@argumate has been talking recently about hypothetical problems with ancap/libertarian-paradise-world, and it’s making me think about a very basic issue that I don’t see talked about enough.
Namely: all of the usual arguments about how markets are great (“aggregating information” and all that stuff) also say that wealth inequality makes markets worse at doing those things. This is not a knock-down argument for having a state that redistributes wealth at gunpoint, but it is a reason to see wealth equality as a relevant concern even if you don’t have it as a terminal value. Even if you don’t care about it, the market needs it to achieve the things you do care about.
I’ll generalize this in a moment, but first, let’s look at an especially clean example case: prediction markets. Prediction markets are nice here because we don’t have to worry about thorny problems about aggregating utility to construct a “social welfare function.” There isn’t a role for disagreements about values. Everyone agrees about what we want out of a prediction market. (Or rather, the disagreements that exist are technical rather than ethical.)
What we want out of prediction markets is a price that corresponds to the actual observed frequency of events. Of course, this is not always possible – sometimes there is relevant information that no one in the market knows, so even a perfect information-aggregator (say, a rational being that knows everything that anyone in the market knows) would not get the right answer.
So at best, we can only ask for some sort of information-aggregating property, something like “prices reflect the average (i.e. mean) belief.” This is desirable because we expect many sources of individual error to be uncorrelated, and these will wash out when we take the average.
But the prices in prediction markets reflect, at best, a wealth-weighted average of beliefs. (For “wealth” here, read “quantity of money the individual is willing to invest in this market,” which is obviously constrained by wealth in a straightforward way.) This is easy to see informally: if there are 1000 people who are only willing to buy $1 worth of shares each, and 1 person willing to buy $1000 worth of shares, the market mechanism will get an equally large signal from the one big spender as from the 1000 small spenders.
A formal version of this is derived in this paper: with logarithmic utility, prices equal the wealth-weighted mean of beliefs. (If you’re worried about the log utility assumption, note that this is arguably the most favorable possible result for prediction markets, and much of that paper is dedicated to showing that other plausible utility functions do not yield very large deviations from it.)
Is it a problem that the results are wealth-weighted? Well, not necessarily. But it’s important to note that there are two different reasons it might be a problem.
First, assume (as in the paper) that we’re in the “many traders” limit, so there is a continuous distribution of beliefs, we have integrals rather than sums, etc. In this case, what matters is the (Pearson) correlation of belief and wealth. (If they are uncorrelated, the wealth-weighting will be invisible.) This correlation will either help or hurt depending on whether the bigger spenders have more accurate beliefs in any given case; it seems hard to argue that they’ll have less accurate beliefs in general, which makes this concern easy to dismiss.
But second, suppose we are not in the “many traders” limit. The worry with finitely many traders is a situation like the “1 vs. 1000″ example mentioned earlier, where the intuition that we are getting an average becomes misleading because the prices are so heavily affected by a small number of people.
Recall that the whole reason we’re interested in getting the average belief is that we expect uncorrelated errors to wash out if we average over a large number of people. In situations like the “1 vs. 1000″ example, the inequality is making the effective population size smaller, i.e. making our law-of-large-numbers argument weaker. From basic statistics, we’d expect the uncorrelated errors to get smaller by a factor of sqrt(N) when we average over N people. That corresponds to the errors getting about 32 times smaller for N = 1001. But in the 1 vs. 1000 case, half of the answer comes from the belief held by the single big spender, which (by hypothesis) carries random errors of the same size as everyone else’s, so the error is only cut down by (approximately) a factor of 2, not 32.
Now let’s extend this to more general markets.
This case is harder, because we don’t have an analogous law-of-large-numbers argument for the claim that the the price should reflect an unweighted population average. To argue for that sort of claim in general, we must (horror of horrors!) introduce some sort of ethical assumption, say about no one being inherently more important than anyone else.
I was being facetious in the last sentence when I said “horror of horrors,” but there are real difficulties here. The problem is not that some people might really be inherently more important than others, but that we are trying to do some sort of utility aggregation, and this is a famously thorny area. So it may help to be more concrete.
The basic intuitive appeal of “invisible hand” type ideas is that the market will learn to provide what people want. The phrase “what people want” has the same thorny issue just mentioned – how do we translate statements about what individual people want into a general statement about “what people want,” so that we can judge whether it is being provided (relatively well or poorly)?
