## Tuesday, July 16, 2013

### Commentary on Brady and Arthmar (2010)

Brady and Arthmar (2010) (according to this, to appear in History of Economic Ideas as “Boole, Keynes, and the Interval Approach to Probability”) is a fascinating paper. I have not yet properly digested it, but two posts here on various other blogs discuss the paper or issues related to it:
Dave Marsay, 2012. “Brady+ on Keynes’ Interval Probability,” Djmarsay, Reasoning about Reasoning, Mathematical, July 28.

Isaac Marmolejo, 2012. Michael Brady on Shackle and Post Keynesianism, The Radical Subjectivist, July 28.
Isaac Marmolejo raises a fundamental issue: how in the face of true uncertainty can government diminish it?

The answer, quite simply, is that uncertainty comes in degrees and is capable of being diminished or increased, even though, generally speaking, one does not eliminate it.

First, what is certainty?

True certainty exists only in very limited cases: for example, it can be derived from valid and sound deductive arguments. It might be found in mathematical proofs. Alternatively, if you have proven that a fair and non-fraudulent game of dice is in progress, you can be certain that the probability of rolling a 3 is 1 in 6.

But outside of valid and sound deduction, mathematics, or strict objective numerical probabilities, one must use inductive reasoning, which yields only probability and some degree of uncertainty. That is, in virtually all other areas of argument and knowledge, even in the natural sciences or history, we do not obtain certainty, but probability mixed with uncertainty, at varying degrees, for all inductive arguments yield conclusions which are only, at most, extremely probable.

Consider the following propositions:
Proposition (1) the sun will rise tomorrow (understood scientifically as the earth will continue to rotate on its axis tomorrow).

Proposition (2) Napoleon was defeated at the battle of Waterloo.

Proposition (3) Alexander the Great did not die by poisoning in a conspiracy in 323 BC.

Proposition (4) on January 15, 2014, it will be raining in London at Cleopatra’s needle at 12 noon.
All these propositions are or will be true or false. But do we have absolute certainty that they are (or will be) true or false? No.

Their truth can only be defended with inductive argument, but the truth is probable only.

The probability of (1) seems extremely high, and one faces a very low degree of uncertainty.

Proposition (2) is a historical fact, but even these are ultimately only probable to some degree. As it happens, proposition (2) has a very high degree of historical evidence, and only a low degree of uncertainty, but the degree of uncertainty can be judged greater to some slight degree than that involved in Proposition (1).

Proposition (3) is another historical fact, but its probability of truth is less than Proposition (2), since historians judge, on the basis of good evidence, that there is a small chance Alexander the Great was poisoned, and thus the uncertainty about its truth can be judged higher than Proposition (2).

Finally we move to Proposition (4): this must be judged highly uncertain: the degree of uncertainty is much greater than in all earlier propositions.

It follows that uncertainty does indeed come in degrees, and it can be greater or smaller depending on the proposition and arguments.

It is furthermore the case the uncertainty can be reduced. For example, with regard to economic life, the private sector can, and historically undoubtedly has, reduced the uncertainty faced by agents, e.g.,
(1) holding money is, amongst other things, a method by which agents can reduce (though not eliminate) uncertainty about future liquidity concerns; or money can reduce the uncertainties associated with direct barter trading (N.B. I am not endorsing the universal Mengerian account of money’s origins by this statement);

(2) private sector insurance is a fundamental way in which uncertainty is reduced, though not eliminated.

(3) forward and futures contracts reduce uncertainty, by, for example, locking the price of good to be delivered at a future date, when decentralised production and exchange of many goods in flexprice markets means you cannot predict the future price.
So the private sector is perfectly capable of reducing uncertainty, and so is the government sector, e.g.,:
(1) government provision of law and order reduces uncertainty associated with the threat of crime as faced by businesses and virtually all business activities (e.g., theft during transportation of goods to markets);

(2) government justice systems reduce uncertainty from potential conflicts and failure to fulfil private contracts;

(3) a central bank acting as a lender of last resort reduces uncertainty associated with fractional reserve banking systems;

(4) government social security reduces uncertainty associated with what happens when people are unemployed and have lost their major source of income, and so on.
In these cases, both the private sector and government sector can reduce uncertainty, but not eliminate it, and uncertainty comes in degrees.

The problem with private, decentralised decision-making in capitalism is that it still leaves a significant degree of uncertainty in decisions about investment (i.e., aggregate investment can fluctuate wildly and expectations can collapse), and governments can overcome that through fiscal policy and other interventions.

BIBLIOGRAPHY
Brady, Michael Emmett and Rogério Arthmar, 2010. “Keynes’ Lower-Upper Bound Interval Approach to Probability,” SSRN Working Paper Series, February 2
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1546726