Re: [EM] Will to Compromise
Dear Greg, you wrote: Nondeterminism is a delightful way of skirting the Gibbard-Satterthwaite theorem. All parties can be coaxed into exposing their true opinions by resorting or the threat of resorting to chance. Actually, if I remember correctly, that theorem just said that Random Ballot was the only completely strategy-free method (given some minor axioms such as neutrality and anonymity), so it's not really skirting it but just taking it seriously. However, it seems some minor possibilities for strategizing are acceptable when they allow us to make the method more efficient. FAWRB tries to be a compromise in this respect. I don't dispute that. The nondeterminsitc methods I have seen appear to be designed to tease out a compromise because a majority cannot throw its weight around. Right, that's the main point. The abilities of nondeterministic methods to generate compromises is formidable, but since we speak of utility, I would like to point something out. 1) Using Bayesian utility, randomness is worse than FPTP. Two answers: i) Please cite evidence for this claim, ii) Bayesian utility is not a good measure for social utility in my opinion. We had lengthy discussions on this already a number of times on this list, so I won't repeat them. Instead, I will produce evidence from simulations this weekend which shows that no matter what measure of social utility is used, Random Ballot does not perform much worse than optimal. 2) False compromises are damaging What do you mean by false? If a proposed compromise fails to be desirable by most voters over the Random Ballot lottery, it will not get much winning probability. If it is, on the other hand, it is not a false but a good compromise. The simulations I will report about this weekend show that usually we can good compromises to exist which have quite large social utility. The reduced power of a majority means that at any choice with a greater-than-random-ballot average utility is a good compromise Notice how lousy the Bayesian utility of random ballot is and you begin to see my point. See above. In simulations with well-known preference models, Random Ballot results are not lousy at all. Also note that the method for determining the compromise is majoritarian (to the extent that approval is) so the intermediate compromise procedure is a red herring that produces some nasty side-effects. The compromise is determined to be the most-supported at-least-above-average candidate. How does this avoid the original criticism of majoritarian methods? You are right in that the majority still has some special influence on the *nomination* of the compromise. But the important difference to majoritarian methods is that they can't make any option get more winning probability than their share without the minority cooperating in this. So, yes, they can present the minority with a compromise they value only slightly better than Random Ballot. This is not perfect yet, but it guarantees the minority to get a better-than-average result where a majoritarian method doesn't guarantee a minority anything! Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Some chance for consensus (was: Buying Votes)
Dear Raph, you wrote: I was thinking of a 'stable marriage problem' like solution. Good idea! If it works, the main difficulty will be to make the whole process monotonic, I guess... Yours, Jobst Each voter rates all the candidates. Each voter will assign his winning probability to his highest choice (probably split equally if he ties 2 candidates for first). If 2 voters 'marry', then the candidate with the highest score sum is the compromise candidate. Solve the stable marriage problem. It might be necessary to randomly split the ballots into 2 'genders' to guarantee that a stable solution exists. Using the above example: G1: A1(100) A(70) A2(0) G2: A1(0) A(70) A2(100) G3: B(100) G4: C(100) (unnamed options are rated zero) If a member of G1 'marries', then the compromises are G1: A1 (+0) G2: A (+40), i.e. 100-70 (-30) and 0-70 (+70) G3: A1 and B tie (+0) .. effectively not a 'marriage' G4: A1 and C tie (+0) .. effectively not a 'marriage' Thus rankings are G1: G2G1=G3=G4 Similarly G2: G1G2=G3=G4 G3: all equal G4: all equal Thus the 25 G1s will 'marry' the 25 G2s and compromise on A. The result being A: 50% B: 25% C: 25% Also, what about an iterative method. If the candidate with the lowest probability has less than 1/3 probability, eliminate him and re-run the calculations (and probably rescale the ratings). This is kind of similar to the requirement that a candidate has 1/3 approval before being considered. As an added complication, in the above, it might be worth doing a second pass. Once all the marriages are stable, you could have 'suitors' propose to 'engaged' voters and make an offer with a different compromise candidate. For example, if two voters has ratings, A1(100) A2(90) A3(75) A4(55) A5(0) A1(0) A2(55) A3(75) A4(90) A5(100) The possible compromises are A2, A3 and A4. However, A2 favours the first voter and A4 favours the 2nd voter. It might be the case that after being refused, a 'suitor' could sweeten the deal by offering a better option. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Will to Compromise
Dear Kristofer, you wrote: With more candidates, a minority might find that it needs to approve of a compromise with just slightly better expected value than random ballot, if the majority says that it's not going to pick a compromise closer to the minority than that just-slightly-better candidate. That is, it would give an incentive to compromise early, under the threat that to do otherwise might make the method fall back to random ballot, and the compromise is better than random ballot even if it's not all that much better. True. But for the minority, Random Ballot is usually already much better than the majority preference, so that would be OK, right? Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] language/framing quibble
