Sunday, June 16, 2013

Antony Davies' Allocation Experiment Falls Flat

Right now I'm at the Liberty and Society conference, sponsored by the Institute for Humane Studies (IHS) at Bryn Mawr College this week. For students of a classical liberal persuasion, it's a great chance to network and hear ideas from relevant philosophers and economists.

Today I heard a lecture on "Knowledge, Prices, and Order" by Dr. Antony Davies. While Davies is an excellent speaker and polemicist, the "experiment" which he started his lecture with is overly simplified, and ultimately counterproductive to the conclusion he wants to reach.

The Experiment: each student is given a chart which shows payoff levels for given amounts of red and blue poker chips, which represent consumption goods (as an aside, kudos to Dr. Davies for his persistence in buying out every poker chip in the greater Pittsburgh area in order to make this experiment possible). The goal is to compare different social outcomes under varying systems for allocation.

Scenario One: Dictatorship. The students elect a "benevolent dictator" who will distribute the chips as best he can, although he does not know either how many chips there are or how many students they are to be distributed to. While the distribution rule started out as even amounts (5 red, 5 blue chips) for each person, by the end the red chips were running out. I ended up with just 5 blue chips and a utility level of zero.

Scenario Two: "Chaos" (or first-come-first-served). Students are invited to rush up to the bucket of chips and grab as many as they can. One enterprising fellow at the front got a massive double-handful of chips, while the slower and less motivated (like me) got zero.

Scenario Three: "Private Property." Each student is given a bag of either a dozen all red or all blue chips, then is invited to trade with neighbors to improve their utility level.

At the end, we all report our number of chips in each scenario, then a fancy spreadsheet spits out the total social utility for each. Unsurprisingly, the "private property" outcome is closest to optimal, "chaos" is the worst, and dictatorship falls somewhere in between. This is intended to illustrate how knowledge problems make central distribution by even a perfectly altruistic dictator inefficient.

The Problem: there are several, but I'll focus on the one I find most interesting. This experiment flies in the face of core micro-economic reasoning, and arrives at its conclusion by semantic tricks and ultimately pure assumption.

In fact, this experiment does not compare different politico-economic systems at all, because those are concerned with how goods are exchanged and distributed. Instead, it compares different ways of allocating initial endowments. Assuming that zero trade can occur under dictatorship or chaos is patently false, from observation of the real world. Why would we suppose that people can only trade when property rights are perfectly protected? With imperfect private property divisions there are higher transaction costs to trade, but that does not make trade completely impossible -- if this were so, then three-quarters of the world (or perhaps all of it) would still be in the Stone Age.

Even more interesting, if trade is allowed under each scenario then micro-economics indicates total social utility would be exactly the same in every allocation! Why? Consider the "chaos" case with one guy who controls half the chips. Making some fairly common assumptions such as convex preferences (i.e. I prefer to have a combination of goods rather than all one or the other) and diminishing marginal utility of consumption, his 100th chip has very little value to him, while for me with zero chips, the value is nearly-infinite. We would arrange some trade. These trades would continue occurring until everyone has reached the point where the value of another blue chip is exactly the same as another red chip, and vice-versa. Similarly, under "dictatorship", I'd be willing to trade several of my five blue chips to get just one red.

This is a core result of general equilibrium theory: if all trades are realized, then initial endowments can be changed in whatever way without affecting total social utility. It is this exact finding that makes center-leftist economists so enthusiastic about redistribution from the rich to the poor. While I am sure Dr. Davies disagrees with this application, it is part of the canon of Neo-Classical economics and its implication should not be ignored.

The "private property" allocation where everyone starts with the same number of chips is actually a welfare economist's dream of perfectly equal endowments, which does not exist in any free market economy I've ever heard of; people have varying endowments of talent, entrepreneurial ability, cognitive capacity, and so on. Free markets work because different individual endowments exist (otherwise there would be no need for trade, another result from general equilibrium theory), and it's both misleading and contrary to Dr. Davies' point to suppose that everyone starts with equal chips. In fact, starting with the same amount of chips (but conveniently, in opposite colors) is the exact opposite of his support for low government intervention and deference to private decision-making!

To Recapitulate: Antony Davies experiment presupposes its own conclusion by only allowing trade in the "private property" scenario, when trade in any of the other scenarios would have - at least in theory - resulted in exactly the same total level of utility.

Ironically, a defender of redistribution could actually make much better use of this experiment than a classical liberal. They would simply reframe the "chaos" scenario as the free market allocation: "first mover advantage! Whoever gets to the resources first grabs them all! Look how unfair that is! Government should give everyone some base level to work with, and then markets make it efficient after that!" This argument can be easily refuted but not within the realm of the assumptions given, once the unrealistic "trade can't occur without private property" restriction is lifted.

To give some credit, this experiment is a useful way to show the benefits of trade and troubles of central distribution to an audience unfamiliar with economics. However, when drawn to the logical conclusion, it collapses.