So here’s something odd. Supposing I give you a choice between two drinks, say hot chocolate. And one of them has just slightly more chocolate than the other, but only slightly. And if you taste both, you can’t really tell the difference. Now, supposing I say that the one with less chocolate is just a little bit cheaper, say one penny, or one cent cheaper. So if you’re given the choice between these two. You can’t tell the difference. One actually has a bit more chocolate for the extra penny. But you can’t tell. So what are you going to do? You’re going to choose the cheaper one. Now let me take another chocolate in the sequence.
And we’ll just take a little bit more chocolate out for this one too. A little bit less flavour. And it’s yet another penny cheaper. And we’ll go along the sequence, taking out a little bit more chocolate, and making each successive drink just a little bit cheaper. If you take any adjacent pair, the difference between the flavours is so subtle you can’t tell. So you will always choose the cheaper one. So that seems to me that you will always choose the cheapest in the sequence, along the entire sequence. And to see that, think about it this way. Supposing you start off with the full flavour, really expensive chocolate. You think, oh yeah, this is good. I like it.
But now somebody then offers you something which is pretty much indistinguishable, in fact, indistinguishable for you. And it’s one penny or cent cheaper. So you switch to that one instead. And then they give you the next one in the sequence, and you switch to that one. You say, this is great. It tastes the same. And you go on, and on, all the way down the sequence, until you end up with something utterly tasteless and incredibly cheap. Now, if I then ask you would you like to stick with the incredibly tasteless and cheap thing, or would you prefer the one you started with, you’re almost certainly going to say, goodness me, I definitely want to choose the one I started with.
That had the really lovely flavour, and was worth buying. So this is really odd, because now we can set off again. We can say, OK, so you preferred that one. But even better is the just below it in flavour and price. And even better is one below that. And off we go again around the circle. Now, this seems kind of weird. And it’s really weird when you think about it like this. Supposing every time I give you two options, you decide to switch, you wish to switch, you have to give me, to allow the switch to take place, a tiny amount of money, just maybe a tenth of a penny, or tenth of a cent.
So you start off with the very full flavour, best chocolate, high price. And you think, oh no, but there’s this other one which costs a cent less. I’ll switch to it. I can’t tell the difference in the flavours. You make the switch. But to do the switch, you have to pay me a tenth of a penny. And then you switch, and switch, and switch, all the way down to the end of a chain. Now it’s an insipid, horrible, flavourless drink, but very cheap. Then you switch back to the one you started with. And off you go, around, and around the circle forever. Now what you’re doing now, is going round and around a circle of choices.
And every time you make a switch, you’re paying me. I can get you to go around in a circle forever. And you’re going to keep paying me. This is great. You never actually drink any of the chocolate. You just switch chocolates, time after time after time, and hand over money. This is called being turned into a money pump. So if I could really make you do this, if I could really convince you that those were the choices you wanted to make, I could pump money out of you. You’d just give me a tenth of a penny at a time, all your money forever and ever. Now, that’s obviously not going to happen in true life, of course.
You’re going to think, hang on. There’s something fishy going on here. I don’t know what it is. But all that seems to be happening here is I’m going around in a circle and I’m paying your money. I’m going to stop. But you’re just stopping because you realise something bad is going on. You don’t really understand why. Now here’s an interesting thought. You could say, there must be something wrong with these preferences, that I prefer, let’s say, imagine the chain is a sequence A, B, C, D, E. A’s the full flavour. E’s the insipid one.
If I prefer A to B, and B to C, and C to D, and D to E, but then I turn out to prefer E to A, so I’ve gone around in a circle, there’s got to be something wrong with that set of preferences. They’ve got to, in some sense, be irrational. Because if I really lived by those preferences, you could pump money out of me, a tenth of a penny at a time. So let’s suppose that we say, alright then, a rational being shouldn’t have preferences like that. They may, in reality, have preferences like that. We are not fully rational beings. But a rational being wouldn’t have preferences like that.
Now, suppose you now think about how stock markets work. In stock markets, and in fact the global financial markets in general, there are all kinds of complicated offers on the table, a bit like drinks of cocoa, but much more complicated. And you can switch from one to the other by engaging in financial transactions. And every time you switch you have to pay a little bit of money to a third party to make the switch, very much like what we’ve just talked about. Suppose it turned out you get these same circular sets of preferences in the stock market.
Then that would be great news, because I, as a devious financial wheeler dealer, could pump money out of you, by getting you to swap A for B, and B for C, and C for D, and D for E, and E for A, and round and round foever, and take all you money. Now, in practise, of course I don’t even have to do that with just one person. If somebody prefers A to B, and someone else prefers B to C, and someone else prefers C to D, and so on, then I, as the wheeler dealer, can keep switching from product to product to product, even if I’m making the switches with different people.
And then I can end up with the same thing I started with, with a bit of extra money, because everyone’s paid me, as it were, a tenth of a penny. And I can do it again, and again, and again, and again, and again forever. Now it turns out that, according to finance theory anyway, this kind of thing shouldn’t happen in the stock market. Or it shouldn’t happen for very long. And what will happen if you do see patterns like that, is that lots of wheeler dealers will dive in. They’ll try to exploit the pattern. And they, thereby, will change the prices. This is called an arbitrage opportunity, an opportunity to make, as it were, free money.
But because there’s an opportunity there, all the speculators and wheeler dealers dive in, try to buy up the relevant goods to exploit the opportunity. And the prices will then change so that the option goes away. So in both individual cases, and in the market case, the rational, stable situation is that circular preferences disappear. And yet, weirdly, every day behaviour seems to indicate that we maybe do have very unstable preferences. And those unstable preferences are quite likely often to be circular. But, of course, just like the financial market, I, as an individual, am always looking out for trickery.
I’m looking out for odd situations, where I swap something, I swap it again, and I swap it again, and I get back to where I started, and I feel tricked. So I’m trying to avoid those kinds of situations. Now one perspective, thinking about things like circular preferences, one perspective that’s common from an economic standpoint, is thinking, well, if people are basically rational, their preferences can’t be circular. It would just be ridiculous. Another perspective takes the view that our own behaviour as individuals is quite like the stock market. There’s all kinds of chaos in there. There’s all kinds of strange preferences.
But as soon as someone starts to exploit them, or we start to see ourselves being exploited, we rapidly change our preference. Or say, I’m not dealing. So it’s not so much that my preferences are intrinsically stable, rational, and not circular. It turns out that the process of trading, and living in the world, is continually throwing up to me challenges, the challenge of being stable enough that I can’t be exploited. And, in fact, from the mind is flat point of view, I don’t really have a set of stable preferences anyway. I’m making them all up as I go along.
And as I make them up, I need to be continually vigilant that the answers I give don’t allow me to be deviously exploited. Now that might not seem too worrying if one thought one’s preferences were pretty solid things. But as we’ll see, and as indeed to some extent we’ve seen already, our preferences as individuals are all over the place.