Good Morning, Kristofer There is so much good material in your message that, instead of responding to all of it, I'm going to select bits and pieces and comment on them, one at a time, until I've responded to all of them. I hope this will help us focus on specific parts of the complex topic we're discussing. For today, I'm going to concentrate on two of your comments regarding group (or council) size: 1) Have a council of seven. Use a PR method like STV to pick four or five. These go to the next level. That may exclude opinions held by fewer than two of the seven, but it's better than 50%-1. If you can handle a larger council, have one of size 12 that picks 9; if seven is too many, a group of five that elects two. For small groups like this, it might be possible to make a simpler PR method than STV, but I'm not sure how. 2) It's more like (if we elect three out of nine and it's always the second who wins -- to make the diagram easier) e n wLevel 2 behknqtwz Level 1 b e h k n q t w z Level 1 abcdefghi jklmnopqr stuvwxyzA Level 0 The horizon for all the subsequent members (behknqtwz) is wider than would be the case if they were split up into groups of three. In this example, each person at a level represents three below him, just like what would be the case if you had groups of two, but, and this is the important part, they have input from the entire group of eight instead of just three. Thus some may represent all the views of less than three, while others represent some of the views of more than three. The latter type would be excluded, or at least heavily attenuated, in the triad case. For convenience, I'll work with a group size of 9 picking 3 by a form of proportional representation: Am I correct in imagining the process would function by having each of the 9 people rank the other 8 in preferential order and then resolve the preferences to select the 3 people that are most preferred by the 9? That seems like a really good idea. It is, however, a new idea for me, so it may take me some time to digest all the ramifications of the concept. Even so, the first thoughts that leap to mind are: 1) It would allow voting secrecy. In a group size of 3 selecting 1, secrecy is not possible; a selection can only be made if 2 of the three agree on the selection. Many people say secrecy is important. For my part, I'm not sure. It may be important in the kind of electoral process we have now, but I'm not sure open agreement of free people is not a better option. 2) It reduces the potential for confrontation that would be likely to characterize 3-person groups. We can make the argument that, in the selection of representatives, confrontation is a good thing. Seeing how individuals react in tense situations gives us great insight into their ability to represent our interests. We can also make the argument that a pressure-cooker environment is hard on the participants. 3) Each participant's opportunity to evaluate each other participant is reduced; they must evaluate 8 people in the allotted time instead of two. 4) There is a greater likelihood that, over an evaluation period of 1 to 4 weeks, the group members will tend to form cliques and will be influenced by their compatriots instead of relying on their own judgment. It takes me such a long time to examine new concepts, I'd like to see what objections are raised to both alternatives to be sure I've considered all the possibilities. On re-reading this, I see I haven't addressed your concern; the propagation of minority sentiment. I'm not sure I can. My problem may be that I don't see viewpoints as isolated entities. They are part of a whole, but are not, in and of themselves, the whole. I do not believe that, just because a viewpoint exists, it is entitled to a role in our government. To be adopted, a viewpoint must be shown to have merit. People of judgment will accept different viewpoints if they are presented in a rational and compelling manner. I think the issues that should concern us are the integrity and the judgment of the people we ask to represent us. If we have people of good judgment, we need not fear that a valid viewpoint will be ignored. Fred Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] language/framing quibble
Good Morning, Kristofer In this message, I'll respond on the topic of accountability. I'll also attach a copy of the original draft of the concept which may make my ideas a bit clearer. (Items from your letter, so I can see which ones I've answered.) re: Yes. I think recall and the likes would be important. I'm not sure how you would include other options - other than recall - and not slow down the council, but we'll see. re: I think that's a good idea, as well, as long as it doesn't turn too slow. There's probably a sweet spot in this matter: if it goes too fast, it's prone to being guided by mindless populism. If it goes too slow, you can get a group who grumble about everything that's wrong and say we would change it all if we could just gain power, and that group would grow simply because it has no challenge. Things are going very fast currently, so having something slower might work well. Since parliaments and the likes don't make any direct mention to the sweet spot, yet still work, I'm going to assume it's not very sensitive to it; that is, that methods can work even if they err somewhat in this respect. re: I think that if one were to corrupt your system, it would be through the observation that the levels are only indirectly connected to the people, so, again, we need some countering method