Restricted Choice

 Heuristic  21 Responses »
Feb 252004
 

Eddie Thomas, a better philosopher than he is a statistician, poses the following problem. He is interviewing five candidates for two jobs. Each candidate’s chance of receiving a job offer, a priori, is 40%. After interviewing four candidates Eddie wants to offer a job to the best of the four to protect against his taking another job elsewhere. He is puzzled because it now looks like the final candidate has a 25% chance of a job offer, being one in four remaining, while his chances should be unaffected, remaining at 40%.

This is a type of restricted choice problem. The classic illustration of true restricted choice is the old game show Let’s Make a Deal. Monty Hall shows the player three doors, behind one of which is the grand prize, a Hawaiian vacation or a brand new Cadillac Eldorado. The player chooses one door. Monty then reveals another, behind which the prize is not hidden, and asks the player if he wants to switch. The player should always switch. His chance of choosing the grand prize in the first place was 1 in 3. If he switches, it is 2 in 3, because Monty’s choice of which door to open has been restricted by the choice the player already made. Many people don’t believe this even after it has been explained to them, but it’s true, and can be verified easily by experiment if you doubt it.

Here, on the other hand, because of restricted choice, the probabilities only appear to change. To receive a job offer you must be one of the best two of five candidates. Consider it from the point of view of the first four candidates. Each one has a 25% chance of receiving an offer after four interviews, and a 15% chance (.75 X .20) of receiving an offer after five interviews, for a grand total of 40%, as you would expect. So one way to look at it is that the remaining candidate must also have a probability of receiving an offer of 40% for the probabilities to add up to 200% (two job offers).

Since this will satisfy no one, least of all Eddie, I’ll try another approach. To receive an offer he has to be better than the three remaining candidates. However, his three remaining competitors are not randomly chosen; they have already failed to finish first among the first four. Choice has been restricted. Each one of the three, not having received the first offer, has a far less than 40% chance remaining of securing an offer. In fact, they now have half that chance; for they can only finish second, at best, among the five, while the fifth candidate can still finish either second or first. Therefore their remaining chance is half of their original 40%, since one of the two offers has been closed to them, or 20%, rather than 25%. The fifth candidate still has a 40% chance.

God of the Machine: all probability, all the time!

Time Won’t Tell

 Baseball, Heuristic  16 Responses »
Feb 212004
 

Five years ago, after the 1999 season, a fellow fantasy league baseball owner and I fell into an argument about Roger Clemens. Clemens was 37 years old. In 1998 he had a brilliant season with Toronto, winning the pitching triple crown — ERA, wins, and strikeouts — and his fifth Cy Young Award. In 1999, his first year with the Yankees, he slipped considerably, finishing 14-10 with an ERA higher than league average for the only time since his rookie season. His walks and hits were up, his strikeouts were down, and my friend was sure he was washed. He argued that Clemens had thrown a tremendous number of innings, that old pitchers rarely rebound from a bad season, and that loss of control, in particular, is a sign of decline. I argued that Clemens is a classic power pitcher, a type that tends to hold up very well, that his strikeout ratio was still very high, that his walks weren’t up all that much, and that his diminished effectiveness was largely traceable to giving up more hits, which is mostly luck.

Of course Clemens rebounded vigorously in 2000 and won yet another Cy Young in 2001. He turned out not be finished by a long shot, and still isn’t. Does this mean I won the argument? It does not. Had Clemens hurt his arm in 2000 and retired, would my friend have won the argument? He would not.

Chamberlain wasn’t wrong about “peace in our time” in 1938 because the history books tell us Hitler overran Europe anyway. He was wrong because his judgment of Hitler’s character, based on the available information in 1938, was foolish; because, to put it in probabilistic terms, he assigned a high probability to an event — Hitler settling for Czechloslovakia — that was in reality close to an engineering zero. He would still have been wrong if Hitler had decided to postpone the war for several years or not to fight it at all.

