At 10:45 AM 3/7/2007, Michael Poole wrote: > > 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. > >This is rather hand-wavy in the absence of any definition of "noise" >in an electoral context. Key in traditional noise calculation is >having both multiple outputs and a definition of what the outputs >should be.
What is the "electoral context"? The overall context is that society considers that it must make certain decisions collectively. So by what process does it make decisions? Where the decision is a pure and clean benefit to one group at a cost to another, introducing noise, that is, randomness, could be beneficial, though I would probably argue that deliberation is a better way to get there. The fact is that raw election systems are pretty bad for making complex decisions, in terms of what I'd call "accuracy." How evenly benefit is to be spread is a choice. How is this choice to be made? What I'm asserting is that democratic tradition is strong that, where it is possible to assemble an absolute majority of votes on a Yes/No question, those votes will prevail. The quibbles and apparent deviations from this come from situations where less than an absolute majority is involved, which is normally the case in public elections. In any case, majority rule refers to such decisions, it does not refer to some faction called the "majority," which would simply push somewhere else the question of how decisions are made. That is, there is no such thing as a stable "majority" on all questions, such that all persons belonging to this faction agree. When a faction is able to assemble a disciplined plurality, such that it votes coherently, it can, in many systems, effectively shut out others from the decision-making process; but the result of this is that some faction within the "majority" faction prevails, instead of a true majority of all citizens. This is a frustration of majority rule, not an example of what is wrong with it. Now, what is "noise." Mr. Poole is correct that noise may be various defined, depending on the function of a system. With societies, we are talking about a very general-purpose collective decision-making system. I could try to define what its goal is, but the goal is itself a subject of the system. That is, the goal is something which is determined by the participants. It is enough for me to consider that there is a goal, without assuming that this is a fixed and single thing. People are collectively trying to do something when they hold and participate in elections. What they are trying to do, to the extent that they agree upon this, we may call the "goal" of the election. Now if people are means-oriented, if the goal is to, say, elect their favorite, then it is clear that they are not participating in something directly connected to overall benefit, they are aiming for private benefit. (They may imagine that their favorite will be of overall benefit, but it that overall benefit were their goal, their goal would not be electing their favorite, for electing their favorite is a *means* to an end, not the end, we presume. For some players, some candidates for example, getting elected may be indeed their end, and they will do whatever it takes. Other players, the kind of candidates I generally support, actually are aiming at overall benefit. So I am *assuming* that there is a goal without defining precisely what it is. Maximizing social utility by some measure might be such a goal, but maximizing certain hormone or satisfaction levels might be a goal. However, in living things, and society can be considered a living thing, a default goal is survival. I don't accept survival as the end goal of life, but it, at least, appears reasonably necessary for other goals to be accomplished. I think that we might agree that a society which does not survive has probably failed to reach its goals. So if, for example, we thought of maximizing satisfaction as a goal, what would we think about a decision with which nearly everyone was satisfied, but it was rooted in an error and the result was mass disaster and extinction? A car in every garage ... and global warming? (I'm not making an environmental point, but a point about decisions.) If presented with such a prospect, we chose survival over universal satisfaction, we would have demonstrated that survival was our goal, or closer to our goal, than even supermajority satisfaction. In any case, if we were constructing an information-gathering and analysis device, programming it to make decisions that are intended to maximize its survival or other goal, under what conditions would we introduce random choices? I've argued that there are such conditions, but that they are not the norm. If it turns out that there is some requirement for intelligence and consciousness that there be a certain level of random choice -- entirely possible -- then it might be more normal. However, if we have a relatively simple system that, say, tracks a target and adjusts motion control to keep the system moving toward the target, to minimize arrival time, that system will generate control adjustments that respond to environmental changes in order to maintain the accuracy. Now, no sensor is perfect, and they generally have, in their outputs, a certain level of noise. Digitized outputs may be stable, but, in this case, there is digitization noise, the outputs only appear stable if the noise is below a bit in value, and the signal is stable such that the noise never takes the sensor output to a different least-significant-bit. Such noise is an input to the control system along with the intended inputs, and it will inevitably result in a certain level of inaccuracy. Minimizing such inaccuracy is the goal of noise control. In such a simple control system, we would be vary careful about introducing addtional