there (like recall, as mentioned earlier). re: The accountability problem, I think, lies in the number of levels one has to traverse. Our options is to either compensate for it in the determination process (where candidates travel upwards through the layers), or by having more tools on hand after they've been chosen. I'm not really sure how one would anchor the layers to the people in the first process, though each councilmember will be so to some extent already by the other members of the council of that layer. So that leaves the second. We've already discussed recall. What other tools do you think could be used? One could also fix it indirectly, by strengthening the people's power, such as by initiative and referendum, automatic sunset laws, and the likes. re: Yes. I'll amend that slightly so I don't exclude my own PR versions: The official should be responsible to those who elected him to the degree that their vote contributed to his election. The proposed electoral method uses computers to maintain a database of the electorate, generate random groupings, and record the selections made at each level, This makes the process inherently bi-directional. Each elected official sits atop a pyramid of known electors, so questions on specific issues can easily be transmitted directly to and from the electors for the guidance or instruction of the official. How extensively this capability is used depends on those who implement and administer the process. For example, the town council, state legislature, and/or national congress can decree that certain questions must be referred to the people who selected the representatives serving in the body. In such an event, the representative would instruct the database administrator to send the question down through the chain that elected him. This capability should be used with caution, however. Some of the matters public officials must decide do not admit of simple answers. Some may be unpopular or painful to the citizenry ... restraining the cancerous growth that currently dominates (and threatens) our existence will not be accomplished easily. We want to elect people with the courage and wisdom to improve our society, not destroy it. We can not expect to be happy with all their decisions. We've taken pains to select people of integrity and judgment, we should not restrain them unnecessarily. The matter of how and when this option should be used raises several questions. For example, it leaves open the matters of how the questions should be framed and evaluation of the responses. The answers to questions that elicit 'yes/no' responses can be influenced by the phrasing of the question. On the other hand, anything more complex than a 'yes/no' response requires interpretation which could be difficult, since clarity of written expression does not seem to be an inherent human trait. We must also consider how responses are to be transmitted upward. My initial idea was that the people would give their response to the person they selected from their group, and that person would pass it upward. I anticipate, though, an objection that this method would preserve the biases that influenced the selection of the official in the first place. I think that's a valid guess, but I suspect the matters to be resolved this way are more apt to involve nuances than significant changes of attitude. The method refines the public attitudes. It should not encourage abrupt
Re: [EM] Some chance for consensus (was: Buying Votes)
Dear Forest, good to hear from you again! You said: Not quite as important, but still valuable, is achieving partial cooperation when that is the best that can be done: 25 A1AA2 25 A2AA1 25 B 25 C Here there isn't much hope for consensus, but it would be nice if the first two factions could still cooperate on gettiing A elected, say 25% of the time. (50% seems too much to hope for) That's absolutely true! We both tried to achieve this during the last year. But it is very difficult to make this happen with strategic voters. Perhaps I find the time this weekend to write a summary of what we tried in this respect, so that perhaps someone can build on that an come up with a new idea. It seems to me that if we require our method to accomplish the potential cooperation in this scenario while achieving consensus where possible, the ballots would have to have more levels, and there would have to be an intermediate fall back between the consensus test and the random ballot default. That could work, but I wouldn't bet on it yet. Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Some chance for consensus (was: Buying Votes)
Dear Raph and Forest,
I have a new idea which might be monotonic, generalizing the 2-voter-marriage
idea to larger groups of voters.
I will define it as an optimization problem: basically, the idea is to find the
socially best lottery which can
be produced by starting from the Random Ballot lottery and allowing for one set
of voters to reach a contract in which they transfer their share of the
winning probability from their favourite options to other options. More
precisely, the suggested method is this:
1. Each voter submits a cardinal rating for each option.
2. Amoung all possible lotteries that assign winning probabilities to the
options, we determine the feasible ones. In order to determine whether a
given
lottery L is feasible, we do the following:
a) Compare L with the Random Ballot lottery, RB, and find the set S of options
which have a lower winning probability under L than under RB. Mathematically:
S = { options X with L(X) RB(X) },
where L(X) = probability of option X in lottery L.
b) For each option X in S, determine the number N1(X) of voters who favour X
and like L at least as much as RB, judging from their submitted ratings.
