Re: [EM] Re: Definite Majority Choice, AWP, AM
James Green-Armytage jarmyta-at-antioch-college.edu |EMlist| wrote: James G-A replying to Ted, on the subject of AWP, DMC, and AM... Ted: Summary of discussion: Ted (AKA Araucaria) thinks AWP could do a better job of resisting strategic manipulation in some cases, but doesn't think it is as easy to explain to the public. James thinks they are equally difficult to explain and that relative merit should rule the discussion. I think we are two different planes that can never intersect. But all of my posts thus far have been directed toward finding a strong public proposal, so I can't let the methods stand on their technical merits alone. I can explain DMC in three simple sentences: Eliminate any candidate defeated by any other higher-approved candidate. The remaining candidates form what we call the Definite Majority Set. The winner is the single undefeated candidate in the Definite Majority Set. Would you like me to give a similarly-simple explanation for AWP? I'd be happy to try. Below is a provisional attempt. (1) We say that those who approve A but do not approve B have a strong preference for A over B. (2) We say that a defeat that consists of more strong preferences is stronger than one that consists of fewer strong preferences. (3) If there is no unbeaten candidate, we drop the weakest defeat that's in a cycle (e.g. X beats Y, Y beats Z, Z beats X) until there is an unbeaten candidate. James, I can explain RAV/DMC tally rule in nearly complete detail in one sentence: eliminate the least-approved candidate until a CW is found. The only thing left is how to deal with numerical ties. Your explanation is a high-level explanation that glosses over the details, yet it is still significantly more verbose than my explanation. I'll give you an A for effort and creativity, but as I said before, I think your AWP method is just too complicated for public acceptance. I suggest that you try to explain AWP to several people off the street. See how long it takes to get them to the point where they can explain it back accurately and in enough detail to implement it. I think you will be disappointed in most cases. --Russ Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Re: Definite Majority Choice, AWP, AM
Russ, you wrote: I can explain RAV/DMC tally rule in nearly complete detail in one sentence: eliminate the least-approved candidate until a CW is found. The only thing left is how to deal with numerical ties. Your explanation is a high-level explanation that glosses over the details, yet it is still significantly more verbose than my explanation. I'll give you an A for effort and creativity, but as I said before, I think your AWP method is just too complicated for public acceptance. I suggest that you try to explain AWP to several people off the street. See how long it takes to get them to the point where they can explain it back accurately and in enough detail to implement it. I think you will be disappointed in most cases. I'll agree that RAV has a significantly shorter definition than AWP. On the other hand, AWP has greater resistance to strategy. The relative importance of these two factors should be decided on a case-by-case basis, that is, in a particular electorate considering a change to a new voting system. Thus, rather than saying that one method or the other is useless, I suggest that we should direct our discussion towards clarifying the relative pros and cons of the different systems. Relevant questions are grouped into at least two categories, i.e. strategy/technical merit and explainability: Strategy/technical merit... Is AWP more strategy-resistant than RAV/DMC? How strategically vulnerable is RAV/DMC? How strategically vulnerable is AWP? What is the likelihood that strategic vulnerability in RAV/DMC will lead to abuse, or push voters into making extensive use of compromising counterstrategy? When one takes its strategic vulnerabilities, which systems is RAV/DMC technically preferable to? (E.g. plurality? runoff? IRV? CWO-IRV? margins? WV?) Likewise, which systems is AWP technically preferable to? (By technically preferable, I mean preferable from a standpoint that is not sensitive to factors like explainability.) Explainability... Is RAV/DMC easier to explain than AWP? What is the simplest way to explain RAV/DMC? What is the simplest way to explain AWP? In what kinds of electorates might RAV/DMC be able to gain public acceptance? In what kinds of electorates might AWP be able to gain public acceptance? I suggest that we should address these separate question groups in separate messages and threads. my best, James Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
