[EM] D2MAC can be much more efficient than Range Voting

[Michael Poole]

Abd ul-Rahman Lomax writes:

> 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."

Randomness is not identical to noise.  Stochastic computing methods
use randomness to get "good" results (according to the method's
definition of good) -- in many cases, much faster than naive methods
reach comparable results.

> How evenly benefit is to be spread is a choice. How is this choice to be made?

This is closely related to the question I asked but that you did not
answer: How do you define the proper outcome of an election?

> 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.

You have written a great many paragraphs here that only repeat the
same assertion that I questioned: namely, that elections using
stochastic methods or history introduce noise.  I thought I was rather
clear in saying that you have not defined "noise" in this context.

> 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.

I do not assume that factions are fixed, only that they can be defined
with respect to this choice.  There are many real-world examples where
the factions retain membership or relative sizes, and some where they
do not, but the first case is easier to analyze.

> 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.

Do you have a better word for groups whose votes are equivalent under
the election system?

> 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.

"X is true, except when it is not" is hardly a useful observation.

Above you drew the distinction between factions and individual
preferences.  Just as there is no accounting for taste, there is no
accounting for individual knowledge or priorities.  The goals that
voters seek by selecting a particular candidate vary; if it were so
easy to analytically prove that candidate X should be president, the
United States would look (and behave) very differently than it does.

Because of that, it is important to distinguish between intelligence
in the voter's choice and intelligence in the election method.  It is
desirable to have both, but the two really have very little to do with
each other.  On top of that, the most popular ballot may not be ideal
in terms of intelligence (or other metrics).  The implication that
adding randomness reduces intelligence is hard to reach.

Michael Poole