Re: [EM] Fixing Range Voting
Greg Nisbet wrote: Instant Range-off Voting is an interesting idea. I thought about it once a while ago too. I didn't renormalize the ballots though, I just set the co-highest to 100 and the co-lowest to 0 for each ballot as a sanitation measure. I eventually abadoned it due to nonmonotonicity, but I think the discussion is a valid one. There are some problems with Range Voting, and perhaps tweaking it or adding some new features will fix them, perhaps not. Most of the problems seem to involve voters being coerced into making extreme ballots for fear of being outcompeted by strategic rivals. Assuming people will be honest out of charity is naive. Some of them will, perhaps many of them will, but unscrupulous individuals could manipulate an election if there were enough of them. So, in the spirit of idiotproofing voting, let's discuss Range Voting spinoffs. so for there is: IRNR (Instant Runoff Normalized Ratings) Cardinal Condorcet http://fc.antioch.edu/~james_green-armytage/cwp13.htm Various semi-proposed tweaking of Range Voting to include an elect majority winner first or elect CW first clause. All of these have the same goal and that goal is very simple. To either encourage honest ratings or force more explicit ratings. You could also turn approval methods into Range methods. For example, the Range version of UncAAO (Uncovered Approval, Approval Opposition) would treat Range votes as fractional approval votes. However, for UncAAO you'd still need an approval cutoff (I'd rather not have any candidates below this value), which would make the ballot complex. Also, the methods would have to use the rating information for some other purpose, not just as fractional approval votes (otherwise, approval strategy would still work). That being said, I think the most promising area of development here is based around the concept of a conditional vote that came up a few threads ago. The idea here being that individual ballots should react to a particular candidate being kicked out of the hopeful group or something like that. DSV systems would do something like that. You'd submit an honest ballot, and then the system would strategize maximally (not just for you, but for all others), first on the honest information, then on the previous round's strategic information, until the result settles. That would be a sort of automatic conditional ballot. The idea would be that the system or computer would be so good at strategizing on your behalf (for all voters), that it wouldn't pay off to try to manually use strategy. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
Hi, --- En date de : Dim 19.10.08, Kristofer Munsterhjelm [EMAIL PROTECTED] a écrit : That being said, I think the most promising area of development here is based around the concept of a conditional vote that came up a few threads ago. The idea here being that individual ballots should react to a particular candidate being kicked out of the hopeful group or something like that. Really lots of methods can be defined in that way. You're practically describing IRV for example. A difficult thing is deciding on a good criterion for a candidate to be eliminated. And if you don't eliminate candidates outright, you have a problem in that in some cases there will never naturally be stability: There are always some ballots that want to adjust how they are being counted. DSV systems would do something like that. You'd submit an honest ballot, and then the system would strategize maximally (not just for you, but for all others), first on the honest information, then on the previous round's strategic information, until the result settles. That would be a sort of automatic conditional ballot. The idea would be that the system or computer would be so good at strategizing on your behalf (for all voters), that it wouldn't pay off to try to manually use strategy. Many methods are designed with this goal of course. I could think of this as the mentality behind the Condorcet criterion. Kevin Venzke __ Do You Yahoo!? En finir avec le spam? Yahoo! Mail vous offre la meilleure protection possible contre les messages non sollicités http://mail.yahoo.fr Yahoo! Mail Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
On Oct 15, 2008, at 1:59 PM, Peter Barath wrote: I'm not sure I would vote honestly in such circumstance. Let my honest rangings be: 100 percent for my favourite but almost chanceless Robin Hood 20 percent for the frontrunner Cinderella 0 percent for the other frontrunner Ugly Duckling I think I would vote: 100 Robin Hood; 99 Cinderella; 0 Ugly Duckling If I'm really sure that the race decides between Cinderella and Ugly Duckling, why care too much for poor Robin Hood? And what, if I'm not really sure, because that's the situation which multi-candidate voting is really about? If I lower Cinderella's 99 to her honest 20, I make Robin Hood a little bit more hopeful not to drop first. But more hopeful against whom? Cinderella, of course, because I didn't change Robin and Ugly's obvious rangings. So I made more probable a situation in which more than 50 percent is the probability that the worst candidate wins. This is a doubtful advantage. On the other side, there is the effect that by rising Cinderella's points