Summary of discussion: Ted (AKA Araucaria) things AWP could do a better job of resisting strategic manipulation in some cases, but doesn't think it is as easy to explain to the public. James things they are equally difficult to explain and that relative merit should rule the discussion. I think we are two different planes that can never intersect. But all of my posts thus far have been directed toward finding a strong public proposal, so I can't let the methods stand on their technical merits alone. So James, before you try to once again push CWP and AWP on technical grounds, answer this: I can explain DMC in three simple sentences: Eliminate any candidate defeated by any other higher-approved candidate. The remaining candidates form what we call the Definite Majority Set. The winner is the single undefeated candidate in the Definite Majority Set. This is, IMO, simple and comprehensible to most people, though they may argue the benefit of such a procedure and may worry (possibly with just cause) about its vulnerability to manipulation. Before replying once again with the same restatement of your opinions, could you address these points? - Approval Sorted Margins (AKA Approval Margins Sort?) appears to pick the same winner as Approval Margins or Approval-weighted Pairwise, at least in the examples given by you and Chris Benham. But it has, IMO, a simpler implementation. Could you examine that method in comparison to AWP? http://wiki.electorama.com/wiki/Approval_Sorted_Margins (to digress slightly, I think the name Pairwise Sorted Approval by Minimum Margin or something of that sort might be more descriptive). Just to be clear on why I think ASM might be marginally more feasible but not AWP or CWP: it's the extra pairwise array. Do I have to explain further? Chris Benham's Approval Margins proposal doesn't have an extra pairwise array, but I have yet to see an easy explanation for it. - The Definite Majority Set has a nice ring to it. It gives a favorable standing to non-winning members of that set, which always includes the Approval Winner. The AWP Smith Set won't always contain the Approval Winner. Can you find some alternate definition of the AWP winner that allows higher approved candidates (including the Approval Winner) to 'lose with honor'? - James, I read your paper on CWP, about 6 months ago. I appreciate that you put a lot of work into them. But their technical nature and PDF format render them somewhat inaccessible to even election-methods list members. I think your technical ideas have great merit, but you still need to sell me on implementation. Why not try putting together an electowiki page. If you're going to promote CWP, then design a ballot to go with the page. And then discuss examples. You can always link in your articles as External Links. The worst that might happen is that others could clarify your ideas. ;-) -- Araucaria On 2 Apr 2005 at 19:20 UTC-0800, James Green-Armytage wrote: James G-A replying to Ted, on the subject of AWP and DMC... I agree that AWP (have you decided to pick between RP, Beatpath or River?) No, I haven't chosen, nor do I feel the need to choose. I consider all three of these base methods to be very good, and I see no particular reason to limit the definition of CWP or AWP by choosing one over the other. does a better job in this particular case, and all else being equal, I would be happy with an AWP proposal. But all things are not equal. How do you explain to your 80 year old auntie about ordering the defeats, or that RP sometimes gets a different result than Beatpath or River? If you can show that AWP always causes the 3 strong pair-ranking methods to get the same answer, I would be convinced. This doesn't make sense to me. Are you saying for example that people will look askance at beatpath if they know ranked pairs to be equally good, and that they will look askance at ranked pairs if they know beatpath to be equally good? I doubt it. I think that all three methods are about equally good. If we pick beatpath, people who like ranked pairs are likely to be happy, and vice versa. Also, if the proposal is based on ranked pairs, and I am trying to explain the method to someone who is not comfortable with complex voting theory, I have no need to explain beatpath and river to them. All I have to do is explain ranked pairs. Until then, I think DMC or some variant is the Condorcet method with best chance of public acceptance. That's your opinion. My opinion is that if DMC and AWP are roughly equal in explainability, and that any method that combines some other ballot with a ranking ballot will be more difficult from a superficial standpoint than a method like sequential dropping (wv). Hence, if such superficial considerations are intense, both DMC and AWP are likely to be beyond reach. If the public is open to
[EM] Re: Definite Majority Choice, AWP, AM
Forest, Jobst, Ted and others,
At one point I proposed something very like DMC, which
I referred to as Condorcet completed by Approval
Elimination.
When I first proposed Approval Margins (AM), I wrote
that I was scratching the other method because I'd
discovered that it was vulnerable to (a form of)
Pushover strategy. In the example I gave, this was
combined (mixed up) with Burying.I thought Pushover
was just raising some weak alternative in an
elimination method, hoping to give some preferred
candidate an easier-to-beat opponent in the final
runoff. Checking the definition at Blake Cretney's
website, I see that it (now) specifies ranking
a candidate above your favourite.
