[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
For those who need a system for substituting for a top-two runoff election, I devised two fair methods to suggest to her that do not have all the flaws of IRV/STV. (They both may've been devised by others before me. My goal was to create a fair method without IRV/STV's flaws which solve the problem of one person/one vote which is necessary to get a voting method approved by US courts. -- I believe that these alternative systems (below) are also susceptible to the spoiler effect of a nonwinning candidate changing who wins the election, although I believe that there is a significant difference between the alternative methods below and plurality and IRV where a majority opposed candidate may win the election. In other words, I believe that the winner due to a spoiler in the alternative method below is more likely to be a majority favorite. Both methods below solve the problem of every voter having a vote of value one and, unlike IRV, treat all voters alike by counting all their choices So, here are two possible methods that are fairer than IRV/STV and which are monotonic (unlike IRV/STV): 1. A rank choice ballot method: Any number of candidates may be running for office and any number allowed to be ranked on the ballot. Voter ranks one candidate vote =1 Voter ranks two candidates, denominator is 1+2 = 3 votes are worth 2/3 and 1/3 for first and second ranked candidates Voter ranks three candidates, denominator is 1+2+3=6 votes are worth 3/6 and 2/6 and 1/6 for 1st, 2nd, and 3rd choice respectively Voter ranks four candidates, denominator is 1+2+3+4=10 votes are worth 4/10, 3/10, 2/10, and 1/10 for 1st, 2nd, and 3rd and 4th choice respectively ETC. Just follow the same pattern 2. A point system where a total number of points per voter per contest may be allocated by the voter to any of the candidates running for office: Two candidates running for office, give all voters 2+1=3 votes to cast. They may cast all three votes for one candidate or split the votes any way between the two. Three candidates running for office, give all voters 3+2+1=6 votes to cast. They may cast all six votes for one candidate or split the votes any way they like between the three. Four candidates running for office, give all voters 4+3+2+1=10 votes to cast. They may cast all ten votes for one candidate or split the votes any way they like between the four. Five candidates running for office, give all voters 5+4+3+2+1=15 votes to cast. They may cast all 15 votes for one candidate or split the votes any way they like. The benefits of this system are that it: a. gives the voters more flexibility than plan #1 above as far as weighting the individual candidates b. is easy to assure that all voters contribute 1 total vote during the process by dividing each vote by the total number of votes allowed for each voter for each contest. It would, however, require educating each voter to make sure to use all the points available in any one contest though. The advantage of these two methods over IRV/STV include: 1. easy to count, precinct-summable (unlike IRV) 2. fair, treats all voters' votes equally by counting all choices of each voter (unlike IRV) 3. gives each voter a total of one vote total over the entire vote counting process satisfying the US courts (unlike IRV) 4. is monotonic -- preserves the right to cast a vote that has a positive affect on a candidate's chances of winning (unlike IRV.) 5. Allows all voters to participate in all the rounds since these methods require only one (1) round (unlike IRV) 6. can begin the counting immediately without waiting for all the late-counted provisional and absentee ballots to be ready to count (without fear of having to restart the entire process again from the beginning unlike with IRV/STV) -- Kathy Dopp Town of Colonie, NY 12304 phone 518-952-4030 cell 518-505-0220 http://utahcountvotes.org http://electionmathematics.org http://kathydopp.com/serendipity/ Realities Mar Instant Runoff Voting http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf Voters Have Reason to Worry http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf Checking election outcome accuracy --- Post-election audit sampling http://electionmathematics.org/em-audits/US/PEAuditSamplingMethods.pdf -- Kathy Dopp Town of Colonie, NY 12304 phone 518-952-4030 cell 518-505-0220 http://utahcountvotes.org http://electionmathematics.org http://kathydopp.com/serendipity/ Realities Mar Instant Runoff Voting http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf Voters Have Reason to Worry http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf Checking election outcome accuracy --- Post-election audit sampling http://electionmathematics.org/em-audits/US/PEAuditSamplingMethods.pdf Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
Kathy Dopp wrote (11 Jan 2010): "IRV/STV is fundamentally unfair because a large group of persons whose first choice loses, never has their 2nd choice counted, unlike some other voters. It's a highly inequitable method." Kathy Dopp wrote (13 Jan 2010): "For those who need a system for substituting for a top-two runoff election, I devised two fair methods to suggest to her that do not have all the flaws of IRV/STV. (They both may've been devised by others before me. My goal was to create a fair method without IRV/STV's flaws which solve the problem of one person/one vote which is necessary to get a voting method approved by US courts. -- I believe that these alternative systems (below) are also susceptible to the spoiler effect of a nonwinning candidate changing who wins the election, although I believe that there is a significant difference between the alternative methods below and plurality and IRV where a majority opposed candidate may win the election. In other words, I believe that the winner due to a spoiler in the alternative method below is more likely to be a majority favorite." If "majority opposed" means having a majority-strength pairwise loss, then there is no decisive method that assures that no such candidate can win. I'm not sure what Kathy means by a "majority favorite". That phrase is usually taken to refer to a candidate that is strictly top-ranked by more than half the voters. The "Majority Favorite" criterion is met by IRV and Plurality among many others, but not by