The Confidence Man, His Two-Box Problem

One line from my Kenneth Burke post has set me all a philosophizin': "if they cannot have religion, they should have lotteries." The basis for a reverse Pascal's Wager. Argue for the utility of religious belief on the instrumental ground that certain brands of holy-rolling may encourage a healthy taste for high-rolling long-shot gambles, e.g. lotto. (What are the odds that any one possible one true jealous God is the one true one true jealous God, after all?) Lotto is good because it boosts state revenues in lots of jurisdictions.

I fear this approach is likely to fall foul of potentially mixed strategies of religious belief, however. Mysticism, health-mindedness, the sick soul. Saintliness, sacrifice and confession. See William James on The Varieties of Religious Expected Returns. As Brian Weatherson suggested a few days ago, the same may be true for the original Pascal's wager. (Falls victim to mixed strategies, that is.) But perhaps Pascal suspected as much. James quotes a prayer from the great theological gambling man: "I know not which is most profitable to me, health or sickness, wealth or poverty, nor anything else in the world. That discernment is beyond the power of men or angels, and is hidden among the secrets of your Providence, which I adore, but do not seek to fathom."  The trouble is understanding how you can really go through life regarding every choice as ... well, not quite a canonic two-box problem, but a situation in which the values of all things are enclosed in an opaque evelope of Providence and potentially vary widely.

At this point I am compelled to quote from Melville's Confidence Man, His Two-Box Problem:

Here we meet the Cosmopolitan (who may be a man of confidence or a confidence-man), engaged in epistemological and decision-theoretic theology with a devout old man in the bowels of the good ship Fidéle on its journey down the mighty Mississip. Someone is sleeping in the next berth:

After reading for some minutes, until his expression merged from attentiveness into seriousness, and from that into a kind of pain, the cosmopolitan slowly laid down the book, and turning to the old man, who thus far had been watching him with benign curiosity, said: "Can you, my aged friend, resolve me a doubt - a disturbing doubt?"

"There are doubts, sir," replied the old man, with a changed countenance, "there are doubts, sir, which, if man have them, it is not man that can solve them."

"True; but look, now, what my doubt is. I am one who thinks well of man. I love man. I have confidence in man. But what was told me not a half-hour since? I was told that I would find it written - 'Believe not his many words - an enemy speaketh sweetly with his lips' - and also I was told that I would find a good deal more to the same effect, and all in this book. I could not think it; and, coming here to look for myself, what do I read? Not only just what was quoted, but also, as was engaged, more to the same purpose, such as this: 'With much communication he will tempt thee; he will smile upon thee, and speak thee fair, and say What wantest thou? If thou be for his profit he will use thee; he will make thee bear, and will not be sorry for it. Observe and take good heed. When thou hearest these things, awake in thy sleep."'

"Who's that describing the confidence-man?" here came from the berth again.

"Awake in his sleep, sure enough, ain't he?" said the cosmopolitan, again looking off in surprise. "Same voice as before, ain't it? Strange sort of dreamy man, that. Which is his berth, pray?"

"Never mind him, sir," said the old man anxiously, "but tell me truly, did you, indeed, read from the book just now?"

"I did," with changed air, "and gall and wormwood it is to me, a truster in man; to me, a philanthropist."

"Why," moved, "you don't mean to say, that what you repeated is really down there? Man and boy, I have read the good book this seventy years, and don't remember seeing anything like that. Let me see it," rising earnestly, and going round to him.

"There it is; and there - and there" - turning over the leaves, and pointing to the sentences one by one; "there - all down in the 'Wisdom of Jesus, the Son of Sirach.'"

"Ah!" cried the old man, brightening up, "now I know. Look," turning the leaves forward and back, till all the Old Testament lay flat on one side, and all the New Testament flat on the other, while in his fingers he supported vertically the portion between, "look, sir, all this to the right is certain truth, and all this to the left is certain truth, but all I hold in my hand here is apocrypha."

"Apocrypha?"

"Yes; and there's the word in black and white," pointing to it. "And what says the word? It says as much as 'not warranted;' for what do college men say of anything of that sort? They say it is apocryphal. The word itself, I've heard from the pulpit, implies something of uncertain credit. So if your disturbance be raised from aught in this apocrypha," again taking up the pages, "in that case, think no more of it, for it's apocrypha."

"What's that about the Apocalypse?" here, a third time, came from the berth.

