An information theoretic view of the UBI

2017 February 24
by Daniel Lakeland

I know, I know, I’m all about the UBI these days. Well, I’m not going to apologize. The world really needs better solutions to poverty and even just to working and middle class. For example, 2011 data from the Census says that in the US the median black family has a net worth of $6300, which is just about enough to buy a used Toyota Corolla. This means a single $200 a week summer camp for a black child costs about 3% of the median black families whole net worth!

So, here is my intuition about the information theoretic properties of UBI. In a high dimensional space, a frequency distribution over anything always has a typical set that is far from the highest density region (translation into English: most people have many ways in which they are not like the average). Why is this? Even if your “histogram” has a peak density at some location, call it 0, the volume of a spherical shell at radius r away from that point grows like $$r^d$$ where $$d$$ is the dimension, whereas because the density is at a peak, it falls slowly at first, so as you move away from the “most probable” (highest density) location you find that the volume of the shell grows much faster than the density of the function declines. So, it’s far more probable to be at some radius $$r^*$$ away from the “most probable” location, and the volume of this space is itself very large (there are LOTS of attributes so many many ways to be different from “average”). Eventually when you get far enough away, the requirement that the probability distribution integrate to 1 requires the density to fall extremely fast, and then the probability to be at very large radius also falls (very few people who are different from the average in EVERY way).

Now, suppose the space we are considering is the space where we talk about the quantity of each good purchasable in the market. Suppose we even just consider markets like in Rural Kenya. There must still be something like tens of thousands of goods you could purchase, fishing nets, tin roofing panels, plywood, goats, chickens, eggs, fish, rope-making labor, cart wheel repair labor… so if you were going to choose something to give to someone, you’d need to choose a vector of 10000 or more numbers to say how much of each good you’d give them. Of course, a charity typically isn’t going to give people a massive basket of goods (one bean, one square inch of plywood, two fish scales)… they’ll give 1 or 3 or 10 goods, a water pump, a cow, some fishing tackle, fencing to keep predators away from their livestock, whatever…. a few things.

Now, the mathematics of high dimensional spaces says that EVEN IF you choose a thing which is near the maximal frequency of desirability for an individual thing (ie. almost everyone wants a cook stove)…. it will be pretty far from the region where you need to be. So for example, giving people a cow, or an apartment in a section 8 housing authority (why limit ourselves to Rural Kenya?) might be a pretty good thing to have, but it’s nowhere near as good as the best set of things for a given individual that costs the same.

So, from an information theory perspective, we expect giving people Money and letting them choose a basket of goods that meets their individual needs, would be potentially VASTLY improved over even giving people some average basket of goods or some most-desirable among all people individual good etc.

So, from the perspective of why we should favor UBI over all other forms of welfare, it’s ultimately that *real wealth* will be vastly increased, at no dollar cost.

The same argument applies, whether it’s in Rural Kenya or Brooklyn. The best most efficient way to eliminate the bad effects of poverty, is to give some basic quantity of money.

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