Borda or Range. "Both methods below solve the problem of every voter having a vote of value one and, unlike IRV, treat all voters alike by counting all their choices So, here are two possible methods that are fairer than IRV/STV and which are monotonic (unlike IRV/STV): 1. A rank choice ballot method: Any number of candidates may be running for office and any number allowed to be ranked on the ballot. Voter ranks one candidate vote =1 Voter ranks two candidates, denominator is 1+2 = 3 votes are worth 2/3 and 1/3 for first and second ranked candidates Voter ranks three candidates, denominator is 1+2+3=6 votes are worth 3/6 and 2/6 and 1/6 for 1st, 2nd, and 3rd choice respectively Voter ranks four candidates, denominator is 1+2+3+4=10 votes are worth 4/10, 3/10, 2/10, and 1/10 for 1st, 2nd, and 3rd and 4th choice respectively ETC. Just follow the same pattern" 51: A>B 40: B 09: C>A A: (51 x 2/3 = 34) + (9 x 1/3 = 3) = 37. B: (40 x 1 = 40) + (51 x 1/3 = 17) = 57 C: (9 x 2/3) = 6. Kathy's proposed point score method here elects B in violation of Majority Favourite. Also of course if the A supporters had not ranked B then A would have won, a big violation of Later-no-Harm. "2. A point system where a total number of points per voter per contest may be allocated by the voter to any of the candidates running for office: Two candidates running for office, give all voters 2+1=3 votes to cast. They may cast all three votes for one candidate or split the votes any way between the two. Three candidates running for office, give all voters 3+2+1=6 votes to cast. They may cast all six votes for one candidate or split the votes any way they like between the three. Four candidates running for office, give all voters 4+3+2+1=10 votes to cast. They may cast all ten votes for one candidate or split the votes any way they like between the four. Five candidates running for office, give all voters 5+4+3+2+1=15 votes to cast. They may cast all 15 votes for one candidate or split the votes any way they like." This is effectively the same thing as the single-winner Cumulative Vote, and is likewise strategically equivalent to Plurality, but allowing voters to unwisely split up their votes mean that it also fails Majority Favorite. 51: A2, B1, C0 40: B3, A0, C0 09: C2, A1, B0 A: (51 x 2 = 104) + (9 x 1 = 9) = 113 B: (40 x 3 = 120) + (51 x 1 = 51) = 171 C: (9 x 2) = 18. "The advantage of these two methods over IRV/STV include: 1. easy to count, precinct-summable (unlike IRV) 2. fair, treats all voters' votes equally by counting all choices of each voter (unlike IRV)" I think judgements of "fair" (and "equitable") or not of a voting method should be based on their possible results, and not on some (presumably just aesthetic) prejudice about its algorithm. "3. gives each voter a total of one vote total over the entire vote counting process satisfying the US courts (unlike IRV)" If IRV doesn't satisfy the US courts, then how come IRV is used in the US? "4. is monotonic -- preserves the right to cast a vote that has a positive affect on a candidate's chances of winning (unlike IRV.) 5. Allows all voters to participate in all the rounds since these methods require only one (1) round (unlike IRV)". I am sure the majority of voters whose favourite was A in my examples would be very pleased that they were "allowed to participate in all the rounds". Is being "monotoni
[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
Abd ul-Rahman Lomax wrote (14 Jan 2010): >Why does Kathy elsewhere defend Top Two Runoff which isn't monotonic? "This opinion, stated as fact, is false. Top Two Runoff is a two-step system, and monotonicity doesn't refer to such. It refers to the effect of a vote on a single ballot as to the result of that ballot only. A vote for a candidate on a primary ballot in TTR will always help the candidate supported to make it either to a majority and a win, or to make it into the runoff. It never hurts that candidate. " A vote for any candidate X in any given IRV counting round will likewise "help X to a majority win or to make it into the next round". The contention that a "two-step system" (meaning requiring voters to make two trips to the polls) to elect a single candidate isn't allowed to be judged in aggregate is absurd. "Did supporters of the Lizard vote for the Wizard in order to create the Lizard vs. Wizard election in Louisiana? I rather doubt it. But this wouldn't create a monotonicity violation, and the problem is created by eliminations, it doesn't exist with repeated balloting." With "repeated balloting" there are no eliminations? As I undersatnd it, in "Top Two Runoff" all but the top two first-round vote getters are eliminated if no candidate gets more than half the votes in the first round. Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
Abd Lomax wrote (17 Jan 2010): "Chris is Australian, and is one of a rare breed: someone who actually understands STV and supports it for single-winner because of LNH satisfaction. Of course, LNH is a criterion disliked by many voting system experts, and it's based on a political concept which is, quite as you say, contrary to sensible negotiation process." I endorse IRV (Alternative Vote, with voters able to strictly rank from the top however many candidates they choose) as a good method, much better than Plurality or TTR, and the best of the methods that are invulnerable to Burial and meet Later-no-Harm. Some of us see elections as primarily a contest and not a "negotiation process". I endorse IRV because it has a "maximal set" of (what I consider to be) desirable criterion compliances: Majority for Solid Coalitions (aka Mutual Majority) Woodall's Plurality criterion Mutual Dominant Third Condorcet Loser Burial Invulnerability Later-no-Harm Later-no-Help Mono-add-Top Mono-add-Plump (implied by mono-add-top) Mono-append Irrelevant Ballots Clone-Winner Clone-Loser (together these two add up to Clone Independence) As far as I can tell, the only real points of dissatisfaction with IRV in Australia are (a) that in some jurisdictions the voter is not allowed to truncate (on pain of his/her vote being binned as "invalid") and (b) that it isn't multi-winner PR so that minor parties can be fairly represented. I gather the Irish are also reasonably satisfied with it for the election of their President. "I've really come to like