“Time will tell who’s right” is a staple of the barroom pedant. Of course it will do no such thing: time is deaf, blind, and especially, mute. Yet it is given voice on blogs all the time; here’s Richard Bennett in Radley Balko’s comments section: “Regarding the Iraq War, your position was what it was and history will be the judge.” It’s not an especially egregious instance, just one I happened to notice.

Now you can take this too far. If your best-laid predictions consistently fail to materialize, perhaps your analyses are not so shrewd as you think they are. You might just be missing something. Or not. But this should be an opportunity for reflection, not for keeping score.

We fumble in the twilight, arguing about an uncertain future with incomplete knowledge. Arguments over the future are simply differences over what Bayesian probability to assign the event. There is a respectable opposing school, frequentism, which holds that Bayesian probability does not exist, and that it makes no sense to speak of probabilities of unique events; but it has lost ground steadily for the last fifty years, and if it is right then most of us spend a great deal of time talking about nothing at all. Like Lord Keynes, one of the earliest of the Bayesian theorists, we are all Bayesians now.

This, for argument, is good news and bad news. The good news is that history won’t prove your opponent out. The bad news is that it won’t prove you out either. You thrash your differences out now or not at all. Then how do you know who won the argument? You don’t. Argument scores like gymnastics or diving, not football. It will never, for this reason, be a very popular American indoor sport.

Playing Possum

 Culture  16 Responses »
Feb 182004
 

Didja miss me? You know you did. After a week and change of goofing off, I have a good bit of lost time to make up pissing on other people’s parades. Let’s start with Terry Teachout’s. Terry asks his co-blogger, Our Girl in Chicago, and, one presumes, the rest of us, to ponder the following questions:

(1) What book have you owned longestthe actual copy, I mean?
(2) If you could wish a famous painting out of existence, what would it be?
(3) If you had to live in a film, what would it be?
(4) If you had to live in a song, what would it be?
(5) Whats the saddest work of art you know? And does experiencing it make you similarly sad?

Question 1 is very good. Questions 2 through 5 have likely raised Lord Snow from the dead and set him sighing about the Two Cultures all over again, and I’m giving out demerits to, or at least withholding little gold stars from, any blogger who ups and answers these questions without a considerable preamble. (Oooh. Demerits. My little list already includes at least one guy who knows better.) Questions like these are why many serious people believe, though they are usually too polite to say so, that art talk should be confined to cocktail parties and teatime at the ladies’ auxiliary.

Question 1 is good principally because it is unambiguous. If you gather a large sample of answers it will be with some assurance that they are mostly to the same question. This is the rock-bottom requirement for intelligent discussion of any topic, and a shocking amount of ink has been spilled in literary criticism, even at a very high level, because it is so seldom met.

I’ll even answer Question 1 myself before proceeding because that’s the kind of sport I am. It’s Norton Juster’s The Phantom Tollbooth, illustrated by Jules Feiffer, which I’ve owned since the age of seven or so and which was my favorite until Dostoevsky came along at 13 to upend my universe. In The Phantom Tollbooth Milo, a bored and as drawn by Feiffer impossibly dour child, receives a gift of a magic tollbooth that transports him to an extremely Platonic kingdom of blooming buzzing words and numbers, where he receives a great many valuable lessons, including one bearing on today’s topic. He encounters four doors, each with a nameplate: “The Dwarf,” “The Giant,” “The Fat Man,” “The Thin Man.” He knocks on each door and the same ordinary-looking man answers each time, with the same explanation: “I’m the world’s tallest dwarf — shortest giant — thinnest fat man — fattest thin man.”

Question 2 is the world’s fattest thin question. Interpreted the obvious way — which famous painting do you like least? — its results will not be interesting. I think this is the most hideous famous painting in the history of the world, and I’ve got my reasons. You think something else and you have yours. We part amicably and unenlightened, having exchanged opinions. Conversation is not an exchange of opinion, it is a sifting of opinion. Unfortunately Jacques Barzun said that, not me.

