# Prices and information part 2

My previous post has received some feedback from Paul Cockshott on Twitter (nitter link). I have responded to this over email, but I thought I should post it here too. I've also had some additional thoughts in the last three days that I have added further down.

Hardin is being over generous to the Misereans

I think 26 bits is overestimating

It is leaving out uncertainty. Go round 5 shops selling cauliflowers they will not all sell at the same price to the last cent or penny. One may be 90p, one may be £1.00, one may be 95p etc. One really needs to have a two level analysis

1. The % uncertainty for a given commodity : cauliflowers, loaves of bread, etc - say this is 10%

2. The dynamic range contrasting cauliflowers with really expensive things like nuclear submarines. So what you need is a floating point representation with perhaps 7 bits of mantissa and an exponent. I am pretty sure you could handle it with 16 bit IEEE floating point

It is true that commodities have different prices locally. But with stocks and the futures market you end up with a single global price, or very nearly so. This thanks to mechanisms like arbitrage.

The point isn't really the exact number of bits, but rather that it is a small number of bits and that it is a projection of many things onto a scalar. The Austrian argument is that this is good because it makes apples and oranges commensurable. My point is the opposite. In planning we have a much richer collection of data to work with. We can think in terms of use-values rather than just exchange-values. We don't compare apples and oranges, but rather make sure there's enough of both for everyone. If investing in machinery is not enough to meet demand then we must either use remuneration, a lottery or rationing to distribute the limited supply.

Regarding planning having access to richer data, remember that prices supposedly contain information about supply and demand. But how much information actually makes up supply and demand themselves? For simplicity I will focus only on demand.

Let us assume we are dealing with goods that are consumed in integer amounts, for example cars. Assume everyone wants either zero or one cars of a certain type. Call the total number of cars k and the number of people n. Then the amount of information is at most $E={\mathrm{log}}_{2}\phantom{\rule{0.167em}{0ex}}\left(\genfrac{}{}{0}{}{n}{k}\right)$. If we have some way to estimate which people are actually interested in this specific car then n shrinks and so does E. It doesn't take much for E to exceed the very generous 26.6 bits. A single car in a population of 100,000,000 or two cars among 14,000 people. If half the population wants a car then E is just below n bits, or eight gigabits for the current size of the world population. Clearly this is much larger than 26.6 bits. Therefore prices must always be a very aggregated and approximate piece of information. Yet somehow to the Austrians, the market is the best way of fulfilling demand. But the market can't actually know the demand because the price mechanism doesn't contain enough information to properly signal it. A similar argument can be made for supply.

I have by this point talked to Austrians online enough times to know that, as praxeologists, they don't actually care about mathematical points like this one. When confronted with evidence that contradicts the ECP they will just shift the discussion instead. "You can't compute this" becomes "you can't gather the necessary data" becomes "actually it's about enterpreneurship". Nevermind that enterpreneurship is perfectly compatible with planning or that in a socialist economy we can implement more of people's ideas, ideas that are currently left undeveloped because they are not profitable. Doing stuff outside the profit motive, especially deciding democratically to tackle climate change, is unthinkable to these people, since it amounts to putting oneself above God-the-market.