[EM] it's pleocracy, not democracy
[sorry if this comes twice, but it didn't seem to get thru the first time] Dear folks, some clarification because in recent posts democracy and majority rule were confused quite often... In a dictatorial system, almost all people have no power. In a majoritarian system, up to half of the people have no power. In a democratic system, ALL people HAVE some power, that is, the people rule. Hence, majoritarian systems in which a majority of 50% + 1 voter can make all decisions are NOT democratic. The greeks called them pleocratic. Can a system be democratic? Can it even be democratic without using significant randomization? If we are faced with a whole sequence of decisions instead of only one, we could distribute the power over all decisions in the sequence: Naive solution: assign each decision to a (different) single voter so that each voter decides something in turn and hence all people have some power. Obviously, there are many deep problems with this. More sophisticated solution: Remember for each voter in what fraction of the decisions so far the voter's then-favourite option has been elected; call this that voter's actual success rate. Also remember for each voter the average (over all decisions so far) fraction of voters that had the same then-favourite as the voter at hand; call this that voter's to-be-expected success rate. Now, in each decision, elect that option which minimizes the sum of squared errors between the voters' current to-be-expected success rate (including the current decision) and the voters' resulting actual success rate if that option were elected. In the long run, this sum of squared errors should converge to zero (remains to be proven), so this method can be called asymptotically democratic. For example: Assume a sequence of A/B-decisions, voter 1 votes always A and voters 2-4 vote always B. Then the following would happen: to-be-expected actual success sum of round success rates winner rates afterwards squared errors 1 .25 .75 .75 .75 B0 1 1 11/4 2 .25 .75 .75 .75 A.5 .5 .5 .5 1/4 3 .25 .75 .75 .75 B.33 .67 .67 .67 1/36 4 .25 .75 .75 .75 B.25 .75 .75 .75 0 5 .25 .75 .75 .75 B.2 .8 .8 .8 1/100 6 .25 .75 .75 .75 A.33 .67 .67 .67 1/36 7 .25 .75 .75 .75 B.29 .71 .71 .71 1/196 8 .25 .75 .75 .75 B.25 .75 .75 .75 0 ... A little mathematics shows that this method is equivalent to a kind of weighted plurality in which each voters vote is weighted with the following (not necessarily positive) history-dependent weight: (current to-be-expected successes) - (earlier actual successes) - 1/2 The latter indicates a potential problem: Knowing my success rates so far, I may deduce that my vote in the current decision is actually negative, in which case I may have incentive to vote for the strongest competitor of my favourite instead of for my favourite. So far, we see that an asymptotically democratic method without randomization is possible when there is a whole sequence of decisions, but this method suffers from strong incentives for strategic voting. Of course, WITH randomization allowed, there is a perfectly democratic and absolutely strategy-proof method: random ballot. However, both methods have another problem: They do not easily support cooperation between voters since it is either optimal to vote for the favourite or for the strongest competitor, while there is no incentive to vote for compromise options. Therefore, the results are just but not particularly efficient with respect to utility. The method D2MAC aims to improve upon this. It is: Draw two ballots at random; the winner is the most approved option of those approved on both ballots, if such an option exists, or else the top option on the first ballot. Yours, Jobst __ XXL-Speicher, PC-Virenschutz, Spartarife mehr: Nur im WEB.DE Club! Jetzt gratis testen! http://freemail.web.de/home/landingpad/?mc=021130 election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] it's pleocracy, not democracy
From: [EMAIL PROTECTED] [sorry if this comes twice, but it didn't seem to get thru the first time] Dear folks, some clarification because in recent posts democracy and majority rule were confused quite often... In a dictatorial system, almost all people have no power. In a majoritarian system, up to half of the people have no power. In a democratic system, ALL people HAVE some power, that is, the people rul . Hence, majoritarian systems in which a majority of 50% + 1 voter can make all decisions are NOT democratic. The greeks called them pleocratic. Can a system be democratic? Can it even be democratic without using significant randomization? snip detail of system I had some proposals for a legislature that was targetted to achieve the same kind of thing. One option is to split all taxes collected by the government between all the legislators. A bill that spends money (creating tax breaks is harder to define) must be supported by enough legislators to cover the cost. The total is then subtracted from the 'bank' of each legislator which supported the bill. Each legislator who supports the bill pays the same, except that none can pay more than they have. Alternatively, it is like an auction, each legislator bids how much they would spend to support the bill. If enough bids are received, then the bill is passed and funded. Also, there could be a rule that money can be spent with only the support of say 1/3 of the legislature. This allows minorities get stuff done, without extreme minorities spending money. Something like the above would be best with a constitutionally defined method of tax collection, or perhaps having the people vote on the tax rates. Another system was to allocate each legislator a fixed number of votes per term. If the bill passes those who voted lose the votes that they voted. (The actual rule is that those opposed lose their voted votes and those in favor lose the same number, split in proportion to how many each voter voted). If a bill is passed 120 to 80, those in favor lose 2 votes for every 3 cast (with some rounding rule). In fact under this system, there is no problem with legislators voting more than once, they would just be burning votes that they could have used later. I actually prefer a 2-1 majority being required to pass something. The reason is that otherwise, the majority can just blow the minority out of the water. Also, under this system, those in favor would lose twice the number of votes in total than those against. This is a little fairer as those against didn't get what they wanted. If party A has 51 legislators and party B has 49 and each gets 100 votes. Party A can propose something and if party B votes against it party A can just out-vote them by 1 vote. Eventually, party B will run out of votes and then party A can pass anything as there is no opposition. It gets complex when repealing laws comes into effect. If only those in favor lost votes, then a large party could let a law be passed and then reverse it since the other side would have 'spent' all its votes. With 2-1 and both sides losing votes when a bill is passed but not when one fails, it is possible to have a bill passed and then use your remaining votes to block it being repealed. Also, I would suggest that under that system that multiple bills be passed at once. This allows compromises to be proposed. Raphfrk Interesting site what if anyone could modify the laws www.wikocracy.com Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] When and how can we speak of individual utility and social utility?