from the honest 20 to 99 I made more probable the similarly unlikely but positively desirable effect of Ugly dropping first instead of her. So, which does have more weigh? The doubtful little hope for Robin Hood, or the clear little hope against Ugly Duckling? I think the latter. Maybe at some point, let's say Cinderella's 5 percent, I like Robin so much more that I chose the first one. In that case I probably would vote 100-1-0 These voting are not the honest although by one percent honer than the simple Approval voting. But I would be open for persuasion. If you vote (100,20,0), (100,99,0) or (100,1,0), if your 100 hero loses in the first round, your vote in the second round is (x,100,0). So, what are the various consequences in the first round vote, in case it makes a difference there? I think the normalization comes into why you want to vote differently. (100,20,0) = (98.1,19.6,0) (100,99,0) = (71.1,70.4,0) (100,1,0) = (99.995,0.5,0) I think the tradeoff is that in a many-candidate race your lower preferences might contribute to runoff-disqualification order. You can put the vast majority of your vote on your favorite, and that's ok and your vote will get transferred to the remaining candidates if you don't get that favorite, but your lower rated choices might still be affecting which choices are disqualified or remaining at that time. The 100,99 vote looks tempting because it normalizes to a lot of absolute value, but that does come at the price of losing some weight on your favorite and making your 2nd choice a bunch more likely to win. I think it's this tradeoff that will squeeze people towards voting honest ratings. I could see honest voting want any of these three votes. Wanting A or B vastly more than C, wanting A vastly more than B or C, or some more gradual falloff. Does IRNR not do the right thing for those three voters? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
2008/10/16 Brian Olson [EMAIL PROTECTED]
On Oct 15, 2008, at 1:59 PM, Peter Barath wrote:
I'm not sure I would vote honestly in such circumstance.
Let my honest rangings be:
100 percent for my favourite but almost chanceless Robin Hood
20 percent for the frontrunner Cinderella
0 percent for the other frontrunner Ugly Duckling
I think I would vote: 100 Robin Hood; 99 Cinderella; 0 Ugly Duckling
If I'm really sure that the race decides between Cinderella and
Ugly Duckling, why care too much for poor Robin Hood?
And what, if I'm not really sure, because that's the situation which
multi-candidate voting is really about?
If I lower Cinderella's 99 to her honest 20, I make Robin Hood a
little bit more hopeful not to drop first. But more hopeful against
whom? Cinderella, of course, because I didn't change Robin and Ugly's
obvious rangings. So I made more probable a situation in which more
than 50 percent is the probability that the worst candidate wins.
This is a doubtful advantage.
On the other side, there is the effect that by rising Cinderella's
points from the honest 20 to 99 I made more probable the similarly
unlikely but positively desirable effect of Ugly dropping first
instead of her.
So, which does have more weigh? The doubtful little hope for
Robin Hood, or the clear little hope against Ugly Duckling?
I think the latter. Maybe at some point, let's say Cinderella's
5 percent, I like Robin so much more that I chose the first one.
In that case I probably would vote 100-1-0
These voting are not the honest although by one percent honer
than the simple Approval voting.
But I would be open for persuasion.
If you vote (100,20,0), (100,99,0) or (100,1,0), if your 100 hero loses in
the first round, your vote in the second round is (x,100,0). So, what are
the various consequences in the first round vote, in case it makes a
difference there?
I think the normalization comes into why you want to vote differently.
(100,20,0) = (98.1,19.6,0)
(100,99,0) = (71.1,70.4,0)
(100,1,0) = (99.995,0.5,0)
I think the tradeoff is that in a many-candidate race your lower
preferences might contribute to runoff-disqualification order. You can put
the vast majority of your vote on your favorite, and that's ok and your vote
will get transferred to the remaining candidates if you don't get that
favorite, but your lower rated choices might still be affecting which
choices are disqualified or remaining at that time.
The 100,99 vote looks tempting because it normalizes to a lot of absolute
value, but that does come at the price of losing some weight on your
favorite and making your 2nd choice a bunch more likely to win.
I think it's this tradeoff that will squeeze people towards voting honest
ratings.
I could see honest voting want any of these three votes. Wanting A or B
vastly more than C, wanting A vastly more than B or C, or some more gradual
falloff. Does IRNR not do the right thing for those three voters?
A few months ago I thought a Condocret variation of INRN:
1. Calculate the Smith set using range ballots.
2. Eliminate candidates outside the Smith set
3. Rescale the votes. For example, if some vote was: A:100, B: 70, C:30, D:
10, E:0, and Smith = {D, C, D}, the rescaled vote would be: B: 100, C: 33.3,
D: 0
4. Elect the candidate with the highest sum.
Because Smith implies local IIA, this problem would be arguably reduced.
