Victorian Non-ergodic Economics
In the appendix of a forgotten probability textbook written in 1870, the Victorian mathematician and clergyman, William Allen Whitworth, explained why the expectation of a gamble does not correspond to the price an individual might prudently pay for it. Instead, he considered indefinite repetitions of the gamble to determine the price at which it becomes advantageous. He used this result to resolve the notorious St Petersburg Paradox, crucially without resort to arbitrary methods such as utility theory. Sadly this work lay hidden and it was another eighty-six years before similar ideas reappeared in the context of economic decisions in the independent work of Kelly (1956). The astonishing clarity of Whitworth’s arguments is surpassed only by those of Peters, who brought full order to this field in 2011 by applying the concepts of ergodicity and irreversible time. A guided tour of this remarkable but obscure piece of Victorian mathematics will be given.