Re: [Election-Methods] Partisan Politics
At 10:52 PM 5/7/2008, Fred Gohlke wrote: Good Evening, Juho re: I already commented earlier that the groups of three based method that you have studied does not implement proportionality in the traditional way. You're right. It's not traditional, but it sure is proportional. One of the unspecified conditions I intended for the 'groups of three' method was that participation in the election process should be mandatory, as it is in (I believe) Australia, Singapore and New Zealand. If every person in the electorate participates in the process of selecting those who will represent them in their government, there can be no greater proportionality. The problem is that selection takes place in assigned groups, and that causes proportionality to disappear beyond the very primitive proportionality that can exist in a group of three choosing one. The groups will indeed represent factions; however, I haven't seen any analysis from Mr. Gohlke as to how this affect proportionality, just assertions. Mandatory participation is just one aspect of the coercive nature of this proposal. Highly restrictive rules on how representatives are chosen are its nature. It requires trusting the authorities in ways that could be extraordinarily difficult to prove. By selective assignment of people to the groups, one could actually bury any minority effectively. Just insure that few groups have two members of that minority. Coerced voting requires the participation of people who have no idea what they are voting about. In Australian, donkey voting is common, where people just mark the ballots in the most convenient way in races they don't know about. It's great to make voting easy. Not great to require it. Participation bias is actually a phenomenon which can be shown, through social utility analysis, to improve election results from the point of view of overall social satisfaction with the results. It's a form of rough Range voting. As to proportionality, STV is in common use -- including in Australia -- and, with large enough districts (i.e., many members) it is quite good, but still depends on the political system. However, there is another method which is far, far simpler and which is *totally* proportional, in which all voters actively participate, and all voters and votes count, and a resulting Assembly is as proportional as is possible. I.e., any faction large enough to command a quota of votes is seated. It's now called Asset Voting, but it was first proposed by Lewis Carroll in about 1886. A ballot could be as simple as a standard vote-for-one Plurality ballot, though there are better possible designs. (Warren Smith, who named it Asset Voting, used real numbers for each vote in the range of 0-1, with the constraint that all votes must add up to 1 (or less. That's probably impracticably complex, but there is a simpler variant I called FAAV: Fractional Approval Asset Voting. Pretty simple: vote for as many as you like. Your single vote will be divided equally among them.) Then, if any candidate receives a quota of votes, they are elected. All surplus votes are assets of the candidate receiving them, and the candidate may recast them at will to create seats. They do this deliberatively. And Delegable Proxy could make this renegotiation very simple, even for candidates holding as few as one vote. And direct democracy for the Assembly becomes possible, i.e., direct voting becomes a possibility, even though representation in deliberation must be restricted to elected seats. (I call candidates who have received votes electors, because that is what they are, they are public voters. If an elector, who doesn't have a seat, votes, his or her vote is subtracted frationally from the vote of the seat. Normally, these direct votes, I expect, would only be a small fraction of the total votes on any issue, but that they are possible means that citizens would be directly represented by people they chose, without restriction beyond simple eligibility to receive votes, which could be very simple indeed. Probably registration of consent to receive votes, being already a registered voter and not otherwise disqualified, would do it.) re: Large parties (or whatever opinion camps) tend to get more representatives to the higher layers (more than their proportional size is). Is that assertion not based on the assumption that large parties (or opinion camps) must dominate our political existence? No. It's a statement of fact, as to what will happen if such parties exist. Now, given that they do exist, another feature of this method might be that they will be outlawed, and anyone found guilty of voting in accordance with party recommendations would be disqualified from voting. Asset Voting makes parties irrelevant for the purpose of finding representation. If you want to elect based on party, fine. You can do it. The method doesn't care. What is, is not
Re: [Election-Methods] [english 95%] Re: [english 94%] Re: method design challenge +new method AMP
