At 05:06 AM 3/7/2007, Jobst Heitzig wrote: >it is frequently claimed that methods which involve randomness may be >fairer than other methods but will give "worse" results.
Given that it couold appear that I have made that claim, let me be explicit that I have not. I have claimed something which could be misread as that claim, and the misreading shows, if this is what happened, that my actual claim has not been understood. Of course, Jobst may simply be making a general statement and, in general, he will be correct that such claims, as he has stated them, are false. My actual claim is that *ordinarily*, where the use of random choice allows a minority to prevail over a majority *without the consent of the majority*, introducing this randomness is introducing noise. And "noise" is precisely the correct term. If we have an electronic decision-making system that depends on logic and/or pattern recognition to make choices, and we introduce into that system electronic noise that causes the built-in choice functions to be ignored, *under most conditions* this will degrade the performance of the system. There *are* conditions where this is not true. For example, suppose there is a missile guidance system that is designed to vary the path of the missile in order to avoid attacks against it. If the path of this missile can be predicted, the avoidance can be defeated. But if the path is random, to a certain degree, it becomes much more difficult to predict where the missile will be when the intercepting missile reaches the incoming one. But, of course, if *too much* randomness is introduced to the missile path, it will begin to lose enough fuel efficiency both through the fuel used for making corrections and the extra fuel consumed through increased flight time. There would be an optimum level of randomness. Strictly speaking, this is not noise, because it is an intended part of the process. But typically noise generators will be used to make the random choices. Looking at this missile system, there are two processes going on. There is a process which determines the optimum path to the target. And there is a process which randomly deviates from this in order to make the path sufficiently unpredictable. If not for this need to confuse countermeasures, randomness introduces into the process would be seen as noise and as undesirable if the missile is to fulfill its purpose in the best manner. Put it another way: in the example, noise is counter-intelligent. It deviates from the normal intelligent path in order to defeat an enemy which has that normal intelligence. Any society must be able to make decisions. What we call individuals are even tightly organized societies of cells. How do individuals make decisions? In a situation where a sane individual would find it useful to toss a coin, then in analogous situations a sane society could introduce randomness to the process. Note that there is already a level of noise. Factors which are irrelevant to the decision being made can nevertheless influence it, and there are host of these. All of these distractions are noise. If we could somehow filter them out without harm, we would. I hasten to add that such filters could be quite dangerous. FA/DP *does* filter out such noise, to a degree, but in a particular way that is not likely to be hazardous. >Here's evidence for just the contrary: > >A typical voting situation is > >55%: A>C>B >45%: B>C>A Consider this election as a sincere Range election in a sane society. What has happened is that out of the infinite possible range of choices, these three choices have been preselected. Usually in such a situation truly bad choices have already been eliminated, and the difference between A and B, on some absolute scale, could be seen to be quite minor. What we have here could simply be a difference of opinion on, say, the optimum tax rate to set, not so low as to provide insufficient funding for necessary or desirable projects, and not so high as to injure the economy. In this example, the choices can be represented as numbers. And we would not be surprised to note that numerically, A>C>B. The 55% group generally leans toward higher social spending and thus higher taxes, and the 45% group towards the reverse. The society, collectively, wants to set the tax rate at the optimum level such that the sum of the various effects of the tax rate is maximized (let's presume that all the effects can be quantified as dollar figures). What is the rate to choose? As the problem has been stated, there are only three possible rates. It can easily be that none of these would be optimal; from collective intelligence theory we would expect that the optimum rate is most likely to be the average of A and B, assuming that A would be the free choice of one group and B the free choice of the other. In fact, were this a Range election, A would be the maximum rate reasonably acceptable, and B the minimum rate necessary to fund reasonably desirable services. Some might set the rate at zero. A few, collectivists or true communists, might set the rate at 100%. So, in fact, the Range might be from 0% to 100%. What is likely to be the ideal rate? My suggestion would be that the average of Range votes on this question would be optimal, though there may be more sophisticated methods of analysis. None of them would involve the introduction of noise. Let's see what Jobst does with this: >with C being considered a good compromise by all voters >(in the sense that all voters would definitely prefer C strongly >to tossing a coin between A and B). That would not necessarily be a normal condition, by the way. If C is located