Bucklin, because it allows voters to exercise full power for one candidate at the outset, then add, *if they choose to do so*, alternative approved candidates." The version of Bucklin Abd advocates (using ratings ballots with voters able to give as many candidates they like the same rating and also able to skip slots) tends to be strategically equivalent to Approval but entices voters to play silly strategy games "sitting out" rounds. It would be better if 3-slot ballots are used, in which case it is the same thing as (one of the versions of) "Majority Choice Approval" (MCA). IMO the best method that meets Favourite Betrayal (and also the best 3-slot ballot method) is "Strong Minimal Defence, Top Ratings": *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters have a less strong incentive to truncate. Unlike MCA/Bucklin this meets Irrelevant Ballots. In MCA candidate X could be declared the winner in the first round, and then it is found that a small number of voters had been wrongly excluded and these new voters choose to openly bullet-vote for nobody (perhaps themselves as write-ins) and then their additional ballots raise the majority threshold and trigger a second round in which X loses. I can't take seriously any method that fails Irrelevant Ballots. Compliance with Favourite Betrayal is incompatible with Condorcet. If you are looking for a relatively simple Condorcet method, I recommend Smith//Approval (ranking): *Voters rank from the top candidates they "approve". Equal-ranking is allowed. Interpreting being ranked above at least one other candidate as approval, elect the most approved member of the Smith set (the smallest non-empty set S of candidates that pairwise beat all the outside-S candidates).* Chris Benham __ See what's on at the movies in your area.. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
Dave Ketchum wrote (18 Jan 2010): "In response I will pick on LNH for not being a serious reason for rejecting Condorcet - that such failure can occur with reasonable voting choices for which the voter knows what is happening. Quoting from Wikipedia: >For example in an election conducted using the Condorcet compliant >method Ranked pairs the following votes are cast: >49: A >25: B >26: C>B >B is preferred to A by 51 votes to 49 votes. A is preferred to C by >49 votes to 26 votes. C is preferred to B by 26 votes to 25 votes. >There is no Condorcet winner and B is the Ranked pairs winner. >Suppose the 25 B voters give an additional preference to their >second choice C. >The votes are now: >49: A >25: B>C >26: C>B >C is preferred to A by 51 votes to 49 votes. C is preferred to B by >26 votes to 25 votes. B is preferred to A by 51 votes to 49 votes. >C is now the Condorcet winner and therefore the Ranked pairs winner. >By giving a second preference to candidate C the 25 B voters have >caused their first choice to be defeated. Pro-A is about equal strength with anti-A. For this it makes sense for anti-A to give their side the best odds with the second vote pattern, not caring about LNH (B and C may compete with each other, but clearly care more about trouncing A)." Dave, Your assumption that "B and C may compete with each other, but clearly care more about trouncing A" is based on what? The ballots referred to contain only the voters' rankings, with no indications about their relative preference strengths. If you read my entire post you will see that in it I endorse three methods, one of which is a Condorcet method. Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
On Jan 13, 2010, at 8:06 PM, Kathy Dopp wrote: > 1. A rank choice ballot method: > > Any number of candidates may be running for office and any number > allowed to be ranked on the ballot. > > Voter ranks one candidate vote =1 > > Voter ranks two candidates, denominator is 1+2 = 3 > votes are worth 2/3 and 1/3 for first and second ranked candidates > > Voter ranks three candidates, denominator is 1+2+3=6 > votes are worth 3/6 and 2/6 and 1/6 for 1st, 2nd, and 3rd choice respectively > > Voter ranks four candidates, denominator is 1+2+3+4=10 > votes are worth 4/10, 3/10, 2/10, and 1/10 for 1st, 2nd, and 3rd and > 4th choice respectively > > ETC. Just follow the same pattern This sounds like a variation on Borda count, but with an incentive to vote on fewer candidates. With smaller and smaller votes as I give more information, I should vote for one _maybe_ two choices. Why would I want to give my favorite a 4/10 vote when I could give them a 2/3 vote or a 1.0 vote? This is the wrong incentive. Giving more information on the ballot should be encouraged. > 2. A point system where a total number of points per voter per contest > may be allocated by the voter to any of the candidates running for > office: > > Two candidates running for office, give all voters 2+1=3 votes to > cast. They may cast all three votes for one candidate or split the > votes any way between the two. > > Three candidates running for office, give all voters 3+2+1=6 votes to > cast. They may cast all six votes for one candidate or split the votes > any way they like between the three. > > Four candidates running for office, give all voters 4+3+2+1=10 votes > to cast. They may cast all ten votes for one candidate or split the > votes any way they like between the four. > > Five candidates running for office, give all voters 5+4+3+2+1=15 votes > to cast. They may cast all 15 votes for one candidate or split the > votes any way they like. This is equivalent to any other normalized ratings ballot. People vote ratings, but they all have the same voting power, either by straight sum of ratings or by geometric distance or something. In any system where the voter has to allocate the points themselves, there will be nasty strategic thinking going on to try and allocate the points best. If I vote simply and honestly, allocating points in alignment with how I feel about candidates, points not in differential between the top two candidates are wasted. Kathy, in my investigations of election methods, I started with straight rating summation as optimal, but normalized ratings as more fair, but then ran into the wasted-vote problem and settled on "Instant Runoff Normalized Ratings" ( http://bolson.org/voting/methods.html#IRNR ). Over the course of rounds of counting it reallocates your vote based on your original ballot to always be optimally applied to the choices available. Never mind the "Instant Runoff" part of the name, by using ratings ballots and considering the whole ballot at once, it's much better than the simplistic IRV. It's much less non-monotonic than IRV, and gets better answers in my simulations. You can compare the relative non-monotonic areas in these election space plots: http://bolson.org/voting/sim_one_seat/www/ http://bolson.org/voting/sim_one_seat/www/4a_IRV.png http://bolson.org/voting/sim_one_seat/www/4a_IRNR.png http://bolson.org/voting/sim_one_seat/www/4a_Condorcet.png Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