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--
Diego Renato dos Santos
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Re: [EM] Fixing Range Voting
On Wed, Oct 15, 2008 at 5:46 AM, Brian Olson [EMAIL PROTECTED] wrote: I mean the geometric sense. For ratings a,b,c,etc., sqrt(a*a + b*b + c*c ...) It has the potential to cause cumulative voting like effects. This is especially true in the initial rounds. Approval and range votings main point is that you can give anyone a high rating without it hurting you. Also, you would treat [+5,-5] different from [+10,0] It id heard to determine which plot refers to which method. (bleh, multiple typos) ... meant it is hard, though you pretty much worked that out. In a sense, part of the result is that there's a pretty tight pack of similar (good) results and a few outliers (IRV, pick-one). Fair enough. Maybe use dotted lines and dot-dash for those 2 ones. Alternatively, since the plots don't cross much, you could arrange the names in the same order as the resulting curves. If only 2 candidates remain, then it will set the window as max and min of those candidates. I think that's pretty similar to what I'd planned to implement. I'm still expecting some tinkering will be needed to get it to do solutions with negligible instability. Ofc, the more complex you make it, the harder it is to explain. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
Once upon a time, I designed an election method to fix the strategy problem with Range Voting. The strategy problem: You shouldn't cast a ballot with your honest ratings, you should maximize them along Approval strategy lines. It also fixes the counting problem of how if someone does cast votes throughout the range, they might have done better in the end by different values. The method I call Instant Runoff Normalized Ratings (IRNR): 1. Collect ratings ballots 2. Normalize each ballot so that each has an equal magnitude 3. Sum up normalized ballots 4. If there are more than two choices, drop the one with the smallest sum. If there are two choices remaining, one is the winner. 5. Re-normalize from original ballot values but as if dropped choices weren't there 6. Go to 3 I think it gets very near to a utilitarian ideal solution ( http://bolson.org/voting/twographs.html ) and encourages people to vote honestly and uses those honest votes to the best possible effect. I'm not sure I would vote honestly in such circumstance. Let my honest rangings be: 100 percent for my favourite but almost chanceless Robin Hood 20 percent for the frontrunner Cinderella 0 percent for the other frontrunner Ugly Duckling I think I would vote: 100 Robin Hood; 99 Cinderella; 0 Ugly Duckling If I'm really sure that the race decides between Cinderella and Ugly Duckling, why care too much for poor Robin Hood? And what, if I'm not really sure, because that's the situation which multi-candidate voting is really about? If I lower Cinderella's 99 to her honest 20, I make Robin Hood a little bit more hopeful not to drop first. But more hopeful against whom? Cinderella, of course, because I didn't change Robin and Ugly's obvious rangings. So I made more probable a situation in which more than 50 percent is the probability that the worst candidate wins. This is a doubtful advantage. On the other side, there is the effect that by rising Cinderella's points from the honest 20 to 99 I made more probable the similarly unlikely but positively desirable effect of Ugly dropping first instead of her. So, which does have more weigh? The doubtful little hope for Robin Hood, or the clear little hope against Ugly Duckling? I think the latter. Maybe at some point, let's say Cinderella's 5 percent, I like Robin so much more that I chose the first one. In that case I probably would vote 100-1-0 These voting are not the honest although by one percent honer than the simple Approval voting. But I would be open for persuasion. Peter Barath Tavaszig, most minden féláron! ADSL Internet már 1 745 Ft/hó -tól. Keresse ajánlatunkat a http://www.freestart.hu oldalon! Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
Hi, you wrote: encourages people to vote honestly What makes you believe this? Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
On Tue, Oct 14, 2008 at 2:04 PM, Brian Olson [EMAIL PROTECTED] wrote: Once upon a time, I designed an election method to fix the strategy problem with Range Voting. The method I call Instant Runoff Normalized Ratings (IRNR): 1. Collect ratings ballots 2. Normalize each ballot so that each has an equal magnitude Magnitude = max rating - min rating or Magnitude = sum of ratings (negative ratings allowed) ? 3. Sum up normalized ballots 4. If there are more than two choices, drop the one with the smallest sum. If there are two choices remaining, one is the winner. 