One observation on clone independence and electing a centrist candidate using rankings only and when one of the extremists has majority. Votes: 51: ACB 49: BCA C is the winner. A will be cloned. The votes could be: 51: A1A2CB 49: BCA2A1 C should still be the winner. B will be cloned. The votes could be: 51: ACB1B2 49: B2B1CA C should still be the winner. The problem is that these two sets of votes are identical: 51: X1X2X3X4 49: X4X3X2X1 In the first set of votes the intended winner C is X3 and in the latter X2. It is thus impossible for the algorithm in this case and with this information (rankings only) to satisfy both requirements and to be fully clone independent. Similar conclusions could be drawn at least for normalized ratings. A=100 C=55 B=0 = A1=100 A2=56 C=54 B=0 B=100 C=55 A=0 = B=100 C=56 A1=54 A2=0 or A=100 C=55 B=0 = A=100 C=56 B1=54 B2=0 B=100 C=55 A=0 = B2=100 B1=56 C=54 A=0 One approach to try to avoid this problem would be to use a more limited clone concept: candidates that are ranked/rated equal with each others. Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] method design challenge + new method AMP
Dear Juho, you wrote: One observation on clone independence and electing a centrist candidate using rankings only and when one of the extremists has majority. ... It is thus impossible for the algorithm in this case and with this information (rankings only) to satisfy both requirements and to be fully clone independent. D'accord. This is a good reason to consider rankings insufficient, since from rankings only one cannot determine whether to apparent clones are truly clones in the sense that they are (nearly) equivalent in all relevant aspects. From ratings information, however, one can see this. Therefore I would not at all consider A1,A2 clones in your ratings example: A=100 C=55 B=0 = A1=100 A2=56 C=54 B=0 B=100 C=55 A=0 = B=100 C=56 A1=54 A2=0 For A1,A2 to be considered clones, the ratings would have to be something like 51: A1 100 A2 99 C 55 B 0 49: B 100 C 55 A1 1 A2 0 You also seem to think so, since you wrote: One approach to try to avoid this problem would be to use a more limited clone concept: candidates that are ranked/rated equal with each others. But that would never really occur in practice. I think one should define the notion clone like this: A1,A2 are clones if and only if on each ballot, the difference in ratings between any pair of options is smallest for the pair A1,A2. (Analogously, a set S of options should be called a clone set if and only if on each ballot, all rating differences between two options in S are smaller than all rating differences between other pairs of options. Even more generally, a system Y of disjoint sets S1,...,Sk of options could be called a clone partition if and only if on each ballot, all rating differences between two options which are contained in the same member of Y are smaller than all rating differences between other pairs of options.) With this definition, the problem you described cannot really occur: Assume the rankings are 51: X1X2X3X4 49: X4X3X2X1 If X1,X2 are clones, X2 cannot be considered a good compromise since 49 voters don't like her. Similarly, if X3,X4 are clones, X3 cannot be considered a good compromise since 51 voters don't like her. Yours, Jobst pgp9sEhTbdSjT.pgp Description: PGP signature Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] method design challenge + new method AMP
Dear Raphfrk, you wrote There needs to be some system for providing an incentive for people to give their honest ratings.? A random system with trading seems like a reasonable solution. I am glad that I am no longer alone with this opinion... If a majority has a 100% chance of getting their candidate elected, then there is no incentive for them to trade.? If the voters are 100% strategic, they will know this. Yes, although some Range Voting supporters try hard to convince us of the opposite, it seems. OTOH, a support of a majority should be better than support of a minority. Absolutely! Usually I consider Random Ballot a benchmark method for this very reason: the default winning probability of a candidate should equal the proportion of the voter who favour her. Any deviances from this default distribution should be justified somehow, for example by an increase in some measure of social utility. (The underlying rationale for methods like D2MAC or AMP is even stronger: every voter should have full control over her share of the winning probability, so that in particular when she bullet votes, this share must goes to her favourite. Only such methods are truly democratic.) Optimal utility via trade requires that voters have something to trade, and fractions of a win probability seems to be quite a reasonable solution. I cannot really imagine any other thing unless we consider money transfers... Yours, Jobst pgpQdRGiMeeWy.pgp Description: PGP signature Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Partisan Politics