On Wed, Jan 13, 2010 at 8:55 PM, wrote: > Send Election-Methods mailing list submissions to > election-meth...@lists.electorama.com > > To subscribe or unsubscribe via the World Wide Web, visit > > http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com > > or, via email, send a message with subject or body 'help' to > election-methods-requ...@lists.electorama.com > Date: Wed, 13 Jan 2010 20:30:26 -0500 > From: Brian Olson > To: Election Methods Mailing List > Subject: Re: [EM] Two simple alternative voting methods that are > fairer than IRV/STV and lack most IRV/STV flaws > On Jan 13, 2010, at 8:06 PM, Kathy Dopp wrote: >> 1. A rank choice ballot method: >> >> Any number of candidates may be running for office and any number >> allowed to be ranked on the ballot. >> >> Voter ranks one candidate vote =1 >> >> Voter ranks two candidates, denominator is 1+2 = 3 >> votes are worth 2/3 and 1/3 for first and second ranked candidates >> >> Voter ranks three candidates, denominator is 1+2+3=6 >> votes are worth 3/6 and 2/6 and 1/6 for 1st, 2nd, and 3rd choice respectively >> >> Voter ranks four candidates, denominator is 1+2+3+4=10 >> votes are worth 4/10, 3/10, 2/10, and 1/10 for 1st, 2nd, and 3rd and >> 4th choice respectively >> >> ETC. Just follow the same pattern > > This sounds like a variation on Borda count, but with an incentive to vote on > fewer candidates. Yes perhaps, but normalized to give a value of one in total to all ballots since Borda was rejected by the MN Supreme court as violating one-person/one-vote. > With smaller and smaller votes as I give more information, I should vote for > one _maybe_ two choices. Why would I want to give my favorite a 4/10 vote > when I could give them a 2/3 vote or a 1.0 vote? This is the wrong incentive. > Giving more information on the ballot should be encouraged. Yes. Probably. It depends on how attached to your first choice you are. > >> 2. A point system where a total number of points per voter per contest >> may be allocated by the voter to any of the candidates running for >> office: >> >> Two candidates running for office, give all voters 2+1=3 votes to >> cast. They may cast all three votes for one candidate or split the >> votes any way between the two. >> >> Three candidates running for office, give all voters 3+2+1=6 votes to >> cast. They may cast all six votes for one candidate or split the votes >> any way they like between the three. >> >> Four candidates running for office, give all voters 4+3+2+1=10 votes >> to cast. They may cast all ten votes for one candidate or split the >> votes any way they like between the four. >> >> Five candidates running for office, give all voters 5+4+3+2+1=15 votes >> to cast. They may cast all 15 votes for one candidate or split the >> votes any way they like. > > This is equivalent to any other normalized ratings ballot. People vote > ratings, but they all have the same voting power, either by straight sum of > ratings or by geometric distance or something. Yes. It just standardizes the number of points and makes it seem fair (an equal number of points) to voters who would not understand the "normalization" process if all voters were allowed to cast a different number of votes initially. It also simplifies the calculation and makes it much easier for the public to check. > In any system where the voter has to allocate the points themselves, there > will be nasty strategic thinking going on to try and allocate the points best. > If I vote simply and honestly, allocating points in alignment with how I feel > about candidates, points not in differential between the top two candidates > are wasted. That's a good argument for the first method I suggested since all the voter has to do is rank as many candidates as they feel like ranking, but knowing that the 2nd and 3rd, etc. choices will add points that count against the voter's 1st choice, and may therefore cause the 2nd or 3rd choice to win instead being more popular with other voters. > > Kathy, in my investigations of election methods, I started with straight > rating summation as optimal, but normalized ratings as more fair, but then > ran into the wasted-vote problem and settled on "Instant Runoff Normalized > Ratings" ( http://bolson.org/voting/methods.html#IRNR ). I agree that that method is much fairer than IRV/STV but it is too complex to count and is not precinct-summable which raises other election administration problems and also auditability problems, so it is not a method I'd choose even though it is f
Re: [EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
At 08:06 PM 1/13/2010, Kathy Dopp wrote: For those who need a system for substituting for a top-two runoff election, I devised two fair methods to suggest to her that do not have all the flaws of IRV/STV. (They both may've been devised by others before me. My goal was to create a fair method without IRV/STV's flaws which solve the problem of one person/one vote which is necessary to get a voting method approved by US courts. Unfortunately, Kathy, you are entering a field where a great deal of work has been done, and there is some precedent, and you aren't terribly likely to come up with something new (though it's possible). I'll comment specifically. ... Both methods below solve the problem of every voter having a vote of value one and, unlike IRV, treat all voters alike by counting all their choices So, here are two possible methods that are fairer than IRV/STV and which are monotonic (unlike IRV/STV): 1. A rank choice ballot method: Any number of candidates may be running for office and any number allowed to be ranked on the ballot. Voter ranks one candidate vote =1 Voter ranks two candidates, denominator