Long tails: a semi-technical explanation

Long tails in distributions are troublesome for 2 reasons:

  1. They are hard to test for empirically because they represent rare events. How they look like in any given model is more model-driven than data-driven.
  2. Models which are modular, and construct the distribution of interest from many independent component distributions, tend to underestimate long tails in the distribution of interest. This is a problem of degree, not a black and white issue - theoretical proofs use absolutely independent component distributions, and using those proofs for real work requires an assessment of whether components are independent enough in reality. That assessment is non-trivial and all too often skipped.

Winning an argument

  1. Forcing a concession
  2. Convincing the other person
  3. Maximally updating your own beliefs
2 comments
Qin

Which one is "maximally confusing the other person"? 1 or 2?

Chiao

Heheheh

Consumption is exogenous to Capitalism

"I don't know which is worse... that everyone has his price, or that the price is always so low."
-- Hobbes

The capitalist framework is quite general, because as much as capitalist theories dictate when one should invest, they are completely agnostic as to what/when one should consume.

The idea of consumption is exogenous to capitalism and can be defined to be anything. For investment to take place, all that is required is a sufficiently low discount rate. For example, let's say you want to save starving children in Africa. If you value feeding 10000 starving children in a year more than you value feeding 1000 starving children now, you have a 900% discount rate and should invest in anything with greater than 900% annual return. This particular hurdle rate would almost be impossible to overcome, but most altruistic goals have lower discount rates than that.

Extra credit: does morality have a discount rate?