On May 8, 2008, at 5:52 , Fred Gohlke wrote: re: I already commented earlier that the groups of three based method that you have studied does not implement proportionality in the traditional way. You're right. It's not traditional, but it sure is proportional. One of the unspecified conditions I intended for the 'groups of three' method was that participation in the election process should be mandatory, as it is in (I believe) Australia, Singapore and New Zealand. If every person in the electorate participates in the process of selecting those who will represent them in their government, there can be no greater proportionality. Well, I think proportionality is at its best / strongest when n% of the voters get n% of the seats. Extensive participation in the election process is a good thing but proportionality is not a very descriptive name for this. re: Large parties (or whatever opinion camps) tend to get more representatives to the higher layers (more than their proportional size is). Is that assertion not based on the assumption that large parties (or opinion camps) must dominate our political existence? Only on the (country independent) technical properties of the groups of three method. (If there are e.g. two parties, one small and one large, the probability of getting two small party supporters (that would elect one of them to the next higher level) in a group of three is so small that in the next higher level the number of small party supporters is probably lower than at this level.) Juho ___ All new Yahoo! Mail The new Interface is stunning in its simplicity and ease of use. - PC Magazine http://uk.docs.yahoo.com/nowyoucan.html Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] method design challenge + new method AMP
On May 9, 2008, at 0:56 , Jobst Heitzig wrote: For A1,A2 to be considered clones, the ratings would have to be something like 51: A1 100 A2 99 C 55 B 0 49: B 100 C 55 A1 1 A2 0 Could be also e.g. A C 99 B 0 and after inserting the clones A1 100 A2 99 C 98 B 0 There are thus many cases where separating clones from non-clones is not easy. In this example also the number of rating levels impacts the outcome. You also seem to think so, since you wrote: One approach to try to avoid this problem would be to use a more limited clone concept: candidates that are ranked/rated equal with each others. But that would never really occur in practice. I think one should define the notion clone like this: A1,A2 are clones if and only if on each ballot, the difference in ratings between any pair of options is smallest for the pair A1,A2. Yes, this is one possible definition (that can be used to formulate the clone criterion). Juho ___ All new Yahoo! Mail The new Interface is stunning in its simplicity and ease of use. - PC Magazine http://uk.docs.yahoo.com/nowyoucan.html Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] method design challenge + new method AMP
On May 9, 2008, at 1:09 , Jobst Heitzig wrote: Usually I consider Random Ballot a benchmark method for this very reason: the default winning probability of a candidate should equal the proportion of the voter who favour her. Any deviances from this default distribution should be justified somehow, for example by an increase in some measure of social utility. I commented this point also in my reply to raphfrk. Random ballot is a perfect benchmark for many elections. But there are also elections that should be benchmarked against different methods / criteria. Sometimes the intention is to elect a candidate that is e.g. considered to be a good compromise, and one could e.g. intentionally try to avoid electing extremists. It would be good to always make it clear what kind of election method one is looking for. Both probability based and deterministic methods are needed. Juho ___ Now you can scan emails quickly with a reading pane. Get the new Yahoo! Mail. http://uk.docs.yahoo.com/nowyoucan.html Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Partisan Politics
At 05:33 PM 5/8/2008, Juho wrote: (If there are e.g. two parties, one small and one large, the probability of getting two small party supporters (that would elect one of them to the next higher level) in a group of three is so small that in the next higher level the number of small party supporters is probably lower than at this level.) Okay, let's do the math. Suppose the ratio of voters who are of some group is p, where 0 p 1. If x is not-p, then the permutations and probabilities for the four possibilities of 0 members, 1 member, 2 members, and three members, are: xxx, (1-p)^3 = P(0) xxp, xpx, pxx, 3 * (1 - p)^2 * p = P(1) xpp, pxp, ppx, 3 * (1 - p)* p^2 = P(2) ppp, p^3 = P(3) expanding those, P(0) = 1 - 3p +3p^2 -p^3 P(1) = 3p -6p^2 +3p^3 P(2) = 3p^2 - 3p^3 P(3) = p^3. To check, the sum simplifies to 1. These four are the only possibilities. If the group selects based on majority p, then we have a p choice with P(2) and P(3). That occurs with probability 3p^2 -2p^3. If p = 0.1, then the probability of a group choosing a p representative is .03 - .002 equals .028. p is 10% of the population, but is represented in the next layer with only 2.8% of the elected representatives. And then the same phenomenon occurs in the next layer, etc., with the proportion of p declining more rapidly with each layer. I get 0.23% for the next layer. With many layers, as is necessary for this system to represent a large population the proportion of p rapidly approaches zero, and it becomes extraordinarily unlikely for the minority to be represented at all, even with an Assembly of, say, 100 members or more. And that is already a fairly large assembly, in my opinion. Assemblies that large tend to function mostly in committee. Now, perhaps my math is wrong, I'm rusty and all that, and I make mistakes even when I understand clearly what to do. Mr. Gohlke, do you care to look at this? Election-Methods mailing list - see http://electorama.com/em for list info