is 1+2 = 3 votes are worth 2/3 and 1/3 for first and second ranked candidates Voter ranks three candidates, denominator is 1+2+3=6 votes are worth 3/6 and 2/6 and 1/6 for 1st, 2nd, and 3rd choice respectively Voter ranks four candidates, denominator is 1+2+3+4=10 votes are worth 4/10, 3/10, 2/10, and 1/10 for 1st, 2nd, and 3rd and 4th choice respectively ETC. Just follow the same pattern This is a variation on Bucklin, something similar was tried in Oklahoma. It's similar, also, to Borda Count. Bucklin is instant runoff approval. It counts each rank as additional votes in an Approval election with a sliding scale down as to approval cutoff with each rank's counting. You seem to be under the impression that counting more than one vote simultaneously is a problem with Approval Voting. That isn't a position that has been sustained by the U.S. courts in general. Minnesota is an exception, and they knew that they were contradicting the general position of the courts, and no other court confirmed Brown v. Smallwood, the relevant case; further, that case has been misunderstood: the objection was to *any kind of multiple voting*, it's not clear that the vote splitting scheme decided would have avoided the opinion of the MN Supreme Court. With the scheme you proposed, and without any 'runoff' ranking, voting for additional candidates would seriously weaken the voter's power. Consider it this way. Suppose the voter wants to vote for a frontrunner. But the voter prefers someone else and wants to express that. If they vote for an additional candidate who is not a frontrunner, they have wasted part of their vote, it will be moot, it could be eliminated and have no effect on the outcome (that is, the fraction that isn't for a *winner* could be struck!) So if they prefer a non-frontrunner, and dare to express that as their first preference, they only get one-third of a vote to use in the real contest. That's quite a penalty to pay for a sincere vote! Oklahoma Bucklin was a little more sensible. It's a Bucklin method, counted in rounds until a majority is found. The first rank vote was a full vote, the second rank vote was 1/2 vote, the third rank vote was 1/3 vote. The method was never actually used in an election, because it was found unconstitutional, not because of the fractional voting, per se, though that might have been involved, but because adding additional ranked votes, under some conditions (more than two candidates?) was mandatory or the ballot was spoiled. I agree with the Courts decision, though they could have left the method in place and only struck the mandatory part. Instead, they tossed the whole thing out. Basically, Kathy, sorry, but the method is a bad idea. There have been equivalent suggestions with Approval Voting, i.e., if you vote for two, each vote counts as a half-vote. This essentially means that if the voter votes for two, they end up having only a half-vote of real voting power. Bad idea. I'm not at all sure that it's better than Plurality. If a majority is required or there is a runoff, maybe. You can do a lot of things with a majority requirement. The method is a variation on Warren Smith's Asset Voting, only with fixed ratios rather than purely voter-determined quantities (the vote must sum to one in Smith's Asset). It's legitimate there because no votes are wasted in Asset, and both half-votes, say, could end up being assigned to the same candidate, or to different ones, and this is a multiwinner method, as proposed, and so both votes can even go to different candidates and still be effective votes. A way of looking at it is that if the voter votes for one, the voter is creating a voting proxy, and if the voter votes for more than one, it's a virtual proxy committee that can amalagamate the voter or split i
Re: [EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
At 09:32 PM 1/13/2010, Kathy Dopp wrote: > This sounds like a variation on Borda count, but with an incentive to vote on fewer candidates. Yes perhaps, but normalized to give a value of one in total to all ballots since Borda was rejected by the MN Supreme court as violating one-person/one-vote. No. Borda was never considered by the MN Supreme Court. You are thinking of Bucklin, which was simply called Preferential Voting then, as I recall, after the ballot. FairVote created some propaganda that claimed that the rejection was based on one-person, one-vote, but that's not supported by a full reading of the decision. And Brown v. Smallwood wasn't confirmed anywhere else, it was disliked even within Minnesota, bucking the general opinion of the legal profession. You can read Brown v. Smallwood on rangevoting.org, there is a copy there. There was an appeal for reconsideration, be sure to read it all. The decision was quite remarkable. It quoted another decision, with approval, that it was the number of voters supporting a candidate that mattered, not the number of votes. And then, next breath, it counted the number of votes and noted that there were more votes cast than voters. The principle was correct: it's the number of voters that count, and a voting system like Approval or Bucklin simply finds ways to allow a majority of voters to assemble through making compromise choices on the ballot. In the end, if only one full vote is effective, or none, should the voter not have supported the winner at all, then we have one person, one vote. Because we have counted the number of *voters* supporting the result, not the number of votes, per se. Bucklin, with a majority requirement, simulates what happens in repeated single-vote elections, which is standard democratic process, as does Approval. Each election, if the voters want to move toward resolution, they will lower their approval cutoff to include more candidates. With Bucklin, the method does this for them, allowing them to participate in a limited series of such elections. If they want to. They can just vote for one, if they want. It depends on what they would prefer to see happen: completion or a runoff. It's like IRV, in that way, but without the top-N eliminations, which are what cause the trouble with IRV. There are no eliminations in standard repeated-election, majority-required elections, there are only voluntary withdrawals (which can't happen with Bucklin, presumably, there isn't the time provided and it would