One possible reinterpretation is: which painting do you think has had the most baleful influence? We still have matters to clear up. If I excise, say, Picasso’s Les Desmoiselles d’Avignon from art history, do I kill only the picture or do I kill its progeny too, all the pictures that could never have been painted without it? Is it possible at once to admire a painting and deplore its influence? It’s certainly possible in literature; consider Ulysses, Madame Bovary, and Paradise Lost, all great masterpieces, all catastrophic influences.

You may wonder why Terry didn’t put the question as I did when he is obviously perfectly capable of doing so. I suspect that he found it too forbidding. To answer you would need to know quite a deal of art history, and then think some on top of that. I wouldn’t consider myself, for instance, with my undergraduate background in art history, up to scratch. But Question 2, in its actual, cuddly phrasing, invites all comers. All you have to do is dislike something to play, and we can all manage that.

Several questions precede Question 3, including, but not limited to: What does it mean to “live” in a film? Do we have to live the backstory too? As which character, since, as the social theorist Mel Brooks has noted, it’s good to be the king? Do we have Wardrobe privileges? Most important, is lunch catered? I’m going to have beg off Question 4, since I’m pretty sure songs never cater lunch.

Terry’s conscience finally pricks him into an explanation at Question 5 — strangely, as it’s the clearest of any of the last four. Asking where “sadness” resides if not in the mind of the viewer is a useful question. Asking which work of art provokes this emotion in you is a clear and unthreatening question. Conjugating these questions can lead only to confusion.

NORML, the pot-legalization people, used to sell a T-shirt that read, “Free America. Drug-free America. Choose one.” Serious cultureblogging. Inclusive cultureblogging. Choose one. Not quite as catchy, but then I’m not in the T-shirt business.

(Update: Y’know, you try to slap a little sense into these kids these days and this is the thanks you get. I would not, however, dream of cracking wise about Terry’s knowledge of art history, which vastly exceeds my own. I meant to exclude myself from offering an intelligent answer to the question of which single painting exerted the worst influence. In fact Terry’s answer would be worth hearing in at least four arts, while I would be uninteresting outside of literature. Not everybody gets to play in every reindeer game, which was my point.)

Perfect Justice; or, Why Political Arguments Never Convince Anybody

 Philosophy, Politics  42 Responses »
Feb 082004
 

Put a libertarian and non-libertarian in a room and you get an argument, always the same argument. Yesterday at my place it was over whether people who got cancer from industrial emissions would be able to collect fifty years hence. A few weeks back at David Sucher’s it was over whether houses would collapse in earthquakes without building codes. The other day at Radley Balko’s it was over whether without animal cruelty laws the evil neighbors would buy up puppies and kittens and torture them without fear of reprisal. Only the details vary.

Thomas Sowell wrote a book on this subject, A Conflict of Visions, in which he claimed that the fundamental divide is between those who believe in the perfectibility of human nature and those who do not. In fact it is less momentous: it’s between those who believe in the perfectibility of the state and those who do not. Some people think that the state can mete out perfect justice, some don’t. Libertarianism fails, in the eyes of the first group, if any evil goes unpunished. Now no one, not the most ardent statist, believes that the state can mete out justice in every case. But a surprisingly large number of people, a substantial majority, believes that, for every case, a theoretical mechanism for redress or punishment ought to exist. They readily concede that in practice eggs must be broken to make omelets. Mistakes are made. But if the mechanism exists, conscience is assuaged, and that is enough.

Good law sometimes produces unjust outcomes; a famous maxim expresses this, conversely, as “hard cases make bad law.” In Waube v. Warrington, a classic torts case from 1935, a woman watched a negligent driver strike and kill her daughter. The woman died a month later, allegedly of shock, and her husband sued. Maybe it was true, maybe not, but the Wisconsin Supreme Court never reached the question, dismissing the suit on the grounds that damages for mental distress require physical contact, and there was none in this case. If the woman really did die of shock, then the outcome was unjust. Yet the law was sound, based on a bright-line, predictable, common-sense standard. Like any such standard, it does not fit every case. Too bad. Law is collective, justice individual. You can swallow this or you can’t.

