Talk:Range voting

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Articles for deletion This article was nominated for deletion on November 18, 2007. The result of the discussion was keep.
Tactical voting is pretty much useless, especially in

multiple-candidate elections. Any possibility that a favorable result will occur due to inaccurate rankings is overwhelmed by the possibility that a non-favorable result will be more likely to occur.

I'm pretty sure that it's been proven that correct range voting strategy is to vote it as approval, at least when the counting method is total score.

Contents

[edit] Inaccurate example figures

If each city votes honestly on a scale of 1-10 with their favorite candidate at 10 and their least favorite at 0 and the remaining candidates proportional to their relative distance, the results are:

Memphis to Knoxville, 554 km
Nashville to Memphis, 311 km
Nashville to Knoxville, 255 km
Nashville to Chattanooga, 183 km
Memphis to Chattanooga 428 km
Knoxville to Chattanooga 158 km
Chattanooga voters;
Chattanooga, 0 - 10 * 15 = 150 points for Chattanooga
Memphis, 428 - 0 * 15 = 0 points for Memphis
Knoxville, 158 - 6 * 15 = 90 points for Knoxville
Nashville, 183 - 6 * 15 = 90 points for Nashville
Memphis voters;
Chattanooga, 428 - 2 * 42 = 84 points for Chattanooga
Memphis, 0 - 10 * 42 = 420 points for Memphis
Knoxville, 554 - 0 * 42 = 0 points for Knoxville
Nashville, 311 - 4 * 42 = 168 points for Nashville
Knoxville voters;
Chattanooga, 158 - 7 * 17 = 119 points for Chattanooga
Memphis, 554 - 0 * 17 = 0 points for Memphis
Knoxville, 0 - 10 * 17 = 170 points for Knoxville
Nashville, 255 - 5 * 17 = 85 points for Nashville
Nashville voters;
Chattanooga, 183 - 4 * 26 = 104 points for Chattanooga
Memphis, 311 - 0 * 26 = 0 points for Memphis
Knoxville, 255 - 2 * 26 = 52 points for Knoxville
Nashville, 0 - 10 * 26 = 260 points for Nashville
Chattanooga total; 457
Memphis total; 420
Knoxville total; 312
Nashville total; 603

I plan on editing the results of the example to fit these more accurate figures. —Preceding unsigned comment added by Monkthatgotfunk (talk • contribs) 21:02, 8 May 2008 (UTC)

[edit] Strategy

I removed the following text, because it doesn't make any sense. Obviously candidate will do everything in their power to win. That is assumed. The question is not whether candidate can manipulate voters (isn't that the point of a campaign?) but rather whether voters can manipulate the system by not voting sincerely. However it can be mathematically proven that any deviations from what the voter sincerely desires will reduce the likelihood of the outcome the voter desires. If a voter so strongly favor his favorite candidate that he rates other voters lower, that is an expression of his preferences, not a "strategy." It is also possible to show mathematically that it is not in the best interest to vote either 0 or 1 on everybody (as someone has already pointed out in the disucssion below). The proof is statistical. You look only at the case where the person's vote actually decides the outcome. However, since the person doesn't know what the vote tally will be when he casts his vote there is no way to apportion his vote that will increase the likely of a positive outcome, other than a sincere rating.

One reason that range voting is not used in any public or private election is that, like approval voting, it is easily subject to candidates' strategic manipulation. A candidate would have an obvious incentive to urge his or her supporters privately to give a low rating to all other candidates even as professing interest publicly in reaching out to other candidates' supporters. Even without a candidate directly communicating this strategy to supporters, they would grasp the adverse impact on their favorite candidate of rating other candidates highly and be in a difficult position of not knowing how best to vote in order to help their preferred candidate.
Range voting advocates suggest that in most cases (when the population is large or not much is known about how others will vote), the optimal strategy for range voting is to vote as under approval voting, so that all candidates are given (to very good accuracy) either the maximum score or the minimum score. They also acknowledge that it is possible to devise examples in which voting maximum and minimum scores for all candidates is not optimal.[1] Because of the near-equivalence of range and approval voting with 100% strategic voters, range voting can only exhibit substantial advantages over approval voting in situations in which at least some voters are actually expressing their personal feelings rather than doing everything they can to cause their most favored outcomes, i.e. in which there are some amount of nonstrategic "honest" (or at least partially honest) voters. Situations where range voting is used such as in judging olympic events are not usually secret ballots so they discourage obvious forms of strategic voting.
Approval voting inventor Guy Ottewell now endorses range voting.[2] No elected official in the United States is known to endorse range voting.

Analysis of Range Voting with respect to manipulability (also see: Gibbard-Satterthwaite_theorem) First I want to examine people's incentives for sincere voting in the absence of perfect information of everybody else's votes. Perfect information seems like an overly strong assumption, that, for many reasons, would never fully obtain. (For one, its a condition that is impossible to achieve on a large scale. I.e., its impossible to give everybody full knowledge of how everybody else will vote, before they have voted.) Instead the degree of precision in predicting other's votes should be incorporated into the analysis dirrectly.

It can be shown that in a range voting system, even a very small number of voters will generate enough uncertainty about how people are voting, so that it will generally be in the interests of each voter to vote sincerely.

This is because any individual's vote only matters when the outcome is really close. Thus any guess he can come up with about how the population will vote will only be relevant when his guess is that the population is closely divided between at least couple options.

Say we are using a range voting system where participants can choose any rational number from 0 to 1 for each of three options A, B, and C.

The manipulability concern is that if a voter's sincere preferences were A= 0.0, B=0.9 and C=1.0, he could instead vote A=0.0, B=0.0 and C=1.0, thus increasing the chance that his favorite candidate C, will win.

For example, if the vote tally before he casts his vote is, A=100.1, B=100.5, and C= 100.0, then by casting his insincere vote he can make, B=100.5 and C=101, resulting in his favorite candidate, C, winning. But by casting his sincere vote he would make, B=101.4 and C=101, resulting in his second favorite, B, winning. Thus the manipulation argument is that he would have an incentive to cast insincere votes.

The problem with this manipulation is that it also increases the chance that his least favorite candidate, A, will win. Lets say A has gotten one more point so that the tally before his vote had instead been, A= 101.1, B=100.5, and C=100, then his manipulation would result in A=101.1, B=100.5, and C=101, resulting in his least favorite candidate A winning. If he voted sincerely the result would have been A=101.1, B=101.4, and C=101, resulting in his second favorite candidate B winning.

Thus his "manipulation" is really an expression of his preferences. What he is really saying is that his preference for C isn't just .1 more than his preference for B, because in that case it wouldn't be worth risking a victory for A whom he despises. Instead his preference for C is so much stronger than his preference for B, that its worth taking a higher risk of getting A. In other words, the difference between A and B isn't so great as the difference between the two of them and C.

This argument assumes that he can't predict the outcome of the vote tallies with a percentage error smaller than 100/(# of voters), which will clearly be true for even very small populations.

However, what if he doesn't believe that all three will be close, but that rather it will look something like this: A=50, B=100, C=100, plus or minus 0.5 for each option.

In this case he wouldn't need to use his spread to reduce option A because option A isn't a threat. Instead he can use his entire spread to express his preference between B and C, voting B=0 and C=1. This case where there are only two close options is the strongest argument for "manipulation," however I think it is still flawed. In the case where the population has so little desire for A that A has no chance of winning, we would want people to use their spreads to indicate their preferences between the likely winners. This is adding valuable information.

For instance, we would not want a single extreme right wing Nazi candidate to squeeze voter's assignments to the legitimate portion of the political spectrum into a range of .99- 1.00, just because "anybody is better than that guy." This is because if mainstream candidates were squeezed into such a narrow range then the outcome between those candidates would end up being essentially random. So its a positive quality, not a manipulable quality, of the range voting system that voters will have an incentive to express their preferences with respect to the realistic candidates.