5. Re-normalize from original ballot values but as if dropped choices weren't there 6. Go to 3 I think it gets very near to a utilitarian ideal solution ( http://bolson.org/voting/twographs.html ) It id heard to determine which plot refers to which method. and encourages people to vote honestly and uses those honest votes to the best possible effect. Maybe, I can't see any obvious strategy and it seems to protect people from casting weak votes. Its Instant Runoff nature does have some drawbacks. It is not summable by parts and requires all the data to be collected in one place. It also has some small discontinuities in the Ka-Ping Yee diagrams: http://bolson.org/voting/sim_one_seat/www/4c_IRNR.png But at least it's not as bad as IRV: http://bolson.org/voting/sim_one_seat/www/4c_IRV.png I have some ideas about smoothing out the discontinuity, but haven't gotten around to trying it yet. I think the key is to make the process more continuous and take smaller steps. Don't disqualify a choice all at once, but over several steps. Blend out the losing choices, blend out the nasty jumps in the decision process. Needs to be experimentally (in simulator) checked, though. I am not so sure candidates need to actually be eliminated. Candidates who are out of the running would still be rated by each voter. However, they would not be used to determine the truncation window used. Ofc, that could mean that the method doesn't converge. This is especially true if there is a condorcet cycle. For example, if a voter votes A: 10 B: 3 C: 0 initially, the vote will just be rescaled to give maximum window = (0,10) A: 1.0 B: 0.3 C: 0.0 Each candidate would be assigned a score based on the result of the first round, then the new window needs to be worked out 1.0 = in the running 0.0 = eliminated For each ballot. 1) work out weighted mean using the scores. - This will be the centre of the window 2) for each candidate work out d(candidate) = (score)*(distance from mean) 3) determine the highest distance 4) Set window to window( mean - dmax, mean + dman ) In the above example score(A) = 1 score(B) = 1 score(C) = 0.5 mean = (1*10 + 1*3 + 0.5*0)/2.5 = 5.2 distance(A) = 1*4.8 = 4.8 distance(B) = 1*2.2 = 2.2 distance(C) = 0.5*5.2 = 2.6 dmax = 4.8 window = (5.2-4.8 , 5.2+4.8) = (0.4, 10) The ballot would be rescaled as A: 1.0 B: 0.27 C: 0 If only 2 candidates remain, then it will set the window as max and min of those candidates. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
Btw, if we are bringing up old posts :p, any views on this page? http://ivnryan.com/ping_yee/results.html since you technically mentioned Yee diagrams. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Fixing Range Voting
With all the talk about Range Voting and its plusses and minuses, I wanted to inject this back into the mix. Once upon a time, I designed an election method to fix the strategy problem with Range Voting. The strategy problem: You shouldn't cast a ballot with your honest ratings, you should maximize them along Approval strategy lines. It also fixes the counting problem of how if someone does cast votes throughout the range, they might have done better in the end by different values. The method I call Instant Runoff Normalized Ratings (IRNR): 1. Collect ratings ballots 2. Normalize each ballot so that each has an equal magnitude 3. Sum up normalized ballots 4. If there are more than two choices, drop the one with the smallest sum. If there are two choices remaining, one is the winner. 5. Re-normalize from original ballot values but as if dropped choices weren't there 6. Go to 3 I think it gets very near to a utilitarian ideal solution ( http://bolson.org/voting/twographs.html ) and encourages people to vote honestly and uses those honest votes to the best possible effect. Its Instant Runoff nature does have some drawbacks. It is not summable by parts and requires all the data to be collected in one place. It also has some small discontinuities in the Ka-Ping Yee diagrams: http://bolson.org/voting/sim_one_seat/www/4c_IRNR.png But at least it's not as bad as IRV: http://bolson.org/voting/sim_one_seat/www/4c_IRV.png I have some ideas about smoothing out the discontinuity, but haven't gotten around to trying it yet. I think the key is to make the process more continuous and take smaller steps. Don't disqualify a choice all at once, but over several steps. Blend out the losing choices, blend out the nasty jumps in the decision process. Needs to be experimentally (in simulator) checked, though. Brian Olson http://bolson.org/ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