very close to A, those voters who prefer A would dislike a coin toss, we could expect, but the B supporters would prefer the coin toss. The condition described only holds where the sincere rating of C is the average of the sincere ratings of A and B by the respective A and B supporters. What would make sense of the preference for C over a coin toss? If C is the average of A and B, a coin toss should have the same expected utility as C. Under these conditions, the "definite" preference described could not be likely. When would it be a reasonable condition? When A and B are sufficiently different that A is not only undesirable to the B supporters but actually unacceptable, and vice-versa. We have a tendency to think of election methods in highly polarized situations, but those are situations where society is in trouble almost no matter what election method is used (though some may be likely to make things worse and others may tend to ameliorate the situation). We need to remember that election methods, in general, are merely methods for aggregating expressions of opinion or preference into a choice or set of choices. So to understand the situation presented, it is polarized and charged, and it is generally recognized, in fact, that there is great danger in merely going ahead and implementing the preference of the majority. This situation is one in which the Majority Criterion will properly be violated. (And it is situations like this where the Majority Criterion will frequently suggest suboptimal results.) If the decision is a minor one, a fully sincere Range election would show the difference between A and B as being small enough that, with the numbers given, a coin toss would, in fact, be reasonably acceptable to most. However, that still leaves the question of what is the best choice. I don't think that tossing a coin is, in fact, optimal given the preferences described. It is introducing noise. Again let's see what Jobst does with this. (I'm writing this, by the way, as I read it, I have not read ahead. Readers are following, if they are following, my understanding process.) >At first, it seems that this is exactly the situation where >methods which claim to maximize "social utility" or "social benefit" >should lead to the "right" answer C. C is not necessarily the right answer. In fact, the example shows the deficiency of methods that don't collect preference strength information. I can presume from the stated conditions that C is the right answer, in general, but I also assume that circumstances can be shown where this is not true. It may be necessary to specify those circumstances. >If all voters were sincere, indeed both Approval Voting and >Range Voting will elect C, since the ballots would then >look like this: > >Approval Voting: > 55%: A,C > 45%: B,C >Winner: C That is correct given the conditions stated. >Range Voting: > 55%: A 100, C 50+whatever, B 0 > 45%: B 100, C 50+whatever, A 0 >Winner: C Remember, the votes have been normalized. But the conditions in fact would be most likely to represent a situation which is like this. Such votes would *not* be the general case in real elections with the preference order described. We must keep in mind that this is actually a special case, even though Jobst asserted that it was common. The tipoff that it is a special case is the restriction regarding random choice between A and B, presumably with equal probability of each. And the rationality of that restriction (i.e., the consensus preference) is dependent upon more information about C than we have. >The problem is, rational voters just *won't* vote sincere in this >situation. This is asserted. I claim that it is false. Voters afflicted with what I consider the disease of polarization and zero-sum political games would behave as Jobst expects. Voters in a non-coerced society, where the general expectation is that collective intelligence is superior to individual intelligence (*for collective choices, not necessarily for individual ones*), where the unity of society is valued and it is understand that peak expectation of utility is likely to be associated with actual realization of benefit (the goal of the whole process!), voters will simply vote what they think best, and they will not modify this in order to "get what they want," because what they actually want is the best choice *and they understand that their own opinion will generally deviate from this*. The irrationality underneath what Jobst considers rational is an assumption that *my* opinions are superior to those of others, and, in particular, my opinions are superior to an efficiently and fairly aggregated opinion of the society collectively. There is a legend that large groups of people can fairly accurately estimate the number of pennies in a large jar by each guessing and the averaging the guesses. I'm not sure that this legend is true in detail, but I would suggest that the average error of the averaged guess, over many such trials, would be less than the average error of the individual guesses. And, in fact, for the large majority of people, they will see a more accurate result if the average guess of all participants is used rather than their personal guess. Now, if the people want an accurate result, they will simply vote their personal estimate, using whatever intuition or method is available to them. There will be a few of them who are "penny-guessing experts," and for this group the individual estimate might be more accurate than the averaged guess. Perhaps the expert is autistic. Problem is, it can be quite difficult to discover who these experts are, and, in democracies, we have decided