Of course there is an equilibrium: the more that mainstream voters ignore the unlikely candidate, and use their spread to distinguish between the likely candidates, the closer the unlikely candidate gets to being likely, because overall scores will be lower. This in turn gives voters some incentive to use some of their spread to vote against the unlikely candidate (by increasing scores for all other candidates). The resulting equilibrium would flatten the entire distribution to a limited degree.

On thing is clear however. Rational voters would never have an incentive to misrepresent their ordinal preferences. It would always make sense to give a preferred candidate a higher score than a less-preferred candidate (even if it was only a .000001 difference). (This is a very different result from ranked voting, and borda count, where you are required to vote lower for one candidate in order to vote higher for another. This trade off doesn't exist in range voting.)

I don't think this is true. A B C are candidates and you have real preferences 100 90 0. However, you know that in the population as a whole, 50% will vote 100 for B, and 50% will vote 100 for C. To prevent C winning, you have to make the gap between B and C as large as possible, so you will vote 100 100 0, which harms your true first choice. —Preceding unsigned comment added by 87.194.220.108 (talk) 22:51, 6 January 2008 (UTC)

Range voters would have an incentive to adjust their cardinal assignments so as best to express their preferences based on two factors: who they like, and who they think is in the running.

Thus, I think, with only the weakest uncertainty assumption (predictions of outcomes with percentage error greater than 100/(# of voters) ), it would always be in voters interest to vote essentially sincerely. (I think the argument could easily be made, that even in the case of no-uncertainty, voter incentive would still be to vote perfectly sincerely. No uncertainty is just carrying the equilibrium description above to the extreme. If you have no uncertainty, then you would want to use 100% of your spread to distinguish between your preferences of the possible winners. Thus you would want to vote 1 for the candidate you most prefered out of those you can make win, and low enough for the other candidates so they don't win. I.e. you are not manipulating, you are expressing your sincere preference.)

And even in the case of no uncertainty, voters would never have an incentive to distort their ordinal preferences (so if non-distortion of ordinal preferences is the measure of sincerity, then votes would always have the incentive to be perfectly sincere).

[edit] Question.

With range voting, is it permissible to leave some of the numbers out?

Say allocate a (4) and a (1) and leave the others as (0) and (0).


In this example of range voting, the weights go 4-3-2-1.

If Formula One races, they give the winner an extra weight, something like 8-4-2-1.

Who choses what weights to give?

Syd1435 05:56, 2004 Nov 23 (UTC)

It is up to the voter within the bounds set by the rules. --Henrygb 18:10, 31 Jan 2005 (UTC)

Range Voting is ratings. The rating you give to one candidate do not constrict your freedom in rating another. A voting method where the voter is forced to give a descending number of points is called Borda count. The restriction with descending numbers was made to prevent voting in extremes but it brings new problems. The Borda count is generally not called a version of Range Voting. 84.144.91.50 08:51, 25 May 2005 (UTC)

[edit] Strategy

The article currently states

In general, the optimal tactical voting strategy for range voting is to vote as if it were identical to approval voting, so that all candidates are given either the maximum score or the minimum score. For more detailed strategies, see approval voting.

However, I don't agree with this. Suppose there are three candidates and you are voting within the range [0, 1], which you would like to give votes of 0, 1/2, and 1, in order. Then the article would suggest that one of the following four voting patterns is optimal, but I wish to show that none of them are:

  • 0, 0, 0: This vote would be silly, and you'd be better off not going to the polls.
  • 0, 0, 1: In this case, the first candidate might win with a margin of victory of less than 1/2 over the second, but you could have prevented that! After all, you prefer the second candidate.
  • 0, 1, 1: In this case, the second candidate might win with a margin of victory of less than 1/2 over the third, but you could have prevented that! After all, you prefer the third candidate.
  • 1, 1, 1: Same as for 0, 0, 0.

Anyone agree or disagree?

Disagree, if we are talking about public elections, in which case you do not have adequate information to usefully use intermediate ratings. User:KVenzke
By "optimal", I think that it means with perfect information, in which case I claim that the article is incorrect currently. Boris Alexeev 03:54, 20 May 2005 (UTC)
Do you mean in the quote above? There "optimal" means "the best possible way"; it doesn't say anything about information. If you had no information at all, then the optimal range voting strategy is to give above-average candidates the top score and below-average the bottom score, just as in approval. KVenzke 14:46, May 20, 2005 (UTC)
I think I still disgree in this situation. If one of the candidates is a lot better than the rest, why shouldn't I give him the top score while others scores progressively in between?
You can vote however you want to vote. The issue is how to vote "optimally," which means "so that the result is as good as possible from your perspective." KVenzke 03:23, May 21, 2005 (UTC)
Can you or MyRedDice (who I think posted the "I'm pretty sure that it's been proven that correct range voting strategy is to vote it as approval, at least when the counting method is total score." above -- emphasis mine) actually give a proof of any sorts, like my disproof above? Boris Alexeev 20:39, 20 May 2005 (UTC)
That was you? Ok, I'll try one explanation before resorting to digging through the election methods list archives:
Unless you have extremely good information (such as, you know down to a single vote that your vote will either break one specific tie or another specific tie), then you have to assume that your vote will have such a small effect on the result as to make no difference. So, suppose the method is approval voting, so that you can only give 1 or 0, and you vote optimally (that is, you approve every candidate who is better than your expectation for the election). Now suppose after you cast your ballot, the officials say, "guess what? For whatever reason, you in fact get to vote an additional time." So how do you vote the second time? The same way as the first time: You can't assume your initial ballot drastically changed anyone's odds of election. And no matter how many additional times the election officials invite you to vote, you would never have any reason to start or stop approving some candidate. (That is, assuming we do not know how many times everyone else gets to vote.)
Let me quote your argument and consider it specifically:
However, I don't agree with this. Suppose there are three candidates and you are voting within the range [0, 1], which you would like to give votes of 0, 1/2, and 1, in order. Then the article would suggest that one of the following four voting patterns is optimal, but I wish to show that none of them are:
  • 0, 0, 1: In this case, the first candidate might win with a margin of victory of less than 1/2 over the second, but you could have prevented that! After all, you prefer the second candidate.
  • 0, 1, 1: In this case, the second candidate might win with a margin of victory of less than 1/2 over the third, but you could have prevented that! After all, you prefer the third candidate.
This argument ignores the fact that the vote 0, 1/2, 1 has exactly the same problems; only the specific margins of victory are different.
To determine the optimal way of voting, you need to know your utility for each candidate (which apparently is 0, 1/2, and 1) and the predicted odds of election (because we need to guess how likely it is that there will be a tie between any pair of candidates). Suppose that all odds are equal, or unknown. In that case, it makes no difference to your expectation what rating you give to the middle candidate. You could give, 0, 1/2, or 1; it makes no difference at all to you.
Suppose now that your favorite candidate is considered slightly more likely to win than the other two, and nothing else has changed. Now your optimal vote is 0,0,1. Giving an intermediate rating like 1/2 just dilutes the influence of your vote, by weakening your ability to resolve the most important and/or most likely ties.
However, if the voters' goal is to elect the candidate who maximizes utility on the whole, for everyone, then they should all just vote honestly. That's what Olympic judges are supposed to do. But I consider Olympic judges to be quite different from voters in a public election. KVenzke 03:23, May 21, 2005 (UTC)
I'm sorry, I don't get this. Three candidates, one I absolutely loathe, one I think is ok but I know that the majority of the country is split 50/50 between this one and the one I loathe, and one I love, but is not well known. I must give the one I think is alright 100% otherwise there is a high risk of the one I loathe being elected. I can't vote more than 100% for my favourite candidate, so I've harmed them, since I've rated them the same as one I think is only mediocre. It seems like the same strategy problem that besets plurality to me. 87.194.220.108 (talk) —Preceding comment was added at 21:00, 6 January 2008 (UTC)
The problem with the statement that Approval Voting is strategically cast Range Voting is that it assumes that by "Range Voting", you mean a Range Vote where you take the median, not the sum- which is fine, as the vocal advocates of Range Voting all refer to the median system. It's only because the article favours the implemented form of Range Voting in the Olympics (and rightly so) that we run into this issue. And yes, in the case of a Range Vote where you take the median, there is a very good point to voting all relevant candidates zero- you dislike a few candidates intensely, but have no preference or little knowledge of the rest.
And to the editor directly above: You're thinking of it the wrong way, essentially. A semi-strategic Range voter will always mark their favourite candidate at 100 and their least favourite at 0. You're free to vote whatever you like for all the intermediary candidates, including exaggerating your opinion of them. It's only because you're exaggerating your opinion of the mediocre candidate that you feel you've betrayed your favourite. Compare this to other systems with ranked ballots- in Borda, you have to put every candidate in order without omission, so if you only really like one candidate and think the rest are horrible, you have to overvote most of them. In IRV, you can actually cause your favourite to lose just by ranking other candidates below them- and Condorcet methods have similar problems. I agree that strategic Range voting is wonky, but it's less wonky than other systems in some important ways, too. --54x (talk) 03:29, 2 March 2008 (UTC)
Followup: I must've been tired when I made that above comment. I should've said it assumes Range Voting takes the mean, not the median. --54x (talk) 12:45, 3 March 2008 (UTC)

