The uncertainty has remained, and it thus had to be reintroduced into the magnificent schemata of rational decision-making—this time explicitly. Champernowne, for example, writes:

Much economic theory is concerned with decisions. These decisions often involve judgments between two alternatives, with regard either to preference or to probability. In many cases, it is convenient to suppose that a set of alternatives can be arranged in some order of preference or of probability.[1]

Furthermore, and somewhat more technically:

An ordering of a set of N elements A, B, …, N will mean a set of N(N-1)/2 relations, one between each of the distinct pairs of elements (A,B), etc. The relation between any pair (A,B) may be any of the following:

A > B, A = B, A < B, A || B, B > A, B = A, B < A, B || A [2]

Champernowne introduces the relation of indecision between any pair (A,B), symbolized by ||, and he thereby departs from the orthodox procedure. This symbol is needed to denote “a state of indecision or uncertainty with regard to the ordering of a pair of elements in respect of preference or of probability.”[3] Moreover, “the important distinction between the relation A = B and the relation A || B is that in most contexts A = B reflects a decision to place A and B on a footing of exact equality in an ordering, whereas A || B reflects no such decision, but rather indicates an inability to compare A and B at all.”[4] Put differently, the former symbol denotes that A and B are regarded as exchangeable, while the latter denotes an inability to state a preference or to regard A and B as exchangeable.

The interpretation of the symbol || is crucial here, however. According to Champernowne,

[i]n general, it will denote an inconclusive relationship or perhaps the absence of any definite relationship. It will always imply the non-assertion of any of the relations >, <, =, ≥ or ≤ between the two elements concerned.[5]

The relation of indecision is clearly residual, since it follows from the non-assertion of any other relation, that is, all the relations that were at the foundation of the orthodox procedure. In short, the relation of indecision is negative, a result of the failure of the orthodox decision-making procedure, a formalized statement of abdication, or a polite gesture in view of ignorance. Still, where positive thought may have found a loop-hole, negative thought might find a foothold. Terra incognita as terra firma… Non-comparability (or, more philosophically, non-identity) offers a refuge from the algorithmic dreams of the administered world.

Footnotes

1. Champernowne, D.G., Uncertainty and Estimation in Economics, Vol. I, Edinburgh: Oliver and Boyd; and San Francisco: Holden Day, 1969, p. 9.

2. Loc. cit.

3. Op. cit., p. 10.

4. Op. cit., pp. 10-11.

5. Op. cit., p. 20 (emphasis added, R.B.). Nota bene, the symbol || indicates non-comparability, and not non-equality, symbolized by ≠, for example. In other words, the relation of indecision cannot possibly be redeemed and thus defused.