to assume that people are equally capable of making choices accurately. And, in fact, the results of the average guess and the expert guess are quite likely to be close to each other. So even the expert would not rationally be disturbed by the use of the average guess unless for some reason the problem is crucial and a very slight error disastrous. Perhaps this is a lottery being conducted by invading and powerful aliens.... Not exactly common! I really think this needs to be understood. What I see as an error of personal arrogance is a very common assumption, I have seen it asserted many times that this behavior is "rational." It is not. It is irrational. Being irrational does not mean that it won't happen! It will, in a society which is structured to encourage such behavior. The strategic behavior would be the equivalent of someone who considers himself an expert, and who expects the guess of the generality to be X, while he thinks it to be Y, voting, instead of Y, whatever value is optimal for this voter to produce an average as close to Y as possible. Usually this would be maximum in the opposite direction of the perceived error. Yet for this behavior to be rational, this voter must expect not only to be correct about the pennies (in that example) but to be correct about the guess of the generality, which might be a set of abilities not likely to coincide in the same person! (The autistic expert may be quite likely to accomplish the first task and quite unlikely to accomplish the second.) If there is error in the second guess, this expert, who could have added weight to his expert choice, will instead cause increased error. However, I'd leave the judgement of the two relative abilities to the individual voter. Voters *can* distort their votes like this where they deem it advisable. *It is all part of the process by which a society aggregates opinions.* > And since Approval and Range Voting are *majoritarian* >methods, the real outcome will rather look like this: > >Approval Voting: > 55%: A > 45%: B,C >Winner: A If voters behave in that way, which is known to be irrational. Remember, I've noted that if there is an irrational majority, society is in deep trouble and it could be very difficult to get out of it. The majority can change the rules! (It ain't easy being paranoid!) >Range Voting: > 55%: A 100, C 0, B 0 > 45%: B 100, C 99, A 0 >Winner: A > >So, both these methods *fail* to do just what they were apparently >constructed to do! No, what has happened is that a majority has exercised its weight and has refused to *use* Range Voting, instead they have clearly abandoned any attempt to find consensus. They have the power to do this, if they are organized, no matter what election method is set up, because they can simply ignore it, change the rules, whatever. And the conditions stated are contradictory. Remember, it was said that all voters agreed that C was superior to a coin toss. Yet a coin toss in the context described will produce a better expected outcome than no coin toss. So an irrational condition has been imposed. Garbage in, garbage out. >Now let us look how D2MAC performs in this typical situation, >a democratic, non-majoritarian method: > >Recall that in D2MAC you specify a favourite and as many "also approved" >options as you want. Then two ballots are drawn and the winner is the >most approved option amoung those that are approved on both ballots >(if such an option exists), or else the favourite option of the first >ballot. > >If voters are sincere, the result will be this: > 55%: favourite A, also approved C > 45%: favourite B, also approved C >Winner: C Look, in contrast to a situation where insincere votes are presumed, we now are going to see how D2MAC performs with sincere votes. Is this a fair comparison? Set up the same condition with majoritarian voters voting strategically, the same results. The majority prevails with its preference. Sauce for the goose is sauce for the gander. >Can the A-faction improve their result upon this by voting differently? > >If they switch to > 55%: favourite A, none also approved >then A will win whenever an A-ballot is drawn first, i.e., with 55% >probability. However, B will win in the remaining cases, i.e., with 45% >probability. For the A-supporters, this "almost coin tossing" is not >preferable to C, so the strategy won't help them. > >Thus, the "obvious" A-strategy cannot destroy the compromise under D2MAC! But the A voters have the power to alter the rules. This is something that is totally ignored in analyses like this. It is as if election methods arise, lotus-born, or are imposed by some benevolent dictator. And as if they cannot be changed. Remember, the conditions were that all voters agreed that C was preferable to a coin toss. Yet here, the method is, to some degree, a coin toss. Therefore all voters would agree that this election method sucks big. And if all voters agree on a change, even if the rule is written into the constitution, what constitution in the world would not allow the change? Given the conflicting assumptions, I'm not taking this one further. With two of the assumptions, Jobst wrote his desired outcome. Those two were the coin-toss rejection by consensus, and the assumption that all voters will vote insincerely (incorporating an assumption that this is rational even though it clearly leads to a suboptimal result). There are conditions where such a choice to vote strategically may be rational. They are not the conditions of the example, though, they conflict with the coin-toss agreement. ---- election-methods mailing list - see http://electorama.com/em for list info