At 01:59 PM 3/1/2007, Michael Poole wrote: You did not specify a method for the runoff election. There are two candidates in the result set I specified; it might itself be the runoff. If the method for the runoff cannot be Range Voting, it is inappropriate to claim that Range satisfies the Majority Criterion, since Range Voting is not the method being evaluated. What I stated was that the entire procedure, which is a Range poll followed by a runoff between the Range and Condorcet winners, satisfied the criterion. I did not claim that Range, alone, satisfied the criterion. If the runoff is Range, theoretically, it would not satisfy the criterion. However, if we have a two-candidate election, and it *is* Range, the majority would allow a minority to prevail only if it votes weak votes. That would be a deliberate decision, I'd suggest, to allow such a victory, and thus majority rule, it could be argued, would be satisfied. This was my point. But I did not think, nor would I advocate, that the runoff be Range. I *assumed* that it would be understood that a runoff between two candidates would represent an ordinary choice. There would seem to be no reason to have the runoff as Range, since the Range data has already been collected. But, as usual, I can think of something. Perhaps the original Range election was distorted by strategic considerations. In the runoff, there is no motive to vote strategically, there are only two candidates involved and only if the voter desires to weaken the vote would one vote other than the extremes. If enough voters did this, then the preference of the majority could be passed over. Deliberately. But this is not at all what I was thinking. (A two-candidate Approval election satisfies MC, but it is fairly easy to construct a three-candidate Approval case where the Majority winner is not in the top two results, so I do not think it is appropriate to say that Approval satisfies MC either alone or with a ratification step.) The kind of runoff specified was not a top two runoff, but rather a contest between the Range winner and a Condorcet winner or plurality winner. How would this work if the election were Approval? Presumably the majority preference would be approved by the majority. So the only case in which the majority preference would not be in the top two would be a case in which more than two candidates were approved by a majority. We should be so lucky So if we apply this to Approval, we would have to specify that the runoff is not top-two, rather it is between all candidates approved by more than a majority. In this case, I'd think, it *would* be an Approval election. So couldn't it theoretically still leave the majority preference unelected? That's right, because I'm suggesting it be such on public policy grounds, not on the grounds of trying to satisfy the Majority Criterion. If the runoff were a simple plurality election, it would unconditionally satisfy the majority criterion. Again, I'm applying the criterion to the whole process, the combination of two polls, not to either poll singly. Certainly one may claim that this is a misapplication of the criterion, and I would say to such a person: bug off. I can apply the criterion to whatever I please. Unless, of course, you can show your Criterion Police card, showing that you have the authority to regulate the application of election criteria. Nobody is obligated to accept anything I write, unless, of course, it happens to be the truth, and, to be sure, that may only happen occasionally :-) election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] it's pleocracy, not democracy
At 05:40 AM 3/2/2007, Jobst Heitzig wrote: some clarification because in recent posts democracy and majority rule were confused quite often... Well, I don't think I personally confuse them, but I might use language loosely sometimes. In a dictatorial system, almost all people have no power. I talk about oligarchical systems, which includes, as a limit, dictatorship. I don't extend oligarchical to rule by the majority, but I do generally assume majority rule within a context that does not fix membership in the majority. That is, the majority shifts, so any given person, on any given issue, may or may not be in the majority. In a majoritarian system, up to half of the people have no power. In a democratic system, ALL people HAVE some power, that is, the people rule. However, something which Jobst seems to neglect is the process by which the people rule. If the system does not allow majority rule, my experience as well as theory indicate that the result is not democracy, but oligarchy, whenever the status quo favors a minority. Majority rule does not refer to a specific group of people, the majority who rule over others who have no power. It simply refers to any given decision, that the majority have the *right* and *power* to make a decision, in spite of opposition by a minority. Systems may limit this, to protect minority rights, but no democratic system of which I am aware limits it absolutely, that is, a majority, and especially a distributed majority, can unconditionally make decisions. That it can do this does not make it wise to do so. Hence, majoritarian systems in which a majority of 50% + 1 voter can make all decisions are NOT democratic. The greeks called them pleocratic. Without caring what the Greeks called them, since I'm not Greek and I never granted the Greeks authority over the English language, words meaning what they mean in current usage, not what they meant, in some cognate form, to some people thousands of years ago, I would disagree. With some cautions and provisions. I know of no stable, long-established democratic system which does not allow some kind of routine majority-controlled decision-making power. There are attempts aplenty to institute consensus rule, or to require supermajority for routine decisions. I've had substantial experience with them. They both