[edit] Using the Median

While calculating the average fails the Majority Criterion I don't see how using the median could fail that. If the highest median is shared by several candidates one could fall back to the average as a tiebraker. Does this introduce new bugs? 84.144.91.50 12:58, 25 May 2005 (UTC)

One implementation of median ratings is Majority Choice Approval. Disadvantages of this are, for instance, the failure of Participation and consistency. KVenzke 15:19, May 25, 2005 (UTC)

D'oh. I already read the MCA article. Thanks for the fast answer. I also read about that version of MCA where the voter can use a ABCDF rating where A,B,C are calculated as the same, so it is merely an expression without having an effect on who the winner is (however, it could be used for having an effect on the winner's salary or suspending him from running for office in two consecutive rounds). But my above description of using the median could be used for any range while avoiding that. Does it introduce new bugs in relation to MCA then? (Maybe this belongs to the MCA discussion)84.144.91.50 19:31, 25 May 2005 (UTC)

I'm not familiar with an MCA variant in which some slots are functionally identical to others. I don't think using the average to break median ratings ties creates problems, but it might be more attractive to break the tie based on which candidate comes closer to having a higher median. KVenzke 20:09, May 25, 2005 (UTC)

[edit] My Sep 12 edit

I had to cut a lot of recent material for being original research, POV, not notable, not cited, and/or incorrect. I'm open to discussing it. KVenzke 05:03, September 12, 2005 (UTC)

As long as we're on the topic of incorrect material, I still disagree with the Strategy section. Can someone find a reference that shows that the strategy in range voting is the same as that of approval voting? The only webpage that I could find online argues that they (the optimal strategies) are different, whereas the only one supporting the claim [3] seems to have gotten the claim from wikipedia.
I may write up some more on this topic later (earlier I gave up probably because I had other things to do), but I don't like this claim from the previous discussion: "then you have to assume that your vote will have such a small effect on the result as to make no difference". If you may assume your vote will make no difference, you shouldn't vote --- saves you standing in line for hours. I also think the effect of a single person on an election is underestimated. In a direct public election of the U.S. President (say, exactly 100 million voters) between two candidates and where everyone votes randomly, the chance of a tie is 1 in 12500 or so. If everyone in my town (100,000 people) votes this same way, then a tie is more likely than 1 in 400. Those are the chances that your vote changes the result (in one model). They're not that low.
If you would like to respond to my claim here, go ahead, but given a choice, I would prefer an outside reference stating what is stated in the strategy section. Boris Alexeev 23:26, 12 September 2005 (UTC)
Here are messages from the thread from which I was remembering the argument I used: Mike Ossipoff Bart Ingles and Bart Ingles Richard Moore Alex Small Adam Tarr Mike Ossipoff regarding non-equivalence with fewer voters
I'll quote Mike Ossipoff:
Say we conducted an Approval vote, collected the ballots, and then said "Now we'll do another Approval balloting, whose results will be added to those of the previous balloting". How do you vote in the 2nd balloting? The same as in the 1st balloting.
At electionmethods.org, in Approval Strategy I, I discuss considerations for voting in Approval. It has to do with how you rate the candidates, and certain probabilities that you estimate. In the 2nd balloting has any of that changed? Your ratings of the candidates haven't changed. Have the probabilities changed? Not unless your own vote could change the probabilties. And in a public election your vote isn't going to significantly change the probabilities.
Therefore, in the 2nd balloting you vote exactly as you did in the 1st balloting. Likewise if there are additional ballotings.
As I said, the votes in these ballotings are added together. Since you're voting for the same candidates each time, some candidates are getting the maximum possible number of votes from you and some are getting the minimum possible (zero).
The election procedure that I've just described is the same as if CR were conducted one point at a time. "To which candiates would you give a point?"; "To what candidates would you give a point in addition to anythng that you might have already given them?"...etc, N times.
That's the same as saying "Give candidates point ratings from 0 to N".
and Bart Ingles:
You can in effect give partial votes [in approval voting] by voting randomly. In other words, if you want to give B a half-approval, you can toss a coin and approve B only if the coin toss is "heads". Assuming other voters do likewise, the outcome is the same as for Cardinal Ratings.
Since weak cardinal ratings (or partial approvals) are never optimal strategy, it's probably better not to entice voters into using them. Since tossing coins requires extra effort, approval voting encourages voters to make the best use of their vote.
By the way: It isn't clear to me what you believe optimal range voting strategy is. KVenzke 04:45, September 13, 2005 (UTC)
I only got a chance to skim this right now (going to bed), but on first glance, it still seems unconvincing (although I see some argument). But to quickly answer what I believe the optimal strategy is: not the same as for approval voting. I don't have to state the optimal strategy to argue that it isn't identical to approval voting. Boris Alexeev 07:18, 13 September 2005 (UTC)
I will wait for you to argue, then. KVenzke 21:27, 13 September 2005 (UTC)
Suppose we are voting with the range [0,1]. Suppose there are three candidates X, Y, and Z for which your utility is X + 1/2 * Y; that is, X promises you a dollar if he's elected, while Y promises you only 50 cents. There are also three voters, yourself and two others. The others vote randomly: each of their votes (6 total) are uniformly distributed in [0,1]. How should you vote? Here's a table of utilities:
Utilities of different votes
Votes Probabilities Utility
X Y Z X Y Z Exact Approx
1 0 0 27/40 13/80 13/80 121/160 0.75625
1 1/4 0 320537/491520 53179/245760 12925/98304 31143/40960 0.760327
1 1/2 0 953/1536 205/768 173/1536 193/256 0.753906
1 3/4 0 18319/32768 27753/81920 16739/163840 29837/40960 0.728442
1 1 0 109/240 109/240 11/120 109/160 0.68125
So voting (1, 1/4, 0) is better than voting (1, 0, 0) and (1, 1, 0). Boris Alexeev 07:19, 16 September 2005 (UTC)
I don't doubt that this scenario is possible. However, it would never happen in a public election. KVenzke 03:29, 17 September 2005 (UTC)
Actually, it has been brought to my attention that my numbers are incorrect in this example. However, I did compute something, so I probably misstated what my scenario was. It escapes me right now, though. I may write more later. Boris Alexeev 02:37, 26 October 2005 (UTC)
—
Okay, I finally read all of those messages, except everything about instant runoff. I want to draw your attention to this part of the last message:
Remember that no one has been claiming that Approval & CR are strategically equivalent in small committees. Only in public elections--many voters.
(snip!)
And I repeat that no one has been claiming that CR & Approval are strategically equivalent in small committees.
Now remember that the article currently states
In general, the optimal strategy for range voting is to vote it identically to approval voting, so that all candidates are given either the maximum score or the minimum score. For more detailed strategies, see approval voting. (emphasis mine)
You must agree the statement is incorrect, if you believe Mike Ossipoff.
No, I don't agree. The only case where it is not optimal is when you have very precise information to predict how other voters will vote. I don't see "in general" as misleading. KVenzke 03:29, 17 September 2005 (UTC)
At the very least, the statement should be changed to reflect that. However, I don't even believe the argument for large populations. It seems to rely on the fact that there is not enough information to take advantage of intermediate votes. I don't believe, however, that that is a sufficient argument. If you take that approach, then it's unclear that there is even enough information to rank the candidates; in a multi-candidate U.S. presidential election, do I really know how candidate Joe Blow will perform as president, compared to Richard Roe?
I don't understand your comparison. It has nothing to do with your certainty that a given candidate will do a good job. It has to do with your knowledge of how others are voting. KVenzke 03:29, 17 September 2005 (UTC)
If you take Ossipoff's argument above, he relies on "in a public election your vote isn't going to significantly change the probabilities." I claim that this is also an insufficient argument for two reasons: (1) in a certain sense, assuming that your vote doesn't change probabilities means that there's no point in voting at all, and (2) it relies on a particular model of voting in approval voting. In (2), what I mean is that it relies on the "judge the probabilities of others' winning" model of approval voting. What if the other people are uniformly distributed or something (see above)? Boris Alexeev 07:47, 16 September 2005 (UTC)
(1) is misguided. Your vote is unlikely to change the probabilities especially because in Ossipoff's scenario, everyone gets to cast the same number of votes. If you want to, you can conclude that there is no point in voting at all in public elections. One's conclusion on that topic is pretty irrelevant. But it is absurd to use the argument "surely there must be some point in voting" to argue that a range voter should vote as though his vote may be pivotal between every pair of candidates. KVenzke 03:29, 17 September 2005 (UTC)
(2) makes no difference. If the other voters are "uniformly distributed," then you can simply "judge the probabilities of others' winning" based on this information. In your example above, the voter is unusually knowledgeable about how others are voting. It is nothing like a public election. KVenzke 03:29, 17 September 2005 (UTC)