Mathematically:
N1(X) = no. of voters V with V(L) = V(RB),
where V(L) = sum of V(X)*L(X) over all options X
and V(X) = rating voter V assigned to option X.
c) Also, determine the number N2 of those voters who favour X which must agree
to transfer their share of the winning probability from X to other options in
order to produce L. Mathematically:
N2(X) = (RB(X)-L(X)) * N,
where N is the no. of all voters.
d) Then check whether N2(X)=N1(X) for all X in S. If this is fulfilled, then
this means that a group of voters exists who have both the means and the
incentices to change RB into L by transferring winning probability from their
respective favourite options to other options. So, if the condition is
fulfilled, L is considered feasible.
3. Finally, find amoung the feasible lotteries the one that maximizes a given
measure of social utility, e.g. total utility or Gini welfare function or
median voter utility or whatever. Apply this socially optimal feasible
lottery to determine the winner.
With sincere voters, the method achieves what we desire:
1. With 55 having A(100)C(70)B(0) and 45 having B(100)C(70)A(0), the
optimal lottery L would be L(A/B/C)=0/0/1. This is feasible since it has
S={A,B}, N1(A)=N2(A)=55, and N2(B)=N2(B)=45.
2. With 25 having A1(100)A(90)A2(70)B(0), 25 having
A2(100)A(90)A1(70)B(0), and 50 having B(100)A,A1,A2(0), the optimal lottery
L would be L(A/A1/A2/B)=.5/0/0/.5 with S={A1,A2},
N1(A1)=N2(A1)=N1(A2)=N2(A2)=25.
I did not yet analyse the strategic implications, though. So we need to check
that and the hoped-for monotonicity. The crucial point for the latter will be
what happens when some voter changes her favourite, I guess.
Some final notes:
- There are always feasible lotteries since the Random Ballot lottery itself is
feasible by definition (with the set S being empty).
- For the same reason, the method gives no lower social utility than Random
Ballot.
- Geometrically, the set of feasible lotteries is a closed, star-shaped
polyeder, but it is usually not convex. (It would be convex if more than one
contracting group of voters were allowed.)
What do you think?
Jobst
-Ursprüngliche Nachricht-
Von: Raph Frank [EMAIL PROTECTED]
Gesendet: 31.10.08 15:35:30
An: Jobst Heitzig [EMAIL PROTECTED]
CC: [EMAIL PROTECTED], election-methods@lists.electorama.com, [EMAIL
PROTECTED], [EMAIL PROTECTED]
Betreff: Re: Some chance for consensus (was: [EM] Buying Votes)
On Fri, Oct 31, 2008 at 11:17 AM, Jobst Heitzig [EMAIL PROTECTED] wrote:
Dear Raph,
you wrote:
I was thinking of a 'stable marriage problem' like solution.
Good idea! If it works, the main difficulty will be to make the whole
process monotonic, I guess...
Yours, Jobst
I think the method which eliminates the lowest probability candidate
will be non-monotonic.
In the single run case, the fundamental problem is that bilateral
monopolies can exist. You can gain by not offering compromises.
However, assuming competition, you might be 'outbid' by another
voter/party if you do that.
-Ursprüngliche Nachricht-
Von: Raph Frank [EMAIL PROTECTED]
Gesendet: 31.10.08 15:35:30
An: Jobst Heitzig [EMAIL PROTECTED]
CC: [EMAIL PROTECTED], election-methods@lists.electorama.com, [EMAIL
PROTECTED], [EMAIL PROTECTED]
Betreff: Re: Some chance for consensus (was: [EM] Buying Votes)
On Fri, Oct 31, 2008 at 11:17 AM, Jobst Heitzig [EMAIL PROTECTED] wrote:
Dear Raph,
you wrote:
I was thinking of a 'stable marriage problem' like solution.
Good idea! If it works, the main difficulty will be to make the whole
process monotonic, I guess...
Yours, Jobst
I think the method which eliminates the lowest probability candidate
will be non-monotonic.
In