work and don't work. Often those involved in them are quite enthusiastic about them, because the power and energy in discovering consensus can be invigorating. *However*, in the long run, the work involved can be debilitating; those who continue to support these systems don't seem to notice, or perhaps don't care, that the organization bleeds members who find the intensive and often long meetings necessary to work out consensus solutions more than they can spare. And then, eventually, the organization runs into a problem, an entrenched minority which is favored by the status quo. They can, with the rules, block changes desired by the majority. This is why I claim that supermajority requirements eventually lead to minority rule. Yet, in fact, obtaining supermajority consent, even universal consent (i.e., consensus), is highly desirable. It is making it into a rigid rule that is the problem. Thus, I've concluded, the majority has the *right* of decision, but it is quite proper that the rules force the majority to make decisions cautiously and deliberately, with full awareness of the possible damage. Whenever a majority runs roughshod over a minority, it weakens the organization. So, I'd suggest, there better be a good reason. And thus my preference for election methods that look for more than majority consent to outcomes. Yet, at the same time, my consideration that it can be desirable to provide a means for the majority to withhold consent and to insist on its preference. But consciously, not as an outcome of a Majority Criterion satisfying election system, which goes ahead and implements the first preference of a majority without qualification. Social utility analysis of the most basic kind shows that the Majority Criterion conflicts with maximizing social utility, and it does this in situations where the maximum utility is completely clear. I use the pizza example because it is so blatant, and I use the civil-war-trigger examples because they show that this is something that can be, under some circumstances, crucially important. I really would like to see Range systems that require majority consent to the outcome, and it is *impossible* to incorporate that in the first stage, though Approval and Approval-cutoff Range may attempt it. The problem is that what I will accept as a compromise depends upon information about what others prefer and their preference strength. If I don't realize how seriously some of my friends will suffer if the majority choice of pepperoni is implemented, I may insist upon it, after all, don't I have the same rights as them?
Re: [EM] UncAAO
Forest W Simmons wrote: Here are the main advantages of UncAAO over other Condorcet methods: 1. It is resistant to manipulation ... more so than Beatpath or Ranked Pairs, if I am not mistaken. 2. It always chooses from the uncovered set. 3. It is at least as easy as Ranked Pairs to describe. No mention of the possibility of cycles is needed, since the covering relation is transitive. 4. It is easier than Ranked Pairs or Beatpath to compute. One never has to check for cycles, since the covering relation is transitive. 5. It takes into account strength of preference through appropriate use of Approval information. With regards to point 1, consider the following example (sincere votes): 45 ACB 35 BCA 20 CAB Here C is the CW. Is this example right? This is not a Nash Equilibrium for Margins, Ranked Pairs, PC, etc. because the A faction can improve its lot unilaterally by reversing CB to BC. Under winning votes the C faction can take defensive action and truncate to 20 C. The resulting position is a Nash Equilibrium. Taking such defensive action causes B to win, so why would they want to do that when they prefer A to B? And I don't see why the resulting position is a Nash Equilibrium (according to the definition I googled up), because the sincere CA faction can change the winner from B to A by changing their votes from C to CA. * *DEFINITION: Nash Equilibrium* If there is a set of strategies with the property that no player can benefit by changing her strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute the Nash Equilibrium. *http://william-king.www.drexel.edu/top/eco/game/nash.html Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] UncAAO
Forest had correctly said: Under winning votes the C faction can take defensive action and truncate to 20 C. The resulting position is a Nash Equilibrium. Chris writes: Taking such defensive action causes B to win, so why would they want to do that when they prefer A to B? And I don't see why the resulting position is a Nash Equilibrium (according to the definition I googled up), because the sincere CA faction can change the winner from B to A by changing their votes from C to CA. I reply: The Nash equilibrium isnt one in which the offensive order-reversal takes place. In the Nash equilibrium, the C voters truncate, and the would-be order-reversers dont order-reverse. The B voters wouldnt benefit by changing their vote, and the would-be order-reversers would suffer if they order-reversed. Thats the Nash equilibrium. The B voters, by truncating, make the would-be reversers accept the Nash equilibrium or suffer the consequences. Mike Ossipoff DEFINITION: Nash Equilibrium If there is a set of strategies with the property that no player can benefit by changing her strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute the Nash Equilibrium. http://william-king.www.drexel.edu/top/eco/game/nash.html election-methods mailing list - see http://electorama.com/em for list info
[EM] typo
I said: The B voters, by truncating, make the would-be reversers accept the Nash equilibrium or suffer the consequences. I meant The C voters instead of The B voters The C voters, by truncating, make the would be reversers accept the Nash equilibrium or suffer the consequences. Mike Ossipoff election-methods mailing list - see http://electorama.com/em for list info