Response to KVenzke 03:29, 17 September 2005 (UTC) by Boris Alexeev 06:30, 20 September 2005 (UTC)

For simplicity, I'm writing with zero indentation.

At this point, I don't think there's any chance that either of us will change our opinion. I think it's a shame that there is an article on Wikipedia that I believe could be better, but that's just too bad. I will answer one or two of your points, as well as suggest changes, so as to complete the discussion.

Responses

"I don't doubt that this scenario is possible. However, it would never happen in a public election. KVenzke 03:29, 17 September 2005 (UTC)"

I'm actually unconvinced of the fact that in certain, reasonable models with many people, the same thing doesn't happen. I may do some analysis myself to determine the optimal vote in certain situations, although only because I am interested and not for this article. Unfortunately, your statement is not "provable".

"No, I don't agree. The only case where it is not optimal is when you have very precise information to predict how other voters will vote. I don't see "in general" as misleading. KVenzke 03:29, 17 September 2005 (UTC)"

I'd venture to say that using intermediate votes is helpful when either there are a small number of voters, or you have good information. As for why "in general" is confusing, see Mathematical jargon:

"In mathematics, in general is used to mean "in all cases". (Contrast this with the usual meaning of in general: "in most cases".)"

I think the quote speaks for itself, but in short, I interpreted "in general" to mean "always". See below.

"In your example above, the voter is unusually knowledgeable about how others are voting. It is nothing like a public election. KVenzke 03:29, 17 September 2005 (UTC)"

In my example, I assume the other voters are voting randomly. It's hard to have less information about the other voters. Indeed, if I actually knew how they were voting, I would simply vote as in approval and make sure that the best candidate that I can make win does win.

Suggested changes

For the reason described above, the phrase "in general" can be misleading. I suggest changing it to "in most cases" as well as an explanation of where this statement is supposedly true, e.g.:

In most cases (when the population is large and not much is known about how others will vote), the optimal strategy for range voting based on the sum of votes (as opposed to Median Ratings) is to vote it identically to approval voting, so that all candidates are given either the maximum score or the minimum score. For more detailed strategies, see approval voting.

My purpose in suggesting this change is four-fold: (0) to finish this discussion and compromise, (1) to clear up what the article says, (2) state everything that is "known" about the topic, and (3) make the article applicable even in cases with small population. I think range voting can be very useful in small committees (indeed, I use it myself), and is not only applicable to public elections. Of course, feel free to reword.

Boris Alexeev 06:30, 20 September 2005 (UTC)

Responses
At this point, I don't think there's any chance that either of us will change our opinion. I think it's a shame that there is an article on Wikipedia that I believe could be better, but that's just too bad.
I'm not clear on how you want to make this article better when you don't claim to know what the strategy section should actually say.
I'll change my opinion when I see an example that would be plausible for a public election!
In my example, I assume the other voters are voting randomly. It's hard to have less information about the other voters. Indeed, if I actually knew how they were voting, I would simply vote as in approval and make sure that the best candidate that I can make win does win.
It is not true that it is "hard to have less information about the other voters." In your example you are able to perfectly calculate that your ballot could reasonably be expected to break a tie between any pair of those candidates.
My purpose in suggesting this change is four-fold:
I largely adopted your suggestion. KVenzke 03:22, 21 September 2005 (UTC)
Thank you. Boris Alexeev 03:30, 21 September 2005 (UTC)

[edit] Arrow's impossibility theorem

I call b.s. on this passage, and I'm going to remove it:

One of the advantages of range voting is that Arrow's impossibility theorem doesn't apply to it. Indeed it satisfies the criteria of a deterministic voting system, with non-imposition, non-dictatorship, monotonicity, and independence of irrelevant alternatives.
The reason that range voting is not treated as a counter-example to Arrow's theorem is that it is a cardinal voting system, while Arrow's theorem is restricted to the processing of ordinal preferences; two different sets of range votes may express the same individual ordinal preferences but lead to different overall rankings.

There are several things wrong here:

  1. Arrow's theorem does apply. Range doesn't pass universality. It's possible to express the same social ordering using different magnitudes to achieve different results.
  2. Let's pretend for a second that Arrow's theorem doesn't apply. That's not an advantage of the system, as characterized by the passage above. That's like saying "One of the advantages of using coal is that it doesn't have a high price per gallon, since coal isn't sold by the gallon".

-- RobLa 18:55, 9 May 2006 (UTC)

That is one interpretation. Your POV. But read what it says
"unrestricted domain or universality: the social welfare function should create a deterministic, complete societal preference order from every possible set of individual preference orders. In other words: the vote must have a result that ranks all possible choices relative to one another, the voting mechanism must be able to process all possible sets of voter preferences, and it should consistently give the same result for the same profile of votes—no randomness is allowed in the process."
Range voting produces a deterministic, complete preference order from every possible set of range votes. There is no randomness in the process. Range voting mechanism can process all possible sets of voter preferences - indeed it can process a wider collection of voter preferences than simple ranked voting methods. So your objection is that there can be different sets of range votes which correspond to the same ranking of individual preferences, and these can lead to different social preferences. Arrow's theorem deals with a smaller universe than range voting; your view is that this means that Arrow's theorem applies in this smaller universe of ordinal preferences, but an equally valid view is that Arrow's theorem does not apply in the larger universe of cardinal preferences. --Henrygb 10:55, 26 May 2006 (UTC)
This is like saying Arrow doesn't apply to Condorcet methods because they don't satisfy IIA... If by "doesn't apply to" you mean "isn't disproven by" then that is what should be said. KVenzke 17:24, 6 June 2006 (UTC)
Henrygb, the text you cite is the Wikipedia paraphrasing of universality, not Arrow's actual text. A method doesn't have to be random to fail universality, it's merely an example of a potential failing. -- RobLa 18:40, 13 June 2006 (UTC)

It is enormously controversial to claim that any voting system is exempted from Arrow's theorem. For example, first past the post clearly isn't exempted, yet isn't a ranked system. In particular, my complaint is about this paragraph:

As it satisfies the criteria of a deterministic voting system, with non-imposition, non-dictatorship, monotonicity, and independence of irrelevant alternatives, it may appear that Arrow's impossibility theorem fails for it. The reason that range voting is not regarded as a counter-example to Arrow's theorem is that it is a cardinal voting system, while Arrow's theorem is restricted to the processing of ordinal preferences; two different sets of range votes may express the same individual ordinal preferences but lead to different overall rankings, so range voting could be said to fail Arrow's criterion of universality as applied to ranked preferences.

