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).
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