do harm if done mid-counting) or presumably increased voter compromise and respect for an appearing majority and possible willingness to accept it and terminate the process. That multiple votes are cast simultaneously is confused with one person one vote violation. They wouldn't have to be counted simultaneously, there could be a way to count Bucklin votes so that only one vote is counted at a time, it would be an iterative process. But why do an iterative process to just count one vote at a time, when you'd get the same result by counting them all at once? (Okay, I'll describe the algorithm: just consider each pairwise election, and only count votes, in any round, for each pair of candidates. Count them as votes are presently counted, where overvotes void the ballot -- but these votes will be counted later, if needed. Is there a candidate who beats all others? Consider this the tentative winner, or just the winner, period, if a majority isn't required. If a majority is required, count all the votes up to the final round, for the winner. If no majority of valid ballots, then move to the next round of counting and repeat. If no majority after the last round, follow runoff rules.) (If a method violates one-person, one-vote, surely it would produce a different result when only one vote is considered at a time! With IRV, voters cast more than one vote at a time, but only one vote from each voter is considered at a time. Or none. Same as Bucklin. The difference is in how the votes are counted; IRV is counting different ranks on different ballots, at once, based on having eliminated the higher ranked candidates on some of the ballots. And the result is that some votes, cast by a voter, are not effective and are passed over, whereas had the voter voted for another candidate in that exact same position, it would be counted. An argument can indeed be made that IRV violates basic voting principles of equality. Bucklin doesn't, in spite of Brown v. Smallwood, which made its argument defectively, and, as written then, clearly would have applied to IRV as well as Bucklin. We know that some very smart lawyers were on the Bucklin side (not to mention the political scientists who generally loved Bucklin), but they were unable to prevail. And they did not have the political clout to follow the Supreme Court's advice: if you want to do this, get the constitution changed to allow
Re: [EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
At 12:51 PM 1/14/2010, Chris Benham wrote: I'm not sure what Kathy means by a "majority favorite". Yeah, she's not necessarily precise, being a voting security expert, not a voting systems expert. That phrase is usually taken to refer to a candidate that is strictly top-ranked by more than half the voters. There are other possible interpretations, especially if equal ranking is involved. We must take equal ranking as equal ranking, I claim, the voter has decided that, even if the candidate isn't the strict favorite, the preference strength is low enough that the voter decides, under the circumstances, to conceal it and to apply equal voting power to both candidates. The usage of voting systems criteria based on concealed preferences is fraught with hazard, it produces results that don't really correspond to real-world performance or value. The "Majority Favorite" criterion is met by IRV and Plurality among many others, but not by Borda or Range. No method passes the Majority favorite criterion if the voters don't vote strict preference, with a full-power vote. Borda and Range allow voters to express weak votes. If the "strict preference" described is expressed with weak votes, then, sure, the majority criterion fails. Consider this. It's a Range 100 election. Half plus 1 voter votes this way: A: 1, B: 0, C: 0. What is the meaning of this vote? Unless half the voters are stupid, rather unlikely, it means that they dislike, almost fully, A, B, and C. These are really votes *against* all three candidates, but just not quite as strongly against A, who gets 1/100 vote. Now come the rest of the voters, who vote this way: A: 1, B: 0, C: 100. The result is C. I would guess that if an approval cutoff is part of the method, say it's midrange, there will be majority failure as per the rules, because we are looking at a majority expressing a vote *against* A (unanimity, actually!), but the conditions of the Majority Criterion were set up only to consider pure ranking, not approval or preference strength or Yes/No or For/Against. So, Yes, the majority criterion fails. By using examples that are closer to reality than this extreme example, it is made to appear that there is a serious criterion failure, but that depends upon an interpretation of the criterion that didn't at all consider preference strength or approval status, and the latter is crucial in traditional deliberative elections, the bedrock of democracy. A truly democratic organization does *nothing* with the explicit approval of a majority, excepting situations where an officer states an intention to rule absent objection, where the approval isn't necessarily explicit but can be assumed. No election is valid in such organizations without a vote from a majority of those voting approving of the result. If any voting system makes general use of approval status (to determine majority acceptance of the result) or preference strength (to give more weight to strong preferences than to weak ones, which clearly makes sense when voting is based on actual utilities), it will fail the Majority Criterion as written previously, before Range was on the table. And when voting systems experts were paying no attention at all to repeated balloting, it wasn't even considered an election method because it isn't deterministic. And, note: there goes Arrow's theorem and the rest of the impossibility theorems, they depend on the method being deterministic, and some other characteristics that require new interpretations, such as Independence from Irrelevant Alternatives. (A voting system should obviously be independent of irrelevant alternatives. The problem is that voters aren't. If voters modify their preference strength expressions based on some perception of strategic value, then the presence of an irrelevant candidate can -- if the voters misjudge the situation -- alter the results. Range with so-called "sincere votes" does obey IIA, and if voters would vote these sincere votes, in most situations they would get optimal results. If there were a way to weight votes according to overall preference strength, there would be *no* situation where there is a violation. In studying IIA as it applies to ranked voting systems, it's assumed that the voters vote their sincere preferences. So, the analogous vote with a range system would be the sincere vote. But this is the problem. Normalization. Normalization, however, is a voting strategy that is voluntary. In order to make Range fail, a candidate must be introduced who alters the normalization strategy by extending the range. (Or with removal by reducing it.) And then this example is asserted as a violation of Range. But with any system, if the voters alter their vote by the presence of an irrelevant alternative, the system will fail IIA. I presume this is why Warren Smith claims that Range satisfies IIA "under some interpretations. I am sur
Re: [EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
At 09:29 AM 1/15/2010, Chris Benham wrote: With "repeated balloting" there are no eliminations? As I undersatnd it, in "Top Two Runoff" all but the top two first-round vote getters are eliminated if no candidate gets more than half the votes in the first round. Yes. The standard voting method under Robert's Rules of Order (and I think under other standard parliamentary rules) is vote-for-one, with repeated election until a single candidate gains a majority. As many rounds are used as necessary, and there are no eliminations; in fact, "the election is repeated" which means the whole election process including nominations. But someone might move to mass-nominate existing candidates, though that's probably a bad idea. I'd vote against it! After all, that candidate set produced majority failure, and some of them might simply withdraw, and that's what really happens, it only gets tricky when three candidates insist on staying in, but these people may directly negotiate outside the election process itself. If the voters don't compromise, they don't get to go home. (Seriously, they can go home, all it takes is a majority on a vote to adjourn. They decide, by majority vote, like nearly all decisions in parliamentary procedure, which is more important, hammering away and getting a result, or getting some rest and trying again the next session. They can also decide, by majority vote, on some caretaker office-holder pending final resolution. There is no way that, where it's practical, I'd trade deliberative procedure for a mere voting system that is satisfied with less than a true, voluntary majority to resolve.) Yes, that's top two runoff. The major down side is, of course, center squeeze, but it turns out that in nonpartisan elections, center squeeze may be vanishingly rare. The famous examples were partisan elections. I think this is a major discovery: in nonpartisan public elections, voter rankings tend to average out such that voters with a particular first rank preference have little overall bias, compared to the rest of the voters. The implication of this is that Plurality, as long as the number of candidates does not climb too high such that noise has a big effect, reproduces what IRV does, because the vote transfers don't affect the rank order, they merely raise the vote totals proportionally. This doesn't hold with partisan elections, where a candidate's party affiliation is disclosed on the ballot, thus providing a handy guide to voters which allows them to fall into partisan grooves, which, then, cause the supporters of a particular candidate to be, indeed, biased with respect to the rest of the population. In the U.S., on average, a Green voter will prefer a Democrat over a Republican. This is of great practical importance. In the U.S., top two runoff is *mostly* used with nonpartisan elections, or with party primaries, which amounts to the same thing. (Voters in party primaries get no guidance from party affiliation!) Because of the expense and inconvenience of runoff elections, FairVote was able to sell IRV as a method to "gain majority results without runoff elections!" But the results of IRV and Plurality, we are seeing, are the same. (We can argue that with IRV, voters are more likely to vote their sincere first preference, and I'd agree, but in terms of results, this is highly unlikely to affect them, because if the first preference is at all perceived as possibly winning, in nonpartisan elections, voters will sincerely vote for them if they prefer them, and the only additional votes will be from other voters compromising, and in nonpartisan elections, these votes won't shift the results, so the determining factor is the initial first preference position of the electorate, unless it's close.) With real runoffs, though, the electorate gets to scrutinize the top two. In San Francisco, there was a winner of an IRV supervisorial election, with almost 40% of the valid ballots after transfers, in a field of, as I recall, about 23 candidates. It turned out that he did not live in the district and was ineligible to serve. In a runoff, it's practically certain that this information would have come out. The same is a general truth: in a runoff, voters now have a reduced set to consider, and will make more intelligent choices, overall. So FairVote has been damaging the most advanced voting system in general use in the United States, replacing it with a method that is allegedly cheaper, but with high implementation costs, and, in reality, the reduction in expense could have been accomplished by abolishing the majority requirement. Which the IRV implementation did, the measure explicitly took it out of the election code. But my point is that there is a much better way, which is to use a better system for primary elections *without* abolishing the majority requirement. Because there are no eliminations and, if necessary, all th
Re: [EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