Instant Range-off Voting is an interesting idea. I thought about it once a while ago too. I didn't renormalize the ballots though, I just set the co-highest to 100 and the co-lowest to 0 for each ballot as a sanitation measure. I eventually abadoned it due to nonmonotonicity, but I think the discussion is a valid one. There are some problems with Range Voting, and perhaps tweaking it or adding some new features will fix them, perhaps not. Most of the problems seem to involve voters being coerced into making extreme ballots for fear of being outcompeted by strategic rivals. Assuming people will be honest out of charity is naive. Some of them will, perhaps many of them will, but unscrupulous individuals could manipulate an election if there were enough of them. So, in the spirit of idiotproofing voting, let's discuss Range Voting spinoffs. so for there is: IRNR (Instant Runoff Normalized Ratings) Cardinal Condorcet http://fc.antioch.edu/~james_green-armytage/cwp13.htm Various semi-proposed tweaking of Range Voting to include an elect majority winner first or elect CW first clause. All of these have the same goal and that goal is very simple. To either encourage honest ratings or force more explicit ratings. We walk a fine line here. If we flat out enforce normalized distribution, we get Borda... A method so dismal, so appaling, so monumentally bad that it may even be worse than FPTP. If you were to make more score diverse ballots count more, it would suffer from the DH3 pathology unless it exactly counteracted the weight of voting honestly. That being said, I think the most promising area of development here is based around the concept of a conditional vote that came up a few threads ago. The idea here being that individual ballots should react to a particular candidate being kicked out of the hopeful group or something like that. Anyway, if anyone has any idea for multiwinner ranked/rated methods, those are always appreciated for the study. IRNR STV looks interesting... Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Fixing Range Voting
On Oct 14, 2008, at 12:11 PM, Raph Frank wrote: On Tue, Oct 14, 2008 at 2:04 PM, Brian Olson [EMAIL PROTECTED] wrote: Once upon a time, I designed an election method to fix the strategy problem with Range Voting. The method I call Instant Runoff Normalized Ratings (IRNR): 1. Collect ratings ballots 2. Normalize each ballot so that each has an equal magnitude Magnitude = max rating - min rating or Magnitude = sum of ratings (negative ratings allowed) ? I mean the geometric sense. For ratings a,b,c,etc., sqrt(a*a + b*b + c*c ...) 3. Sum up normalized ballots 4. If there are more than two choices, drop the one with the smallest sum. If there are two choices remaining, one is the winner. 5. Re-normalize from original ballot values but as if dropped choices weren't there 6. Go to 3 I think it gets very near to a utilitarian ideal solution ( http://bolson.org/voting/twographs.html ) It id heard to determine which plot refers to which method. In a sense, part of the result is that there's a pretty tight pack of similar (good) results and a few outliers (IRV, pick-one). and encourages people to vote honestly and uses those honest votes to the best possible effect. Maybe, I can't see any obvious strategy and it seems to protect people from casting weak votes. Its Instant Runoff nature does have some drawbacks. It is not summable by parts and requires all the data to be collected in one place. It also has some small discontinuities in the Ka-Ping Yee diagrams: http://bolson.org/voting/sim_one_seat/www/4c_IRNR.png But at least it's not as bad as IRV: http://bolson.org/voting/sim_one_seat/www/4c_IRV.png I have some ideas about smoothing out the discontinuity, but haven't gotten around to trying it yet. I think the key is to make the process more continuous and take smaller steps. Don't disqualify a choice all at once, but over several steps. Blend out the losing choices, blend out the nasty jumps in the decision process. Needs to be experimentally (in simulator) checked, though. I am not so sure candidates need to actually be eliminated. Candidates who are out of the running would still be rated by each voter. However, they would not be used to determine the truncation window used. Ofc, that could mean that the method doesn't converge. This is especially true if there is a condorcet cycle. For example, if a voter votes A: 10 B: 3 C: 0 initially, the vote will just be rescaled to give maximum window = (0,10) A: 1.0 B: 0.3 C: 0.0 Each candidate would be assigned a score based on the result of the first round, then the new window needs to be worked out 1.0 = in the running 0.0 = eliminated For each ballot. 1) work out weighted mean using the scores. - This will be the centre of the window 2) for each candidate work out d(candidate) = (score)*(distance from mean) 3) determine the highest distance 4) Set window to window( mean - dmax, mean + dman ) In the above example score(A) = 1 score(B) = 1 score(C) = 0.5 mean = (1*10 + 1*3 + 0.5*0)/2.5 = 5.2 distance(A) = 1*4.8 = 4.8 distance(B) = 1*2.2 = 2.2 distance(C) = 0.5*5.2 = 2.6 dmax = 4.8 window = (5.2-4.8 , 5.2+4.8) = (0.4, 10) The ballot would be rescaled as A: 1.0 B: 0.27 C: 0 If only 2 candidates remain, then it will set the window as max and min of those candidates. I think that's pretty similar to what I'd planned to implement. I'm still expecting some tinkering will be needed to get it to do solutions with negligible instability. Election-Methods mailing list - see http://electorama.com/em for list info