I've been asking around about this page, (see Talk:Social Choice and Individual Values) and it was pointed out that this claim isn't cited. I'm removing the paragraph, and asking that a source be cited before reinserting it. -- RobLa 18:40, 13 June 2006 (UTC)

I did not think the obvious needed to be cited. A quick Google search turns up Section 7 of http://epub.ub.uni-muenchen.de/archive/00000653/01/thecaseforutilitarianvoting.pdf or the final comment of http://www.rangevoting.org/BackAtKlarreich.html So now you have citations, and no citations the other way, please put it back. --Henrygb 15:00, 21 July 2006 (UTC)

[edit] Theoretical

I added some wording indicating that this system is not actually in current use "for single seat election", "political elections", etc. Also, especially in the "Properties" section, the writing seems to be getting fairly close to WP:NOR - it is not a "Condorcet method" to "many people", but "Center for Range Voting" has improved the relevant definitions to show that it is. Given that the Center appears to be primarily Warren Smith, who is the key person behind this conception of Range Voting, most non-voting-system-wonk readers such as myself can't help but feeling the article may not be properly neutral. Is Range Voting studied more widely under other terms, or has Dr. Smith's work been taken up elsewhere. There are no independent references. - David Oberst 03:06, 26 June 2006 (UTC)

I have previously cut the alternate Condorcet interpretation due to WP:NOR. I note that even if it's true that Condorcet need not have been interpreted to apply to rated ballots in the way it typically is (i.e., "if more voters prefer one candidate over another candidate than vice versa, no matter who the other candidate is, then this candidate must win"), noting this fact doesn't teach us anything relevant to range voting. It just allows range voting to satisfy a hypothetical criterion that no one uses. KVenzke 03:51, 26 June 2006 (UTC)
I think it would be fine to include the Condorcet line as something like "Range Voting advocate Warren Smith claims that Range Voting satisfies a modified Condorcet criterion" or similar. --54x (talk) 03:51, 2 March 2008 (UTC)

[edit] Tendentious editing by ip address users

Someone with a dial-up internet connection who has not registered as a user continues to make changes to article content without discussion or citation. I am reverting these changes. --Fahrenheit451 22:12, 8 March 2007 (UTC)

Here is an example of this anonymous user's editing and use of personal attacks. From history log: "14:02, 9 March 2007 71.252.98.213 (Talk) (←Undid revision 113762512 by Fahrenheit451 (talk)This does not need discussion. Fahrenheit451 is a hack)"--Fahrenheit451 14:46, 9 March 2007 (UTC)

On the substance, this is is one phrase that the anonymous user is inserting:

Range voting in which only two different votes may be submitted (0 and 1, for example) is equivalent to approval voting. As with approval voting, voters must weigh the adverse impact on their favorite candidate of ranking other candidates highly. It shares with approval voting failure to meet the majority criterion or the later-no-harm criterion.

The last sentence is this user's insertion. It is a redundancy. The paragraph is noting that Range with only two options is "equivalent" to Approval. Actually, it *is* Approval. Thus the comment that "it" -- i.e., Approval, shares with Approval [characteristics] is a tautology. If any additional comment is needed on the Properties of Range, it should be in the Properties section.

In particular, the term "failure," while used technically by election methods writers, is a loaded word. It is not a "failure," in more common language, of Range and Approval to not satisfy the Majority Criterion, rather, it would be quite equivalent to say that the Majority Criterion will, under some circumstances, require a clearly inferior election result that Approval and Range would rectify. Abd 05:50, 11 March 2007 (UTC)

[edit] Majority criterion

There is an open issue as to whether Range voting satisfies majority criterion. In reading the Majority criterion wiki entry, it appears to me that range voting does not satisfy it. Let me try to prove that by contrary example:

Consider this case:

 Three candidates X, Y, and Z.
 Three voters Able, Baker, Charlie.

They vote as follows (scale is 1 to 100):

 Able:    X: 3 of 100  Y:   2 of 100   Z: 1 of 100
 Baker:   X: 3 of 100  Y:   2 of 100   Z: 1 of 100
 Charlie: X: 1 of 100  Y: 100 of 100   Z: 1 of 100

As I am reading the range voting definition, candidate Y wins while a majority (Able and Baker) range candidate X as their first choice. If my analysis is true, then I contend that it is accurate to state that range voting does not strictly satisfy the majority criterion. QED.

Is my thinking correct? Thanks. WilliamKF 23:57, 12 March 2007 (UTC)

Likewise, there is an open issue as to whether range voting satisfies the later-no-harm criterion. If I am understanding this criterion correctly, I believe that the above example demonstrates that range voting does not meet this criteria. WilliamKF 00:03, 13 March 2007 (UTC)
Thinking more about this, I think a simple tweak would cause range voting to meet the above criteria. Perhaps this is the way it already works? If you take each voter and normalize/scale their votes to an average equal to all others, so that their low vote is stretched to 1 and their high vote is stretched to 100 perhaps the above voting anomalies go away? Maybe like this:

Formula would be: f(vote) = (vote - voter's low vote) * (high possible vote - low possible vote) / (voter's high - voter's low vote) + low possible vote.

So for Able, their low vote was 1, their high vote was 3, their high possible vote (same for all voters) is 100, their low possible vote (same for all voters) is 1. f(3) => 100 f(2) => 50.5 f(1) => 1.

 Able:    X: 3 => 100 of 100  Y:   2 =>  50.5 of 100   Z: 1 => 1 of 100
 Baker:   X: 3 => 100 of 100  Y:   2 =>  50.5 of 100   Z: 1 => 1 of 100
 Charlie: X: 1 =>   1 of 100  Y: 100 => 100   of 100   Z: 1 => 1 of 100

Now this makes the analysis more complicated. Can anyone create an example which violates majority criterion or later-no-harm criterion using this change? If not, the question becomes whether my tweak is part of the official definition for range voting or not. WilliamKF 00:25, 13 March 2007 (UTC)

William, I think you have solved a problem. The majority criterion is defined in terms of ranked systems, not rated, the latter of which Range is. You have essentially fixed the definition to encompass range voting.--Fahrenheit451 05:14, 13 March 2007 (UTC)

Nonsense. E.g.

Candidates A B C Daisy 10 9 0 Alice 10 9 0 Janet 1 10 0

Candidate B wins by a landslide, even though the votes are already scaled.

1) Having the majority win makes little sense, compared to having the winner who produces the greatest social utility. That is, it's not a problem if a voting method sometimes fails to elect the Condorcet winner (when there even is one); what matters is the average satisfaction of the electorate with the result. That's expected value. Any voter with an ounce of economics knowledge wants the highest expected value from a transaction. 2) With 5 candidates in a race, there is a 25% chance that no Condorcet winner even exists. With 10 candidates in the race, the odds are 50/50. Worrying about picking a Condorcet winner is therefore often entirely a moot point. 3) Range Voting elects the Condorcet winner (when one exists) more often than plurality any situation, and under some plausible assumptions of voter behavior may actually be a better Condorcet method than real Condorcet methods. --BROKEN LADDER

It appears to me that brokenladder has given us a counter example of range voting satisfying majority criterion. Therefore, unless anyone posts an explanation as to why this is not a counter example, I believe it is accurate to state in the article that it does not satisfy majority criterion. I think his counter example may also demonstrate that later-no-harm is not satisfied either. Anyone want to comment on that one too? WilliamKF 16:20, 13 March 2007 (UTC)

The problem is that no voting system can satisfy the Majority Criterion if the Majority does not vote their *strict* preference. The Criterion was not designed to allow "weak votes." Range allows weak votes. These votes can be considered as partial abstentions. In an example above, a vote of 1, 2, and 3, on a scale of 100, was considered an expression of preference by members of a "majority." In fact, these votes indicate serious dislike of all those candidates. Technically, though, they are "preferences." Yet they are seriously weak ones. Ranked methods treat preferences as absolute, and know nothing of weak votes. Consider it this way: a majority may have a preference, but is this preference guaranteed to win -- with any system -- if the majority abstains from voting? One way of looking at range is that each voter has N votes to cast, and may cast as many as they wish for any given candidate. (In other words, it is Approval voting with 100 votes instead of the normal one.)