Adapting the earlier example that included Burying,
here is a demonstration that DMC fails Approval
Later-no-Help and what I thought was Approval
Pushover.
Sincere preferences:
49: ACB
06: BAC
12: B
06: BCA
27: CBA
ACBA. Approvals: A55, B51, C33.
DMC (and AM and AWP) elects B.
Now suppose the A voters decide to approve C:
49: ACB
06: BAC
12: B
06: BCA
27: CBA
ACBA. Approvals: A55, B51, C82.
Now DMC elects A. (AM and AWP elect C.)
The effect of the action has been to change P from
{AB} to {AC}.
(Recall that in AM, in a 3-candidate cycle the winner
is always one of the approval top-two.Approval
runner-up can only win if
(1) s/he pairwise beats the AW, and (2) if approval
runner-up's approval score is closer to the AW's than
to approval last's.)
I am sure, and might get around to demonstrating in a
future post, that (at least in the 3-candidate
situation) AM meets Approval Later-no-Help.
(To be clear, what I mean by Approval Later-no-Help
is without any change in the rankings, approving
another candidate shouldn't help any already approved
candidate.
Chris Benham
So I no longer support Condorcet completed by
Compressing Ranks, or Condorcet completed by Approval
Elimination. I think they are unneccessarily drastic.
I scratched the Approval
Elimination method when I discovered that it is
vulnerable to Pushover strategy.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-July/013416.html
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Re: [EM] Re: Definite Majority Choice, AWP, AM
James G-A replying to Ted, on the subject of AWP and DMC... I agree that AWP (have you decided to pick between RP, Beatpath or River?) No, I haven't chosen, nor do I feel the need to choose. I consider all three of these base methods to be very good, and I see no particular reason to limit the definition of CWP or AWP by choosing one over the other. does a better job in this particular case, and all else being equal, I would be happy with an AWP proposal. But all things are not equal. How do you explain to your 80 year old auntie about ordering the defeats, or that RP sometimes gets a different result than Beatpath or River? If you can show that AWP always causes the 3 strong pair-ranking methods to get the same answer, I would be convinced. This doesn't make sense to me. Are you saying for example that people will look askance at beatpath if they know ranked pairs to be equally good, and that they will look askance at ranked pairs if they know beatpath to be equally good? I doubt it. I think that all three methods are about equally good. If we pick beatpath, people who like ranked pairs are likely to be happy, and vice versa. Also, if the proposal is based on ranked pairs, and I am trying to explain the method to someone who is not comfortable with complex voting theory, I have no need to explain beatpath and river to them. All I have to do is explain ranked pairs. Until then, I think DMC or some variant is the Condorcet method with best chance of public acceptance. That's your opinion. My opinion is that if DMC and AWP are roughly equal in explainability, and that any method that combines some other ballot with a ranking ballot will be more difficult from a superficial standpoint than a method like sequential dropping (wv). Hence, if such superficial considerations are intense, both DMC and AWP are likely to be beyond reach. If the public is open to more complex methods, they are just about as likely to entertain one method as the other. Once we've reached that point, the important question is which method offers more benefits as an organizing/decision-making tool. I continue to argue that AWP should be chosen over DMC because it provides substantially more stability against tactical voting. If we are ever able to do some serious focus group research comparing ordinary people's reaction to the different methods, while treating each one fairly, and it turns out that DMC does substantially better, I will accept your public acceptability argument. Until then, I suggest that my opinion on the relative public acceptability of the methods is as valid as yours, and that further discussion should focus on the relative merits of the methods in practice. In any case, my general comment about strategy not existing in a vacuum still applies here: though Bush does win under DMC using your proposed strategy, it is very risky. What if 3 of the 5 DKB voters move their cutoff below K? Yes, they would be compromising, but in approval and not in rank. B voters attempting to game DMC are gambling on how important that approval cutoff decision will be, and could end up with a Dean victory for their efforts. That's always the price of the burying strategy. If your sincere is BKD and you vote BDK to increase B's chance of winning, the downside is that you usually increase D's chance of winning as well. However, let's say that we have a large group of voters whose sincere preferences are BDK. That is, they prefer D slightly over K, but they don't really care, but they passionately prefer B over both D and K. (This is totally realistic in polarized political landscapes like the USA.) I suggest that such voters are likely to decide which candidate (D or K) is most likely to beat B pairwise, and to vote that candidate in last place. If the strategy backfires, and D is elected instead of the sincere winner K, then they haven't lost much. However, if the strategy succeeds, and B wins instead of K, they have gained a great deal. Hence, the burying strategy is an obvious choice, without the need for any coordination. This is exactly where CWP and AWP step in. I suggest that the most important kind of burying strategy to guard against is the kind where people try to change the result to a winner who is the ideological polar opposite of everyone in the Smith set. (First, because it is a more severe violation of the process, and second, because the buriers are more likely to have a lot to gain and not much to lose, as explained above.) In CWP and AWP this is always either impossible or absurdly complicated. In DMC, it is often possible and sometimes simple. So to me, the choice is clear. Please consider this argument seriously and read my CWP paper before you make any further pronouncements about the differences (or similarities) in merit between AWP and DMC, because most of the pro-CWP arguments apply to AWP as well, to a large degree.
