TK/B/B: Poe, proto game theorist. Better: bounded rationality!

I’ve missed two of these in a row, as part of my far-too-busy-to-blog period. But I’ve a certain fondness for this bit from The Purloined Letter:

“The measures, then,” he continued, “were good in their kind, and well executed; their defect lay in their being inapplicable to the case and to the man. A certain set of highly ingenious resources are, with the Prefect, a sort of Procrustean bed, to which he forcibly adapts his designs. But he perpetually errs by being too deep or too shallow for the matter in hand; and many a school-boy is a better reasoner than he. I knew one about eight years of age, whose success at guessing in the game of ‘even and odd’ attracted universal admiration. This game is simple, and is played with marbles. One player holds in his hand a number of these toys, and demands of another whether that number is even or odd. If the guess is right, the guesser wins one; if wrong, he loses one. The boy to whom I allude won all the marbles of the school. Of course he had some principle of guessing; and this lay in mere observation and admeasurement of the astuteness of his opponents. For example, an arrant simpleton is his opponent, and, holding up his closed hand, asks, ‘Are they even or odd?’ Our school-boy replies, ‘Odd,’ and loses; but upon the second trial he wins, for he then says to himself: ‘The simpleton had them even upon the first trial, and his amount of cunning is just sufficient to make him have them odd upon the second; I will therefore guess odd’; — he guesses odd and wins. Now, with a simpleton a degree above the first, he would have reasoned thus: ‘This fellow finds that in the first instance I guessed odd, and, in the second, he will propose to himself, upon the first impulse, a simple variation from even to odd, as did the first simpleton; but then a second thought will suggest that this is too simple a variation, and finally he will decide upon putting it even as before. I will therefore guess even’; — he guesses even, and wins. Now this mode of reasoning in the school-boy, whom his fellows termed ‘lucky,’ — what, in its last analysis, is it?”

“It is merely,” I said, “an identification of the reasoner’s intellect with that of his opponent.”

“It is,” said Dupin; “and, upon inquiring of the boy by what means he effected the thorough identification in which his success consisted, I received answer as follows: ‘When I wish to find out how wise, or how stupid, or how good, or how wicked is any one, or what are his thoughts at the moment, I fashion the expression of my face, as accurately as possible, in accordance with the expression of his, and then wait to see what thoughts or sentiments arise in my mind or heart, as if to match or correspond with the expression.’ This response of the school-boy lies at the bottom of all the spurious profundity which has been attributed to Rochefoucault, to La Bougive, to Machiavelli, and to Campanella.”

“And the identification,” I said, “of the reasoner’s intellect with that of his opponent, depends, if I understand you aright, upon the accuracy with which the opponent’s intellect is admeasured.”

“For its practical value it depends upon this,” replied Dupin; “and the Prefect and his cohort fail so frequently, first, by default of this identification, and, secondly, by ill-admeasurement, or rather through non-admeasurement, of the intellect with which they are engaged. They consider only their own ideas of ingenuity; and, in searching for any thing hidden, advert only to the modes in which they would have hidden it. They are right in this much — that their own ingenuity is a faithful representative of that of the mass; but when the cunning of the individual felon is diverse in character from their own, the felon foils them, of course. This always happens when it is above their own, and very usually when it is below. They have no variation of principle in their investigations; at best, when urged by some unusual emergency — by some extraordinary reward — they extend or exaggerate their old modes of practice, without touching their principles. What, for example, in this case of D — – , has been done to vary the principle of action? What is all this boring, and probing, and sounding, and scrutinizing with the microscope, and dividing the surface of the building into registered square inches — what is it all but an exaggeration of the application of the one principle or set of principles of search, which are based upon the one set of notions regarding human ingenuity, to which the Prefect, in the long routine of his duty, has been accustomed? Do you not see he has taken it for granted that all men proceed to conceal a letter, not exactly in a gimlet-hole bored in a chair-leg, but, at least, in some out-of-the-way hole or corner suggested by the same tenor of thought which would urge a man to secrete a letter in a gimlet-hole bored in a chair-leg? And do you not see also, that such recherchés nooks for concealment ar adapted only for ordinary occasions, and would be adopted by ordinary intellects; for, in all cases of concealment, a disposal of the article concealed — a disposal in this recherché manner, — is, in the very first instance, presumable and presumed; and thus its discovery depends, not at all upon the acumen, but altogether upon the mere care, patience, and determination of the seekers; and where the case is of importance — or, what amounts to the same thing in the political eyes, when the reward is of magnitude, — the qualities in question have never been known to fail. You will now understand what I mean in suggesting that, had the purloined letter been hidden anywhere within the limits of the Prefect’s examination — in other words, had the principle of its concealment been comprehended within the principles of the Prefect — its discovery would have been a matter altogether beyond question. This functionary, however, has been thoroughly mystified; and the remote source of his defeat lies in the supposition that the Minister is a fool, because he has acquired renown as a poet. All fools are poets; this the Prefect feels; and he is merely guilty of a non distributio medii in thence inferring that all poets are fools.”

Poe obviously understood not only the basic problem that led to the discovery of Nash equilibrium, but also the problem with assuming that people can do a bunch of inductive steps. See also The Princess Bride, of course.


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