The core of the idea is nonetheless pretty clear. If a bunch of people want something, but not enough to buy it at the prevailing market price, someone will see the opportunity to make a profit by selling it at a lower price that these people will take. After they take that opportunity, everyone else who produces the product will notice and lower their prices, and (after some equilibration) the market price will be low enough that people get the thing they want. Likewise, if there is more demand for something than the low market price suggests, everyone will buy until there’s none of it left, at which point the suppliers will produce more because they can afford to do so by charging a higher price (assuming that supply curves slope upwards, which is not obvious and which I’ve heard is not always true IRL, but let’s grant it). If you don’t allow these things to happen, you get Soviet bread lines and shortages of rent controlled housing. Or so the argument goes.
OK, so here’s a brain-teaser for you: how much are homeless people willing to pay for housing?
Although there may be some exceptions (crust punks?), people do not generally become homeless because they simply value having a roof over their heads less than the average person does. Many homeless people would be perfectly happy to pay the market price for housing if they could. They just don’t have the money to.
In other words, the signal received by the market isn’t “preferences,” it’s “willingness to (actually) pay.” It’s startling how rarely I see the distinction made between “willingness to pay” and “ability/capacity to pay”; in the academic literature it seems to be mainly made by economists interested in healthcare. (See e.g. this paper, which presents the distinction as a novel modeling contribution, and has gotten only 2 citations since it was published in 2008, and this one, 3 citations since 2006. If I am missing some large body of research here, let me know.)
Talking about this presents some technical difficulties, since there is no well-defined concept of “what someone would pay if they didn’t have to worry about their budget.” For instance, what one is willing to pay in principle for vital necessities will scale up with budget in an unbounded fashion: I’m sure you could get Bill Gates to pay billions for a loaf of bread if the alternative was starvation, but this does not mean that a loaf of bread is “really” worth billions, and in fact does not mean much at all. Even for non-essential goods, things can be pretty elastic, since many goods that are provably non-essential for human satisfaction can nonetheless feel effectively essential once one has satiated to them. (You could extract a lot of my money by threatening to separate me from my internet connection, for instance.)
But it’s not as if spending patterns are unrelated to preferences. If you give someone any fixed budget, they will buy some bundle of goods with it (for simplicity, you can view savings as just another good people may buy, so that everyone always “spends” their whole budget). To determine someone’s preferences, give them a series of decreasing budgets, and watch which goods they are priced out of first and which they hold onto until the very end. (If two people have different preferences, one person will buy more of some good than the other given a fixed budget of sufficient size, and as we decrease the budget, there will be some level at which one person is still buying some of it and the other isn’t.)
Thus, the market receives a signal about “what the people want” in the following form: it observes the extent to which the population has been priced out of buying it by their budget.
To clarify what this means, consider an example. Suppose that everyone has the same budget. Their spending patterns will vary, because preferences vary, but there will be trends. For instance, there are some goods that almost everyone will be willing to pay you money for if they don’t have it (food, housing), and some goods that many people will happily do without. Demand curves will be generated by people successively pricing themselves out (in) in response to price increases (decreases). Few people will ever be willing to price themselves out of food or housing, so these goods will have nearly flat demand curves (low price elasticity of demand) with high intercepts, while goods that people will happily prices themselves out of (yachts, tchotchkes) will have steep demand curves (high price elasticity of demand) with low intercepts. If some good has a given supply curve, it will be produced in a large quantity if it is of the former type (food, housing), and in a small quantity if it is of the latter type (yachts, tchotchkes) – interestingly, this is true no matter which way the supply curve slopes.
Thus, in this hypothetical world, a lot of resources go into producing food (or more relevantly, distributing food), and not as much into manufacturing yachts. Because people – you, me, even Bill Gates – value food more than yachts, and the market mechanism responds to preferences. The invisible hand works! Chew on that, socialist planners!
But in our world, many resources are allocated to the production of bizarre luxury goods while billions go hungry. Is this because “the people” want the former more than the latter? Of course not. No one wants the former more than the latter. If you gave me the choice between food and my MacBook Air, I’d take the food, and so would you and Tim Cook and everyone else alive.
Why are resources misallocated in this way? Because the starving have been priced out of food, while I have not been priced out of buying a MacBook Air, and the market only sees preferences in the form of the “what have people been priced out of” signal.
When people’s budgets are all the same (or similar), this signal results in production patterns that track people’s relative preferences about different goods. When people’s budgets are wildly dissimilar, this does not occur. The production patterns don’t even reflect rich people’s preferences, since they prefer essentials over luxuries just like everyone else. (It satisfies rich people’s preferences, which is not the same thing as reflecting them. Being rich means having the opportunity to buy things which have incredibly low, although still positive, marginal value to you.)
Does this mean we have to spread the wealth around at gunpoint? Well, I don’t know. We don’t need to do anything. But the market cannot do its Adam Smithy magic if the wealth is very unevenly distributed. Maybe you value not having a state more than you value the market doing its Adam Smithy magic! But it is worth being clear that these values are in conflict.
