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Preferences, Sorites, and eBay

June 23rd, 2004 · No Comments

Economics is all about preferences. We take for granted that we’ve got a set of goals, desires, and ends; the fun in the model is mostly about figuring out how more-or-less rational people fit means to those ends. And, maybe mostly as a simplifying assumption, we usually think of those as defined pretty precisely well in advance of the act of economic choice. We’ll talk about my reservation price with respect to a certain good, or about the people priced out at the margin by a price increase of ten cents or ten dollars. The term “revealed preferences” is itself revealing, in that it implies there’s something hidden, already there, waiting to expose itself to the world through our choices. But how true is that, really? Bidding on eBay makes me wonder.

Earlier this week, I put in a few bids on a black Armani suit I liked, nice three button affair. It retailed at about $1,700, but it looked as though I might be able to get it for just a couple hundred. (It ended up going for a little over $400, still a good deal, but given that I don’t actively need a new suit, too rich for my blood.) I don’t remember the exact prices I went through, but say I bid $250. The site’s auto-bidding program informs me that someone else has a higher reservation price, and I’ve already been outbid, so the price for the suit jumps to $251. Now, say I’d thought $250 was about what I thought I was willing to pay at the outset. But now there’s a tempting line of thought that goes like this: I was willing to pay $250, and especially relative to the price of the suit, another two bucks is a pretty small amountâ?¦ so shouldn’t I also be willing to pay $252. The problem, of course, is that you can iterate that indefinitely: If I’m outbid again, I might reason that as long as I was happy to shell out $252, I shouldn’t balk at moving up another $2 if that might win me the suit.

Philosogeeks out there will readily recognize this as a variant on the famous sorites paradox. In the classical form, it goes like this: Two or three grains of sand clearly doesn’t count as a heap of sand. And it seems absurd to imagine that one bit of sand wouldn’t be a heap, but could be transformed into a heap by adding just a single grain of sand. But if you take those two premises strictly, you can “prove” that a million grains of sand isn’t a heap either. And if you start at the other end—a million grains clearly is a heap and subtracting a single grain couldn’t make the difference between a heap and a non-heap—then you can just as readily prove that two or three grains are also a heap.

Of course, that’s not a real paradox or problem; it merely shows that the term heap is vague, not defined at high enough resolution to specify in this grain-by-grain way. But if we’re tempted by sorites-type thinking when bidding on eBay auctions—even though, of course, there always is some precise dollars and cents figure where we finally say “this much, and not a penny more”—does this mean that maybe our preferences are also vague, that there just isn’t any fact of the matter about my reservation price until I actually decide to stop bidding?

It’s tempting to say no: We might say that my reservation price isn’t necessarily transparent in the sense that I know exactly what it is before the fact, but if I get to $275.16 and stop, then that must be the amount at which I was “really” prepared to value the suit all along. And that fits with how we talk about some other things: I might aver that I’m not afraid of clowns, until I run into one at a carnival and begin shaking in fear as the memory of some terrible childhood experience at the circus comes back to me. I had coulrophobia all along, and didn’t know it.

But economic transactions, more than a visceral reaction of fear, seems to have an element of choice to it. And if you’re going to say that my reservation price of $275.16 was really “there all along,” it seems as though you might as well say the same thing about all our choices: That when I choose to pursue a career in journalism instead of going into academia, or vice versa, that the decision was “really in me” all along. Now, for those of us who don’t have much use for the notion of free will, that’s no problem—indeed, leaving aside random quantum fluctuations, we might even think it was “in me” in infancy, or “in the universe” before I was born. But that doesn’t seem to be the sense in which we intend the idea that preferences are preexisting. On the other hand, if either for pragmatic and colloquial reasons or because we do believe in free will, we want to distinguish between choices and standing intentions or dispositions, it seems at least as plausible to say that we choose our reservation price in the act of transacting as to say that we really held it, down to the penny, all along.

Does it matter to the economic model? I’m inclined to think that it doesnâ??t matter much for technical reasons, for the same reason that it’s often helpful to assume individual rational calculation, even if most of the time people are following evolved rules of thumb selected because they give the same output as calculating the right answer in individual cases. But it might change the way we think about economics and efficiency. That is, it’s common to divide arguments into different types: My roomie Tim likes markets because they’re efficient, they “satisfy preferences,” while others are more concerned with ways that markets promote freedom or autonomy. (If you’re not a fan of markets, substitute “democratic institutions” or anything else that has this dual character, potentially justifiable in “freedom” and “efficiency” language.) If preferences aren’t so much “revealed” as they are created in transaction, then maybe these turn out not to be two different discourses, but different ways of talking about the same thing.

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