noise. Unless the noise is introduced in a manner where it actually improves accuracy, rather than simply swinging the *output* in a random way that does not increase accuracy, it will degrade accuracy. I have not seen a description of electoral theory that leads me to thing that system goals are advanced by introducing noise. Now, if the goal were simply to alternate "victory," as if victory were something to eat, yes, random choice could advance the goal, but I'd suggest that there might be better ways, with random choice only used at certain critical points. The AA example I gave uses noise -- random choice -- to broaden representation. But, remember, representation, I've emphasized over and over again, is not a matter for majority rule. For the majority to rule on who is to represent all is to deprive members of society of representation. And the decisions of a body selected in that manner will not be majority rule, they will be oligarchical in character. >Suppose a repeated choice is made according to the wishes of factions >in proportion to the factions' sizes. One could easily argue that >this is a more accurate representation of the voters' wishes than one >that always selects the choice of the largest faction or coalition. >Would these variations be signal or noise? Once again, underlying this is an assumption that the faction or coalition is a fixed thing. Where it is, then, yes. This is an example where introducing something other than majority preference could be of value. Writers in favor of random methods seem to be assuming that "majority rule" is about a "majority faction," but, as I've written, this is, in practice, an oxymoron. One can imagine, however, elections where such random choice would totally be in order. Suppose voters are choosing pizzas, and we will *not* consider the case where someone is going to starve if a certain choice is made. They will merely be less than fully satisfied. And we can also assume that there is no choice which will fully satisfy everyone. Now, in such a situation, you could imagine that there is a mushroom "faction" and a pepperoni faction and a tomato faction. In reality these are not factions, they are simply *votes* or individual preferences. So this group of people goes out every day for pizza at lunch. And, for reasons we simply do not understand, they can only choose one kind of pizza each day. Simply rotating pizzas is less than optimal. Making a random choice is also less than optimal, *unless* the probability of the "victory" going to a kind of pizza is proportional to the size of the "faction." And it would not be difficult to arrange that. Random choice, however, to truly maximize satisfaction in a reliable way, would only be used to seed the process. After that, it would proceed through a rotation designed to optimize satisfaction while minimizing, say, the time for voters to wait between days of maximum satisfaction. And to really do this right, simple preference would not be used, rather a method that considers preference strength would be used. We essentially decided at the outset to neglect that.... This is what Poole proposed, and this is a situation where it would be appropriate. Now, are public elections like that? I've argued that methods which will work for pizzas, and work well, should work for politicians as well. Am I hoisted on my own petard? I don't care. I have two goals here, one being public benefit by the increase and dissemination of knowledge and analysis, and the other being my own education. I make no assumption that the "knowledge" to be increased or disseminated is *mine*, and therefore I actually prefer to be wrong. When I can manage to accomplish this without deliberately erring. (Would it be an error if it were deliberate? Never mind, questions like that give me a headache.) I don't, in fact, think that what might be called the simple preference conditions of pizza choice are generally true of public elections. With pizza, we can easily assume that there is no other social benefit involved than individual satisfaction with the pizza. So in a pizza example, we really do want to maximize or share simple satisfaction (typically some combination). But with elections, we may wish to maximize, say, economic prosperity, education, security, a whole series of goals which are *social* goals, not merely individual ones, though some of them *in some ways* may be comparable to pizza. Most of them are not. Most of them are goal-seeking, and the goal is not simply the choice in the election and what it is going to immediately taste like. And here is where intelligence comes in. We would not think of pizza choice, ordinarily, as a matter for intelligence. As they say, there is no accounting for taste. But when we think about social goals, I assume that intelligence is required to seek choices that advance those goals. And my claim is that majority rule is a heuristic device for maximizing intelligence of choices. And if this is true, then introducing random choice -- noise -- will generally reduce the intelligence of the choice. Again, there could be exceptions, I've detailed some examples. >Depending on how you define noise -- and how you model the signal -- >the same kind of behavior in an electrical system could be noise or it >could be accurate signal acqusition. > >If the choice is not repeated, I do not see how a useful definition of >either signal or noise would apply to the election method. The only >noise measure in a one-time election is how accurately ballots capture >the voters' wishes; there is no clear measure of signal or noise for >the single output of "election winner". > >Michael Poole >---- >election-methods mailing list - see http://electorama.com/em for list info ---- election-methods mailing list - see http://electorama.com/em for list info