If the majority have a preference, as shown in weak votes, these votes may be considered as partial abstentions. As if, in the first example above, 97% of that majority stayed home. So, for starters, it is appropriate to consider normalization in applying the Majority Criterion to Range. However, Range still can fail to elect the preference of a fully-voting majority. This happens when the majority also gives votes to another candidate. By doing this, again, the majority is effectively abstaining -- to a degree -- from that pairwise election. And thus, again, the first preference of a majority can fail to win.

Generally, as the Majority Criterion is usually stated and interpreted, it must be said that Range does not satisfy it. However, it only "fails" when the Majority, to some degree or other, *consents* to this by allowing votes to other candidates. The objection Range advocates have is to the loaded use, in articles for the general public, if the term "fail," even though it is technically correct.

The Majority Criterion was designed for ranked methods, and Range is not a ranked method, though one can infer rankings from a Range ballot. Some have proposed a revised Majority Criterion which requires the majority to vote strict preference to guarantee victory for the majority preference. It is the freedom that Range grants to the voter to vote weak preference that creates the ambiguity.

Under Range, the majority has the power to elect its preference. It may choose not to exercise this power. Under Approval, as an example, there may be a candidate preferred by the majority, but if the majority also votes to approve another candidate, that candidate may not win. In this case the permission that the majority has given is quite explicit. They, supposedly, had a preference but they did not use the means that the method provided to express it, which in Approval is to bullet vote. The same is true in Range.

What if, under standard Plurality, the majority were to vote for two candidates? The result would be that the ballots would be thrown out. Under Approval, the effect on the pairwise election between those two candidates is the same. Voting for more than one is abstaining from the pairwise elections between those approved and participating in every other pairwise election. And Range allows intermediate votes.

Really, the first question to address is the much simpler one: does Approval satisfy the Majority Criterion?

If the majority is not aware that it is a majority, it might prefer a candidate but act in such a manner as to elect another candidate. It can do the same under Plurality. We understand that Plurality satisfies the Majority Criterion because, we think, the majority can simply vote for its preference and it will win. However, Approval and Range allow exactly the same voting. If a majority knows that it is a majority (or close to a majority), it is easy for that majority to vote to win its preference under Approval. But what if it does not know? So it hedges its bets -- under Approval it approves additional candidates. Under Plurality, it might vote, instead of for its preference, for another candidate which it imagines is one of the top two. Under Range, it ranks some other candidates than its preference above zero. It is putting some of its weight behind these others. And if others do not support its preference and enough of them do support a candidate which the majority has made room for through its support, again, the first preference of the majority can win. With Approval it is very clear what is going on.

It is ironic that Plurality is universally considered to satisfy the Majority Criterion when it has a *worse* problem with majority preference, which is only not considered because normally the majority is aware of its power. Yet a majority aware of its power and which chooses to use it can prevail under Approval and Range quite the same as under Plurality. Abd 19:04, 13 March 2007 (UTC)

[edit] Proof of no fair voting solution when more than two candidates

I believe that there is a mathematical proof that in any election with more than two candidates, it is impossible to come up with a fair voting system. If anyone can find this in the literature, I think it would be useful to cite. Given there is no such thing as a perfect voting scheme when there are more than two choices, the task them becomes trying to find one that is a good compromise. WilliamKF 21:12, 13 March 2007 (UTC)

You are probably thinking of Arrow's impossibility theorem already mentioned in the article. It doesn't really apply here (relaunch old debate) because it assumes individual cardinal rather than ordinal rankings, but the list of criteria Range Voting fails (of which the most "fair" may be the majority criterion) should be enough. --Henrygb 23:11, 13 March 2007 (UTC)

Yes, there is some esoteric voting method criteria, like later-no-harm, which could be listed, but majority criterion is well-known as accepted as a legitimate criterion.--Fahrenheit451 02:12, 14 March 2007 (UTC)

[edit] multi seat elections

The article says that range voting is a system "for one-seat elections." I disagree, because range voting ranks all candidates, the very same ballot could be used in a multi-seat election. The top n ranked candidates would win seats. Am I missing something? maxsch 21:55, 25 October 2007 (UTC)

Yes, you are missing something. It's easiest to see with Approval, the simplest Range method.

Using a "top n" method for assigning seats would suffer from the same problem as Plurality methods that allow voters n votes. Essentially, the majority can get all the seats! This is why STV methods reweights votes as seats are created, and the multiwinner form of Range Voting, Reweighted Range Voting (RRV) does the same thing. The details are complex, but the basic idea, as an example, is that the votes of someone whose top ranked candidate is elected are then devalued, since they got a representative. RRV is more complicated than that, but it's the same idea.

STV is quite a good multiwinner method, but always is vulnerable to breakdown at the end of the process when actual eliminations start. RRV avoids that. No candidates are eliminated, but winners are declared one at a time until the n seats have been filled. Each time a winner is declared, ballots with votes for that candidate are reweighted. There is a form of Approval voting which can be used similarly, but there is a zealous article deleter, Special:Contributions/Yellowbeard, who has been going about getting election methods articles killed, and the article on it was killed Wikipedia:Articles_for_deletion/Proportional_approval_voting. Apparently not enough of the Voting Methods people are watching for this. We could get it back, if we want. But I can't do everything! (The vote was three to two for delete. Normally, that might not be enough to result in a delete, but it's up to the administrator who decides to take action, and apparently the administrator in question preferred the arguments of Yellowbeard and the other two. Yellowbeard has proposed the deletion of many election methods articles, some of them were actually significant, and this one was cited in many other articles -- so he went around deleting all the references.... which does make sense if the article is inappropriate.)

Abd 14:40, 28 October 2007 (UTC)

[edit] Probem with example

I just wrote a comment on the talk page for Bucklin voting that brought up a problem with the voting example used on this page. We have:

Suppose that voters each decided to grant from 1 to 10 points to each city such that their most liked choice got 10 points, and least liked choice got 1 point, with the intermediate choices getting 5 points and 2 points.

This is actually quite unlikely as a voting pattern. Range works best when votes are proportional to voter utilities, and a Memphis voter has a *far* higher utility for a Memphis capital than for a Nashville one. It is more or less traditional, another small problem, to have the minimum vote in Range be zero, not one, and that is what I'll do here. (My apologies for the very rough formatting, I really should use a table, but this is Talk....

Memph.Nashv. Chatt. Knox.
42: 10=420..2=.64...1=.42...0=..0
26: .0=..0...10=260..2=.52...1=.26
15: .0=..0....1=.15..10=150..2=.30
17: .0=..0....1=.17...2=.34..10=170
Tot ...420.....356.....278.....226

Memphis wins. This is actually the best result, probably! Essentially, it would save the most gas and citizen travel time. But in a real election, we would be much more likely to see Memphis bullet vote, likewise Nashville, and Chattanooga and Knoxville voters would give 10s to Nashville as well as to their own cities; indeed, the latter would probably give 10s to three cities. Essentially, Range reduces to Approval under certain conditions, and this election is one of them; standard Approval strategy is to pick the two front-runners and place the approval cutoff between them. With this strategy, Nashville wins, and the Memphis voters can't really do anything about it; attempts by Knoxville and Chattanooga voters to vote otherwise could lead to Memphis winning, a poor outcome for them.

