It is difficult to choose appropriate titles for some of these posts because my thoughts wander from topic to topic. I’ve been thinking again about my little stoneage tribe that I use as a model for social, political, and economic problems. But let me start at the beginning.

First, my car was returned today. (They did an excellent job — it looks better than new.) I had to pay an excess of R1500, which I now have to retrieve from the guilty party. I’ll do it tomorrow, but it is not an easy task. Not because I think she won’t pay, but just because I find it uncomfortable to ask people for money. It would have been easier if she had purposefully damaged my car and the situation was more clear cut, but in this case I have some sympathy for the lady because we all make mistakes and accidents happen. (The real problem, however, is that asking for the money — my money — is a confrontation, which I prefer to avoid.)

This made me think of how convenient/inconvenient money really is. A R100 note is only a placeholder for those things that people agree is worth R100. Of course this is convenient, but money also causes a lot of awkwardness. Bank robberies. And just think of all the overhead costs involved in banking and other financial organizations that could have been spent in more productive ways. Think of all the woe that the global recession (which is partly psychological) is causing. Nothing physical has changed about the world, but the psychology of the housing market collapse in the USA has changed people’s behaviour.

The problem, at least in the USA it seems, was really “speculation”, which is just a fancy word for gambling. And we all gamble. Insurance, for example, is just a form of betting against a disaster. Technically our society should have enough resources to replace damaged goods and care for people in need — if we don’t, we are playing a losing game. The future is uncertain, but society, seen as a whole, should be able to deal with the uncertainty. Think how wonderful it would be if society — our stoneage tribe — would provide for our needs and care for all of us when something goes wrong.

This approach is anathema to some, especially to Americans. I can understand their opposition to socialism. It suppresses (or may suppress) competition and therefore we may not achieve all that we could. And it is definitely a challenge to ensure that every member of the tribe does his/her part. Slacking off and living off the work of others is unfortunately, is seems, part of human nature. This kind of socialism also takes away some individual freedom.  Since society has to ideally agree on how to spend its resources, dissention is inevitable: even in a homogeneous group there will be differences of opinion on what to do with our “money”. (On the other hand, in a free, purely distributed system, there may significant overhead as tasks related to resource distribution are duplicated.)

And this thought leads me directly to the problem of social choice. Given a set of alternatives and, for each individual member of the society, a ranking of the alternatives, there are many different ways to determine the social choice, i.e., the winning alternative. (Or even alternatives, in the case of a tie.) Majority (plurality) voting is one way, but there are many others such as a Borda count, or the Hare system. There are also some desirable properties of social choice procedures:

1. The Pareto condition: If everyone prefers x to y, then alternative y should not be a social choice.
2. The Condorcet winner condition: if the majority of people prefers x to y, for every possible y, then alternative x should be the single social choice.
3. Monotonicty: If x is a social choice (one of the winning alternatives) and someone changes their mind by making their preference for x even stronger, then x should stay a social choice.
4. Independence of irrelevant alternatives: If x is a social choice and y is not, and people change their minds, but not about how much they prefer x to y, then y should not suddenly become a social choice.

A funny thing is that there is no possible social choice procedure that satisfies both conditions 2 (Condorcet) and 4 (IIA).  Moreover, Arrow’s Impossibility Theorem states that the only social choice procedure that satisfies conditions 1, 3, and 4 is a dictatorship! Moreover, there is the Condorcet voting paradox:

• Suppose we have a social choice x, but 90% of the people are unhappy because there is an alternative y that all 90% find preferable to x.  Should the social choice be changed?

The answer is “not necessarily”.  The situation may be the same regardless of which alternative is declared to be the social choice! So, not only is the future uncertain, but, even if it were certain (to some greater, but limited extent), humans would still have trouble in deciding how to act on the information!