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

[Abd ul-Rahman Lomax]

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
>----
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