(In a just system, the capital would probably be Memphis and certain tax or other advantages would be given, in exchange, to citizens in the other cities to compensate them for the increased travel time. I know of one national organization which has its annual conference every year in the same city. Unjust? No. They have a travel equalization fund, and all delegates pay the same amount to that fund, which then pays the travel expenses for all delegates. So the same travel expenses are paid by all delegates. by having a single city every year, the work of setting up the conference is minimized, and it is also convenient to the national office.) —Preceding unsigned comment added by Abd (talk • contribs) 04:55, 11 November 2007 (UTC)

With all due respect, you analysis is inaccurate. If each city votes honestly on a scale of 1-10 with their favorite candidate at 10 and their least favorite at 0 and the remaining candidates proportional to their relative distance, the results are:
Memphis to Knoxville, 554 km
Nashville to Memphis, 311 km
Nashville to Knoxville, 255 km
Nashville to Chattanooga, 183 km
Memphis to Chattanooga 428 km
Knoxville to Chattanooga 158 km
Chattanooga voters;
Chattanooga, 0 - 10 * 15 = 150 points for Chattanooga
Memphis, 428 - 0 * 15 = 0 points for Memphis
Knoxville, 158 - 6 * 15 = 90 points for Knoxville
Nashville, 183 - 6 * 15 = 90 points for Nashville
Memphis voters;
Chattanooga, 428 - 2 * 42 = 84 points for Chattanooga
Memphis, 0 - 10 * 42 = 420 points for Memphis
Knoxville, 554 - 0 * 42 = 0 points for Knoxville
Nashville, 311 - 4 * 42 = 168 points for Nashville
Knoxville voters;
Chattanooga, 158 - 7 * 17 = 119 points for Chattanooga
Memphis, 554 - 0 * 17 = 0 points for Memphis
Knoxville, 0 - 10 * 17 = 170 points for Knoxville
Nashville, 255 - 5 * 17 = 85 points for Nashville
Nashville voters;
Chattanooga, 183 - 4 * 26 = 104 points for Chattanooga
Memphis, 311 - 0 * 26 = 0 points for Memphis
Knoxville, 255 - 2 * 26 = 52 points for Knoxville
Nashville, 0 - 10 * 26 = 260 points for Nashville
Chattanooga total; 457
Memphis total; 420
Knoxville total; 312
Nashville total; 603
In addition, if there are no objections, I plan on editing the results of the example to fit these more accurate figures. —Preceding unsigned comment added by Monkthatgotfunk (talk • contribs) 21:02, 8 May 2008 (UTC)

[edit] Removal of POV tag

There is a POV tag on this article, placed by StrengthOfNations probably as an outcome of discussions at Wikipedia:Articles_for_deletion/Range_voting, which had been started by that editor. However, the problem with the article is not a POV problem, necessarily, but the use of sources not acceptable (or at least not fully acceptable) under Wikipedia policies, see WP:SOURCE. This is not a POV dispute, which is a content dispute, and no significant content dispute is apparent from Talk, nor is there any edit war going on. In other words, if an editor disputes content here, the editor is free to fix it instead of placing a POV tag, which should be connected with either a specific dispute -- which should be discussed here for resolution -- or a general characterization of the article as being unbalanced, which, again, should be discussed here so that the nature of the dispute is clear and likewise the remedy.

As an example of a *general* POV dispute, see Instant-runoff voting. The tag there was placed by a user not specifically involved in a content dispute, and specific problems were not asserted as part of the placing of the tag, but, the difference is, editors did confirm the reasonableness of the tag placement, and continue, there, to discuss and negotiate, either directly in Talk or indirectly through a series of edits, the remedy to both specific problems with the article and the overall balance problem. It's a process that takes time.

However, here, there has been no assertion of specific POV problems. I could agree that there is an overall balance problem, but the solution to that *in the absence of specific problems* would be to begin to add balancing material. Given that no attempt to do that has appeared either from the editor placing the tag or anyone else, I plan to remove the tag. *However*, any editor is free to put it back, and, if this is accompanied by any sign of an intention to act to remedy either specific problems or an overall balance problem, I would not contest this. I'm only contesting a general placement with no assertion of specific problems and no participation in remedying either them or a general imbalance problem. In that case, it is merely a drive-by shooting, which we must always meet with quick protection of the victim, first, and resolution of any legitimate dispute, later.

In my decision on this, I have also considered the likelihood that StrengthOfNations is a sock puppet or straw puppet (see WP:SOCK), which is reasonably clear to me from Special:Contributions/StrengthOfNations. Because I consider it largely a waste of time to try to *prove* this, at this point, I have not filed the suspicion or a checkuser request, and this consideration alone cannot be used as a counterargument to any edit. Sock puppet contributions, in my opinion, are only to be disregarded, in terms of judging the balance of opinion or the disregard and reversion of clearly meritless edits. Sock puppets may often make good contributions, which is why there is no automated process to remove reversible edits merely on the basis that the user was found to be a sock, and all editors, including suspected sock puppets, have the right of WP:AGF.

In any case, if any editor doesn't like my removal of the POV tag, please, justify its replacement here, preferably with examples of what is wrong with the article, aside from the obvious need for better sourcing, and put it back! (Lots of articles have poor sourcing and are still NPOV, because what is not sourced is still either generally accepted as true or is properly attributed as an opinion.) --Abd (talk) 02:29, 24 November 2007 (UTC)

[edit] original research

Hi, this is James Green-Armytage, and I just read this article for the first time. I'm glad that it wasn't deleted, because I think that this is a theoretically important voting system. Anyway, one thing that struck me when reading the article is that the "empirical tests" section might be considered original research. On the other hand, I find WS's study to be interesting, and think that it should at least get an external link, if not a section in the article. Has this already been discussed?

Also, on first my first skim through the article, I'm not finding a section pointing out the fact that "utility" is a theoretical phenomenon that cannot be measured (i.e. placed on a scale allowing interpersonal comparison). As far as I can tell, the same would apply to "Bayesian regret", but I'll admit that I'm not as familiar with that idea. --Hermitage (talk) 22:19, 29 November 2007 (UTC)