[EM] Re: Definite Majority Choice, AWP, AM
From: Jobst Heitzig [EMAIL PROTECTED] Subject: [EM] Re: Definite Majority Choice, AWP, AM The following proves that the only immune candidate is the least approved not strongly defeated candidate, assuming no pairwise defeat or approval ties: Let A be that candidate, with approval a. To prove that A is immune, assume that B1 defeats A, with approval b1. We show that there is a beatpath A...B1 with all defeats at least as strong as B1A, that is, with all intermediate candidates having approval at least b1. Because of ab1, and since B1 does not defeat all more approved ones, there is B2 with approval b2b1 and B2B1. If ab2, also B2 does not defeat all more approved ones, hence there is B3 with approval b3b2 and B3B2, and so on until we find some Bk with approval bk=a and Bk...B1. Now either Bk=A or ABk, QED. Now assume that B is a candidate other than A, with approval b. We show that B is not immune. If ba then the defeat AB has strenght a but all defeats against A have strength below a, hence all beatpaths B...A have strength below A, so B is not immune. If, on the other hand, ba, then B is beaten by some C with approval cb, but any defeat B... has strength bc, hence any beatpath B...C has strength below c, so again B is not immune. QED. This proves that all immune methods, especially RP, River, Beatpath, are equivalent to DMC when defeat strength := approval of defeating candidate, and when no pairwise ties exist. This is a very nice proof, and another interesting and valuable characterization of DMC: When defeat strength is measured by the approval of the defeating candidate, there is only one possible immune method, namely DMC. All of the main competing Condorcet methods collapse into simple little old DMC by the device of measuring defeat strength by approval. And measuring defeat strength by approval in no way decreases any of the strategy resistance or other nice properties of the winning votes versions of those methods. Also, it's very nice to have the great variety of other descriptions and characterizations of this method that we have seen lately. Watch out IRV ! The only thing that worries me is this: what if DMC gets adopted all over the place, and it turns out that Donald gets the credit because he proves that he came up with an equivalent version before we did? I don't really waste any time worrying about such things, but wouldn't that be irony in the extreme? [I don't care. Let him have the credit. It would be worth it!] Forest Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
On 30 Mar 2005 at 06:51 UTC-0800, Chris Benham wrote: Jobst, You wrote (Thur.Mar.24): First, I'd like to emphasize that DMC, AWP, and AM can be thought of as being essentially the same method with only different definition of defeat strength, so it seems quite natural to compare them in detail as you started. Recall that the DMC winner is the unique immune candidate when defeat strength is defined as the approval of the defeating candidate, so with that definition, Beatpath, RP, and River become equivalent to DMC. Chris Jobst: Please take careful note -- the DMC defeat strength assertion has not been proved rigorously, to my knowledge! It is worth a very careful look before basing any other assumptions on it. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
Dear Ted! You wrote: Chris Jobst: Please take careful note -- the DMC defeat strength assertion has not been proved rigorously, to my knowledge! It is worth a very careful look before basing any other assumptions on it. The following proves that the only immune candidate is the least approved not strongly defeated candidate, assuming no pairwise defeat or approval ties: Let A be that candidate, with approval a. To prove that A is immune, assume that B1 defeats A, with approval b1. We show that there is a beatpath A...B1 with all defeats at least as strong as B1A, that is, with all intermediate candidates having approval at least b1. Because of ab1, and since B1 does not defeat all more approved ones, there