In response I will pick on LNH for not being a serious reason for rejecting Condorcet - that such failure can occur with reasonable voting choices for which the voter knows what is happening. Quoting from Wikipedia: For example in an election conducted using theCondorcet compliant method Ranked pairs the following votes are cast: 49: A 25: B 26: C>B B is preferred to A by 51 votes to 49 votes. A is preferred to C by 49 votes to 26 votes. C is preferred to B by 26 votes to 25 votes. There is no Condorcet winner and B is the Ranked pairs winner. Suppose the 25 B voters give an additional preference to their second choice C. The votes are now: 49: A 25: B>C 26: C>B C is preferred to A by 51 votes to 49 votes. C is preferred to B by 26 votes to 25 votes. B is preferred to A by 51 votes to 49 votes. C is now the Condorcet winner and therefore theRanked pairs winner. By giving a second preference to candidate C the 25 B voters have caused their first choice to be defeated. Pro-A is about equal strength with anti-A. For this it makes sense for anti-A to give their side the best odds with the second vote pattern, not caring about LNH (B and C may compete with each other, but clearly care more about trouncing A). An aside: Note that the same strategy makes sense for IRV - A wins the first vote while B or C wins the second (C as shown; B with a trivial change in votes). LNH may have made sense for the methods that inspired it, but cannot compete for causing trouble for Condorcet, considering IRV's problems. Dave Ketchum On Jan 17, 2010, at 2:30 PM, Chris Benham wrote: Abd Lomax wrote (17 Jan 2010): "Chris is Australian, and is one of a rare breed: someone who actually understands STV and supports it for single-winner because of LNH satisfaction. Of course, LNH is a criterion disliked by many voting system experts, and it's based on a political concept which is, quite as you say, contrary to sensible negotiation process." I endorse IRV (Alternative Vote, with voters able to strictly rank from the top however many candidates they choose) as a good method, much better than Plurality or TTR, and the best of the methods that are invulnerable to Burial and meet Later-no-Harm. Some of us see elections as primarily a contest and not a "negotiation process". I endorse IRV because it has a "maximal set" of (what I consider to be) desirable criterion compliances: Majority for Solid Coalitions (aka Mutual Majority) Woodall's Plurality criterion Mutual Dominant Third Condorcet Loser Burial Invulnerability Later-no-Harm Later-no-Help Mono-add-Top Mono-add-Plump (implied by mono-add-top) Mono-append Irrelevant Ballots Clone-Winner Clone-Loser (together these two add up to Clone Independence) As far as I can tell, the only real points of dissatisfaction with IRV in Australia are (a) that in some jurisdictions the voter is not allowed to truncate (on pain of his/her vote being binned as "invalid") and (b) that it isn't multi-winner PR so that minor parties can be fairly represented. I gather the Irish are also reasonably satisfied with it for the election of their President. "I've really come to like Bucklin, because it allows voters to exercise full power for one candidate at the outset, then add, *if they choose to do so*, alternative approved candidates." The version of Bucklin Abd advocates (using ratings ballots with voters able to give as many candidates they like the same rating and also able to skip slots) tends to be strategically equivalent to Approval but entices voters to play silly strategy games "sitting out" rounds. It would be better if 3-slot ballots are used, in which case it is the same thing as (one of the versions of) "Majority Choice Approval" (MCA). IMO the best method that meets Favourite Betrayal (and also the best 3-slot ballot method) is "Strong Minimal Defence, Top Ratings": *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters have a less strong incentive to truncate. Unlike MCA/Bucklin this meets Irrelevant Ballots. In MCA candidate X could be declared the winner in the first round, and then it is found that a small number of voters had been wrongly excluded and these new voters choose to openly bullet-vote for nobody (perhaps themselves as write-ins) and then their additional ballots raise the majority threshold and trigger a second round in which X loses. I can't take seriously any method that fails Irr
Re: [EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
On Jan 20, 2010, at 12:48 PM, Chris Benham wrote: Dave Ketchum wrote (18 Jan 2010): "In response I will pick on LNH for not being a serious reason for rejecting Condorcet - that such failure can occur with reasonable voting choices for which the voter knows what is happening. Quoting from Wikipedia: For example in an election conducted using the Condorcet compliant method Ranked pairs the following votes are cast: 49: A 25: B 26: C>B B is preferred to A by 51 votes to 49 votes. A is preferred to C by 49 votes to 26 votes. C is preferred to B by 26 votes to 25 votes. There is no Condorcet winner and B is the Ranked pairs winner. Suppose the 25 B voters give an additional preference to their second choice C. The votes are now: 49: A 25: B>C 26: C>B C is preferred to A by 51 votes to 49 votes. C is preferred to B by 26 votes to 25 votes. B is preferred to A by 51 votes to 49 votes. C is now the Condorcet winner and therefore the Ranked pairs winner. By giving a second preference to candidate C the 25 B voters have caused their first choice to be defeated. Pro-A is about equal strength with anti-A. For this it makes sense for anti-A to give their side the best odds with the second vote pattern, not caring about LNH (B and C may compete with each other, but clearly care more about trouncing A)." Dave, Your assumption that "B and C may compete with each other, but clearly care more about trouncing A" is based on what? That one faction votes ONLY for A, and the other faction votes exclusively against A. Then some anti-As vote for both B and C. The B voters considering voting for B>C is consistent with this. The ballots referred to contain only the voters' rankings, with no indications about their relative preference strengths. The voting implies strength of preference. If you read my entire post you will see that in it I endorse three methods, one of which is a Condorcet method. This starts with my dislike for IRV, which started with my first hearing of that method and immediately liking Condorcet as better - before having heard of either method name. From that have to reject LNHarm for incompatibility - and thus respond to your liking of LNH. Dave Ketchum Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