Actually, the concept can be applied, but in most circumstances, , as stated, it cannot be measured. However, there is a way around this, and it's used in Smith's simulations. Basically, the simulation starts with generating utilities according to some model. Various models are used, I'm not up on the exact details. I will note first, however, that some of the alleged vulnerabilities of Range Voting to strategic manipulation are based on assuming certain "sincere" utilities, then supposing that voters will vote *contrary* to the implications of those utilities. This is essentially an incomplete model. For example, supposedly sincere utilities might be, for three candidates, 100, 90, 0. But the voter votes "strategically," 100, 0, 0, because he wants his favorite to win. *This is a contradiction.* "Wanting the favorite to win" is *part* of what makes up the utility model. By positing some abstract "sincere" vote, then behavior that contradicts it, the appearance of "rewarding insincerity" is created. If a voter is seriously partisan (the candidate's mother?), the sincere utility is 100, 0, 0. And that is how the voter votes. (But voters may vote "exaggerated utilities," that's another matter, I'll get to it.
What is generated at the outset in the simulations is a set of utilities on a common scale. I call this the "first normalization," in what I've written about it. It's an assumption that the *universe* of utilities for all voters has the same span, or strength, or overall value. This has also been called the "heaven-hell" scale, the absolute best and the absolute worst. The method for generating utilities is part of the input to the simulator, it's a separate module, I think. These are absolute utilities, if we make the assumption noted: all voters are to be considered equal in overall value. The utilities may be generated on some kind of bell curve around the neutral point. Issue spaces have, I think, been used to generate utilities.
Then there is a module for voter behavior in the face of these utilities. There are various options. A common one is to assume that voters will normalize. That is, voters will consider the universe of realistic candidates, that is, those who might possibly win, and then vote accordingly. Suppose the initial absolute utilities for three candidates are 60, 50, 40. (I'm using Range 100, i.e., 0-100). Normalization would mean that the voter votes 100, 50, 0.
However, there is more than this. There is then strategic behavior that is a separate matter from the insincere vote. Suppose the candidate with the zero utility has no chance whatever of winning. The voter may decide to renormalize utilities to the span of possible winners. In a two-party system, this would mean that the voter would vote 100 (or 99) for the favorite frontrunner and 0 or 1) for the least favorite. The vote would then become, perhaps, 100, 0, 0, or a bullet vote. Or 100, 1, 0, if the voter wishes to preserve a preference order (which might count in some variations of Range).
Now, if Range is won with absolute utilities, it's perfect. It actually optimizes the result, for the electorate as a whole, *by definition*. But voting with absolute utilities is normally impractical. It can be done when, for example, the issues are financial, and the votes are the personal consequences for each voter of each option.
So there are then simulations run with normalized utilities, which reflect, much better, true voter behavior (and which is still "sincere": voters ordinarily don't know the overall social impact, they only know that they are being presented with a choice, they have their opinion about it, and they express the range of values implicit in the choices that present. It's like Yes/No voting, which is full strength voting, no matter how trivial the decision.
Normalization has a small negative effect on Range performance as to how well it optimizes overall benefit; however, this will normally balance out unless there is some systematic bias.
Then there is "strategic voting," which is really a problematic concept when applied to Range Voting, since it has a very different implication there. With ranked methods, strategic voting always means preference reversal. If we think of a vote as testimony by the voter, strategic voting is lying. But with Range, it simply means making decisions on how to vote that depend on the "strategic context," the most common example would be expected to be a voter who prefers a candidate not a front-runner, and/or who has a least-preferred candidate not a front-runner. Suppose that the true normalized utilities for a set of four candidates are 100, 50, 40, 0. The utilities for the frontrunners are 50, 40. This voter votes 100, 100, 0, 0. One recognizes, here, standard Approval strategy. That vote, again, might become 100, 99, 1, 0, so that preference order is preserved with miniscule loss of vote strength. (That is how I would probably vote in Range 100.)
In any case, as I mentioned, if voters can vote fully-sincere absolute utilities, Range is perfect. It is almost perfect, according to the simulators, with normalized utilities. With strategic voting, it is still the best system in overall performance. (Well, actually, Range+2, range with a top-two runoff, is slightly better, I think. This is because, I think, the majority choice involved detects and fixes errors due to normalization and strategic voting anomalies. And this was the clue that led me to my own favorite version of Range: use preference analysis on the votes to detect if a candidate exists who beats the Range winner pairwise. If so, hold an actual runoff between the two (more than two would be extraordinarily rare). The runoff tests preference strength! Normally, we can expect the Range winner to prevail, *unless* there has been some anomaly in how the voters voted, perhaps they were deceived by appearances of who could win, etc.
--Abd (talk) 19:06, 15 December 2007 (UTC)

[edit] Allocation voting merge?

A merge tag has been placed in this article, proposing a merge with Allocation voting. This would be a blatant error: Range and Allocation voting are quite different methods, quite the same as Approval is different from Plurality. Allocation voting *is* similar to (or identical with) Cumulative voting. So, if no objection appears here in short order -- the merge proposer did not start a discussion; the proposer is an obvious sock puppet (see Special:Contributions/Yellowbeard and look at the registration of the account and then the immediate activity) who has been, for a long time, acting to kill voting systems articles (with AfDs and, now, directly) -- I plan to remove the tag. --Abd (talk) 19:46, 15 December 2007 (UTC)

This being a clear error and no response, I'm removing the tag. If anyone disagrees, please replace it and discuss here. --Abd (talk) 18:58, 17 December 2007 (UTC)

[edit] Is Range a Positional voting system?

An editor removed the Category:Positional electoral systems tag from the article, with the summary: "(remove Category:Positional electoral systems, no ranking, no fixed points assigned)."[4]

This is not correct. While Warren Smith has stated that he prefers unlimited resolution Range, which would complicate the issue, but all current proposed and use Range voting systems provide a fixed number of position slots. For example, MSNBC polls taken after early Republican and Democratic candidate debates were what I call Range 3: there were three possible votes: -1, 0, +1. The default vote for each candidate was 0.

A Positional voting system is "a ranked voting method in which the options receive points based on their position on each ballot, and the option with the most points wins." Borda count is a positional system, as is plurality and approval. However, these methods differ, of course, in how the points are assigned, limitations on votes, etc.

Range Voting is precisely equivalent to Borda, except that (1) equal ranking is allowed, (2) some ranks may be empty.

In real Range ballots, there might be, as an example, ten positions for each candidate. As far as the voting equipment is concerned, these are slots, the equivalent of levers on lever machines, or they are bubbles to be filled and counted. Each position produces a particular point for a particular candidate. The meaning of the bubbles on a paper ballot might be points from 0 to 9. The points are summed, and the candidate with the most points wins. This is a positional voting system. I replaced the Category tag. --Abd (talk) 00:51, 22 December 2007 (UTC)

(Now, this seems to conflict with "ranked voting method." Range is a ranked method which allows equal ranking, that's all. However, it is possible that the definition of "positional voting system" requires strict ranking, in which case my argument here would be incorrect, and, contrary to Positional voting system, Approval is not a positional system either. It would take more research than I could do at the moment to confirm either position.) --Abd (talk) 00:55, 22 December 2007 (UTC)

Plurality, anti-plurality voting, approval can qualify by inference as positional systems, imagining a ranking exists, that all ranked candidates get one point (or reverse). I assume category was created for the purpose of analysis rather than implying methods excluded are all unacceptable. I agree we ought to be going to the SOURCES of the category rather than guessing. So I'll remove the category - feel free to re-add IF you can find a source definition. Tom Ruen (talk) 01:04, 22 December 2007 (UTC)
Problem is, reliable sources I could find are behind fee-access restrictions. There is a definition of positional voting in the glossary for the Center for Range Voting:
Weighted positional system: Voting system where a vote is a rank-ordering of all the N candidates. The kth-ranked candidate gets score Wk for some fixed set of "weights" W1≥W2≥W3≥...≥WN. The candidate with the greatest score-sum is elected. (For example, Borda is the weighted positional system with Wk=N-k, and plurality is the weighted positional system with W1=1 and Wk=0 for 2≤k≤N.)
There is then a detail page at: WtPostnl
It seems that Smith (the probable author) does not consider Approval or Range to be a positional systems. With neither system is a vote necessarily a "rank ordering of all candidates." However, if equal ranking is allowed, then both Approval and Range could be described as positional systems. From the point of view of system analysis, there are two major classes of voting systems, and the classes overlap: ranked systems and rating systems. Ranked systems are not concerned with preference strength, rating systems are. Borda is a rating system, restricting the "range votes" such that the ratings of the candidates are spread evenly across the range.
In Smith's analysis of the Favorite betrayal criterion and positional voting, he presents a proof for a theorem: For each number C≥3, every weighted positional voting system exhibits favorite betrayal in some C-candidate election situation except if the top two weights are equal. In other words, the voter may vote for more than one with full weight. The reason why positional voting systems like Borda and Plurality exhibit Favorite Betrayal and fail Independence from clones is that the rating of candidates is not independent. The theorem exempts a system where the top two weights are equal, and Approval is such a system, but it is a stretch. (we have to allow voters to skip ranks.)
My conclusion is that Range is not a positional system, nor is Approval, and the reason why Approval has incorrectly been considered to be one is that there are papers connecting Approval and positional systems, but I see no evidence that they claim that approval *is* a positional system. See [5], where the abstract has: "We also establish a link between approval voting and positional voting methods whenever Falmagne et al.'s (1996) size-independent model of approval voting holds: In all such cases, approval voting mimics some positional voting method." From this source it is clear that Approval is not considered a positional system, or else the author would be claiming a tautology. So not only will I leave the tag out of the Range article, I'll remove it from the Approval article and fix the main article. Thanks to Tom Ruen for finding this.
--Abd (talk) 21:47, 23 December 2007 (UTC)