[EM] The issue of comments about Arrow's theorem

[Abd ulRahman Lomax]

At 11:31 PM 5/17/2005, Russ Paielli wrote:
>If I am not mistaken, Arrow's theorem says that you can't satisfy both the 
>Condorcet criterion *and* the independence of irrelevant alternatives 
>(IIA). Should that bother us? I think it should bother us at least a bit. 
>I am bothered by the fact that eliminating a losing candidate can change 
>the winner. Like failure of monotonicity, it suggests a certain irrationality

Bingo. Here is the core irrationality: even sophisticated election methods 
can fail when an electorate is badly divided. And a divided electorate is 
like a person who is in the middle of an argument with himself, who has not 
yet resolved an issue in his mind, but who, whether out of impatience or 
dire necessity, must make a decision immediately. Such decisions are really 
not going to be made on a rational basis, but by a fast-response mechanism. 
Like plurality. (The predator is hot on my heels, I come to a fork in the 
unfamiliar road, which fork do I take? I'll take whichever one generates 
the most action potentials, there is no time to engage in anything more 
complicated than that. More often than not, my accumulated experience (i.e. 
intuition) and instinct (hard-wired responses) will produce a better 
outcome than a coin toss, but that only gives it survival value, not 
rationality. Rationality takes time and process.

In a real environment, and most of the time, where there has been ample 
time for discussion of an issue, where the alternatives are considered 
openly in a fair forum, where those voting have the leisure to become 
informed and can communicate and discuss with each other, and where all 
alternatives are on the table as part of the process, all the voting 
methods I've seen will produce the same result, *unless* a general 
consensus has not emerged and there is severe polarization of the 
electorate. Or the choices are not important, i.e., there is more than one 
generally acceptable outcome. (In which case an apparent irrationality of a 
result because of its failing one of the criteria is only an appearance, 
just as people will accept a coin toss result if they are not strongly 
attached to one of the possible outcomes. It simply is not worth the effort 
to go through an extended process on that issue.)

Irrational election outcomes are generally the result of an inadequate 
pre-election process. An intelligent and rational person will generally 
avoid making a binding decision, absent urgent necessity, when in a divided 
state of mind. Rather, the person will continue to mull the possibilities 
until a clear path appears. A "clear path" means that there is an internal 
consensus, most of the considerations, when pursued to the end, lead to the 
same conclusion. Or the person considers that it isn't important which of 
various possible outcomes are taken, the person is willing to try one to 
see if it works....

An example presented by Russ exposes a significant aspect of the election 
problem. He used a situation where a group was choosing between vanilla, 
chocolate, and strawberry. Yet these are individual tastes and a situation 
where people are forced to accept someone else's individual taste, absent 
necessity, is oppressive. Regardless of what election method is used, if 
the method chooses one flavor for all, it is going to be the tyranny of the 
majority. So a sane organization is going to try to find a way to satisfy 
as many of its members as possible, which might involve spending a little 
more to buy more than one kind of ice cream.

(Perhaps by buying one flavor, the quantity purchased will be greater, and 
thus the cost might be lower, this might be why the conditions require only 
one flavor. But this would be an artificial constraint. Still, I can think 
of a situation: There is an opportunity to make a bulk purchase for the 
group, but only one flavor can be purchased. In this artificial example, 
off the top, it would seem that approval voting would be used; however, 
what a group would first decide, before voting, would be the goals of the 
election? How important is it that all members be satisfied at least to 
some degree? How serious an outcome is it that some members will be totally 
disatisfied with the chosen outcome? If some members must be dissatisfied 
no matter what outcome, is there some other course of action which could be 
taken which could compensate them for this? For example, suppose the group 
chooses a flavor which reasonably will be enjoyed by all but one member, 
who happens to be allergic to that flavor. The group could pool their funds 
and provide enough to that member to buy whatever flavor the member 
chooses. But there is a general solution which falls out of Free 
Association principles.)

The general Free Association solution is that those who want one flavor 
pool their resources to buy it, and those who want another either pool 
*their* resources to buy it, or they don't buy ice cream at all. Free 
Associations don't collect unappropriated funds, so a member is never 
forced to contribute to a cause which the member does not personally 
support. It is this pooling, normal in most large organizations, which 
creates election paradoxes, for there is a built-in inequity, almost 
impossible to avoid, given that standard structure.

Note that I am not at all arguing against the necessity of such 
organizations, where participation is at least to some degree involuntary. 
But I think that *representation* must be fully voluntary, or it isn't 
truly democratic representation, it is more a tool of governance, where the 
sovereign has decided to consult the people but doesn't want to grant them 
too much freedom to express whatever they actually prefer.

And, indeed, simply establishing organizations where the members have the 
kind of freedom being envisioned (which includes the crucial freedom to 
voluntarily delegate) could be quite revolutionary. But I don't think it 
would be destabilizing, for destabilization is not generally a rational 
choice, it causes far, far too much damage; in a large FA/DP organization, 
deliberation will occur which incorporates the best thinking (as well as 
the worst); trusting FA/DP would involve trusting that truth or wisdom will 
out in a fair contest. That is the core idea of democracy. It works in 
small organizations, in fact. It is scaling it that is the problem. Hence DP.

Note that share corporations in some aspects are FA/DP. (Proxies may not 
seem to be delegable, and there is no automatic delegation mechanism, but 
this defect could easily be rectified by any group of shareholders who 
desired it, and it would restore true shareholder governance. FAs don't 
generally hold property; but because the individual shareholders can 
readily sell their shares, participation remains voluntary at all times and 
thus the resemblance to FA can be seen as strong.) And, regardless of 
whatever we might think about the ethics of modern corporations, and 
regardless of the abuses of proxy power that takes place in corporations, 
the structure has been phenomenally successful, to the point where 
continued abuse of the defects in the system poses a great danger to 
society. Fixing those defects might not be very difficult, once the true 
source of the problem is seen. And people stop waiting for somebody else to 
fix them, and realize that only they, collectively, have the power.

So how would the group of people choose what flavor of ice cream to 
purchase?  There are very many ways, but the ways that I'd consider 
intelligent all involve voluntary negotiation, they involve a process more 
complex than a mere election method. It's obvious that plurality results, 
Condorcet results, and approval results would all provide relevant 
information toward making a decision, but the actual decision, in an 
organization which wants to maximize member satisfaction and ongoing 
voluntary participation, cannot be fixed to any specific method, I'd 
suggest, without resulting in damage. And any method that is unanimously 
accepted [not necessarily the *outcome*, but the method itself] will fully 
satisfy this. That's the ideal, and, having had a fair amount of experience 
with organizations which require full consensus, the ideal can often be 
reached if the result is valued. It's obvious that the larger the 
organization, the more difficult it can be to reach full consensus, and 
beyond some not-well-defined size, full consensus will be impossible on 
many issues. But it can still be approached. How closely remains to be 
seen, for the process methods are still in development (in thousands and 
thousands of experiments; unfortunately, FA/DP is only seeing a very few 
experiments, and I'm aware of no experiment that combines all aspects of FA 
and DP in a single organization).