is B2 with approval b2b1 and B2B1. If ab2, also B2 does not defeat all more approved ones, hence there is B3 with approval b3b2 and B3B2, and so on until we find some Bk with approval bk=a and Bk...B1. Now either Bk=A or ABk, QED. Now assume that B is a candidate other than A, with approval b. We show that B is not immune. If ba then the defeat AB has strenght a but all defeats against A have strength below a, hence all beatpaths B...A have strength below A, so B is not immune. If, on the other hand, ba, then B is beaten by some C with approval cb, but any defeat B... has strength bc, hence any beatpath B...C has strength below c, so again B is not immune. QED. This proves that all immune methods, especially RP, River, Beatpath, are equivalent to DMC when defeat strength := approval of defeating candidate, and when no pairwise ties exist. Yours, Jobst Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
On 26 Mar 2005 at 04:05 UTC-0800, James Green-Armytage wrote: Hi Juho, Some replies follow, on the subject of voter strategy and approval-weighted pairwise. These comments should also be helpful for others who don't understand why I consider AWP to be clearly better than DMC and AM. [... arguments ...] 3 candidates: Kerry, Dean, and Bush. 100 voters. Sincere preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 25: BKD 23: BDK Kerry is a Condorcet winner. Altered preferences 19: KDB 5: KDB 4: KBD 18: DKB 5: DKB 1: DBK 21: BKD 23: BDK 4: BDK (these are sincerely BKD) There is a cycle now, KBDK I agree that AWP (have you decided to pick between RP, Beatpath or River?) does a better job in this particular case, and all else being equal, I would be happy with an AWP proposal. But all things are not equal. How do you explain to your 80 year old auntie about ordering the defeats, or that RP sometimes gets a different result than Beatpath or River? If you can show that AWP always causes the 3 strong pair-ranking methods to get the same answer, I would be convinced. Until then, I think DMC or some variant is the Condorcet method with best chance of public acceptance. In any case, my general comment about strategy not existing in a vacuum still applies here: though Bush does win under DMC using your proposed strategy, it is very risky. What if 3 of the 5 DKB voters move their cutoff below K? Yes, they would be compromising, but in approval and not in rank. B voters attempting to game DMC are gambling on how important that approval cutoff decision will be, and could end up with a Dean victory for their efforts. Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: Definite Majority Choice, AWP, AM
Hi Chris, Nice example. But there is still a counter-strategic incentive under DMC -- see below. On 24 Mar 2005 at 08:11 UTC-0800, Chris Benham wrote: Suppose there is pre-polling and so the L supporters decide to approve C, while the C supporters sincerely divide their approvals. Further suppose that the R supporters all decide to completely Bury C. Then we might get: 49 RLC 06 CRL 06 CRL 06 CLR 06 CLR 27 LCR Now all the candidates are in the top cycle: LCRL. The approval scores are L82, R55, C51. Approval Margins: LC 82-51 = +31 CR 51-55 = -4 RL 55-82 = -27 AM elects L, backfiring on the Buriers! Unfortunately this time DMC eliminates C, and then the Buriers' candidate R wins. Approval-Weighted Pairwise: LC 49 CR 45 RL 06 AWP gives the same good result as AM! Yes, with perfect polling knowledge, the R strategy might work. But Rock/Paper/Scissors strategy like this doesn't occur in a vacuum. If R voters are coordinated enough to bury C in both approval and rank, they have to operate on the assumption that CRL voters might also suspect something and might all disapprove R instead of splitting. Without CRL's 6 approval votes, R would be eliminated by the definitive CR defeat. R's ordinal-burial of C would backfire and elect L. If I were an R voter, that would be the *last* thing I'd want! Ted -- araucaria dot araucana at gmail dot com Election-methods mailing list - see http://electorama.com/em for list info