"He's seeing visions now, ain't he?" said the cosmopolitan, once more looking in the direction of the interruption. "But, sir," resuming, "I cannot tell you how thankful I am for your reminding me about the apocrypha here. For the moment, its being such escaped me. Fact is, when all is bound up together, it's sometimes confusing. The uncanonical part should be bound distinct. And, now that I think of it, how well did those learned doctors who rejected for us this whole book of Sirach. I never read anything so calculated to destroy man's confidence in man. This son of Sirach even says - I saw it but just now: 'Take heed of thy friends;' not, observe, thy seeming friends, thy hypocritical friends, thy false friends, but thy friends, thy real friends - that is to say, not the truest friend in the world is to be implicitly trusted. Can Rochefoucault equal that? I should not wonder if his view of human nature, like Machiavelli's, was taken from this Son of Sirach. And to call it wisdom - the Wisdom of the Son of Sirach! Wisdom, indeed! What an ugly thing wisdom must be! Give me the folly that dimples the cheek, say I, rather than the wisdom that curdles the blood. But no, no; it ain't wisdom; it's apocrypha, as you say, sir. For how can that be trustworthy that teaches distrust?"

In short, you should take the envelope that has more money, certainly not the one that has none. This, the wise of all ages concur, is the soundest strategy. Speaking of which, perhaps consulting a reliable Predictor and/or Metapredictor would be in order (with apologies to Nick Bostrom for liberties taken.)

Call this problem: Newcomb all! Let God sort 'em out! - or - Rochefoucault's Pendulum:

There are two books in front of you and you are asked to choose between believing only book B or believing both book A and book B. Book A contains some cynical but solid, mundane wisdom in the style of Rochefoucault. Book B will contain either nothing (apocrypha) or (salvation-imparting) religious truth. What B will contain is (or will be) determined by the Cosmopolitan, who has an excellent track record of predicting your choices. There are two possibilities. Either Cosmopolitan has already made his move by predicting your choice and putting religious truth in B iff he predicted that you will take only B (somewhat like in the standard Newcomb problem); or else Cosmopolitan has not yet made his move but will wait and observe what book you choose and then put religious truth in B iff you take only B. In cases like this, Cosmopolitan makes his move before the subject roughly half of the time. However, there is a fellow sleeping in the next berth, who has an excellent track record of predicting Cosmopolitan's choices as well as your own. You don't know all this; obviously you can't; but for the sake of argument let's pretend you do. The fellow in the berth slurs out the following sleepy truth functional: Either you believe A and B, and Cosmopolitan will make his move after you make your choice; or else you choose only B, and Cosmopolitan has already made his choice. Now, what do you choose?

I can't quite turn Melville into a parable of causal vs. evidential decision theory. What you just saw was my best shot. Certainly there is a Liar's Paradox quality to the exchange between the Cosmopolitan and the old man. The book says to treat everything as apocryphral. Ergo, the book must be apocryphal. But then it can't be right to treat it as apocryphal. But it's a little more twisty and indirect than that, I think you can see.

Maybe I'll go read the Phil Review paper Weatherson cites about mixed strategies. Honestly, I don't know much about this stuff. I read the Andy Egan paper Brian links (PDF). I haven't digested it, but for theological as well as logical purposes, the following point of distinction between causal and evidential decision theory is the crux:

The crucial difference is that now [with causal decision theory] the assignments of values to actions are sensitive only to the agent’s unconditional credences in dependency hypotheses [i.e. those about how things that the agent cares about depend causally on what the agent does], not her credences  conditional on her performing A. The effect of this is to hold fixed the agent’s beliefs about the causal structure of the world, and force us to use the same beliefs about the causal order of things in determining the choiceworthiness of each candidate action.   

Notice how in my rewrite of Bostrow I am having the agent pick belief-systems, in effect? This is psychologically silly, since you can't collect beliefs in your brain as though they were bucks in a box. But my adaptation displays - with comic exaggeration - the root of the trouble Egan is grappling with. Holding fixed, or not, beliefs about the causal structure of the world. In Egan's paper, there is a lot of concern about what sorts of exotic, dispositionally efficacious lesions you might or might not have. You have thoughts of the form 'it may not be an accident that I'm in this mess'. (Why am I thinking about shooting/pushing the button? Why is the Cosmopolitan picking on me?) In a religious sense, there are analogous concerns about the state of your soul. Rochefoucaultian cynicism and philanthropic confidence imply different causal theories. Not incidentally, A & B may be inconsistent. Mixed strategies cross with cognitive dissonance here. You can't coherently treat causal theories as constants and as variables to be solved for in some causal fashion. (Because then how could you solve for the variables without having first solved for the variables?) Is that right? I'm quite confused.

You can read an e-text of the Confidence Man here, although its not laid out very readably. (I recommend a nice paperback and many hours of satisfaction.) Our passage is from the final chapter, "The Cosmopolitan Increases in Seriousness". Something further may follow of this two-box problem.

And I see that Matt Weiner is getting into the game, too.

Comments

[nnyhav]

Don Mackenzie's upcoming LRB article may be of interest. More background here.