject sincerely). As a result the winner will be someone that could be quite disliked among both A and B supporters. >> >> A linear opinion space might look like this: D - [C] - [A] - [B] - [E] - F - [G] - ... - X - Y - Z where square brackets point out the eliminated candidates. D and F are maybe the most likely winners, but surprises are possible if many A and B supporters explicitly reject (sincerely but incompletely) only few smaller candidates (e.g. D, C, E, F, G) and thereby give default accept to all the others (e.g. X, Y, Z). If candidate Y has more first preference support than other minor candidates, and some support from X and Z supporters, he/she might win. >> >> If this is of concern, the easiest fix is of course to use reject as default value in all ballots. >> >> BR, Juho >> >> >>> On 10 Nov 2016, at 17:39, Jameson Quinn <jameson.quinn@gmail.com <mailto:jameson.quinn@gmail.com>> wrote: >>> >>> >>> >>> 2016-11-10 9:04 GMT-05:00 C.Benham <cbenham@adam.com.au <mailto:cbenham@adam.com.au>>: >>>> 1. Voters can Prefer, Accept, or Reject each candidate. Default is Accept. >>> >>> This seems to assume that all the voters are interested in all the candidates and like checking boxes, whereas >>> I should think that a lot of voters would be only interested in their favourite and content to keep voting the >>> way they did under plurality (and would presumably continue to do so under Approval). >>> >>> They should be allowed to continue giving the most effective vote possible by simply giving a "Prefer" rating to their >>> favourite. In-effect penalising such voters for forgetting to also give "Rejects" to all their non-favourites is unfair >>> and dumb. >>> >>> It will give voters who aren't fans of the new method extra reason to resent it. Suppose that a strong candidate >>> from an established party very narrowly loses just because some of his/her supporters forgot to give out "Rejects". >>> Don't you think that might fuel a movement to dump the method? >>> >>> My thinking was that in most real-world situations, you'd only have to check one prefer and one reject to get maximum effectiveness, and it would be obvious which to reject. >>> >>> But I see your point. So I'm changing the method to: "Default is reject for voters who do not explicitly reject any candidates, or accept for those who do." >>> >>>> 2.Candidates with a majority of Reject, or with under 25% Prefer, are eliminated, unless that would eliminate all candidates. >>> >> >> >> >> ---- >> Election-Methods mailing list - see http://electorama.com/em <http://electorama.com/em> for list info >> >> > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info