Buildings collapse sometimes in earthquakes and kill a lot of people. This happens more often in poor countries than rich ones because taking precautions against a rare catastrophe is a luxury, and rich people can afford more luxuries than poor people. It will continue to happen more often in poor countries, no matter how stringent their building codes, because builders will circumvent regulations that they cannot afford. If the codes are rigidly enforced then fewer houses will be built, and people who formerly lived in shoddy houses will do without instead. You can swallow this or you can’t.

The trouble with animal cruelty laws is that animals are property, and such laws infringe property rights. You can tack on riders like “needless” all you like, but infringement is infringement, and when the only question is how much, the laws become a way to harass people in the animal business. (So far the animal rightists have mostly trained their fire on unpopular targets like foie-gras producers and circus trainers; scientists, assuredly, are next.) Of course without the laws Cruella de Ville can sew herself a nice coat out of Dalmatian puppy hides and there isn’t a damn thing the cops can do about it. You can swallow this or you can’t.

If you’re on Team Perfect and I’m on Team Good Enough, we can argue to eternity and never get anywhere. What say we save our breath and stick to poetry, and stuff like that?

(Update: Spelling and capitalization of “Dalmatian” corrected at the behest of Greg Hlatky, who ought to know. David Sucher professes bemusement. Forager notes that the comments go a long way to prove the thesis.)

Peddling

 Language, Politics  22 Responses »
Feb 062004
 

“In his first 100 days as President, John Kerry will sign an executive order to end influence peddling and secret deals,” Kerry spokesman Mark Kornblau said.

Senator John Edwards proposes new restrictions on lobbyists in an effort to end “the nasty business of influence peddling” in Washington.

Howard Dean doesn’t like influence peddling either. Neither does Bush.

Whatever influence peddling is, everyone’s against it. But what is it?

peddle, v.t., To sell or offer for sale from place to place. Dope peddlers sell dope, toy peddlers sell toys, ribbon peddlers sell ribbons. Pushcart peddlers sell out of pushcarts. “Influence peddlers,” uniquely, buy influence.

“Influence” is also a euphemism, for “bribe.” “Special interests” offer bribes, in the form of campaign contributions; politicians accept them. Lobbyists broker the transaction.

“Special interests” is itself a nice turn of phrase. Where the State can arbitrarily redistribute wealth, where virtually every federal law robs Peter to pay Paul or vice versa, every interest becomes “special” and politics becomes a Hobbesian war of all against all, a race to stick your snout in the government trough. Grandpa Charlie’s interest in free prescription drugs is as special as Archer Daniels Midland’s interest in ethanol subsidies — more so, really, since ADM employs thousands of people while Grandpa Charlie’s operating solo. Oddly, though, ADM is a “special interest” and Grandpa Charlie is not. I have no love for ADM, an especially vile corporate welfare recipient; but under these circumstances every sizable prudent business employs lobbyists to insure, at a minimum, that its own ox is not constantly gored.

One evening a lobbyist for chemical companies tried to explain his job to me. This man was a moral idiot; the interests of his clients circumscribed his universe. He could not, or would not, distinguish between robbing and being robbed, between, say, supporting a subsidy and opposing a regulation. He was no less instructive for that. So many vastly complicated bills come before legislators that they have no idea what they’re voting for most of the time. His job, he insisted, was to inform. He said that it was no secret that he represented chemical companies, that anything he said was discounted accordingly, and that lying is a long-term poor strategy for being listened to. Grossly self-serving; might still be true! And whether it’s true or not, surely the lobbyist, a pathetic figure scratching out his equivocal living, is the least responsible of all the parties involved. To legislate against him is to shoot the messenger.

The problem, if there is one, is that politicians take bribes. The remedy is supposed to be “campaign finance reform.” The abuse of the term “reform” requires an essay in itself, but here it means giving more tax money to political candidates. In other words, legislators, to prevent themselves from taking bribes, vote to pension themselves off, at public expense. This is absurd. Political euphemism makes absurdity plausible.

And not just absurdity, but evil, as Orwell wrote in “Politics and the English Language,” sixty years ago:

Thus political language has to consist largely of euphemism, question-begging, and sheer cloudy vagueness. Defenceless villages are bomabrded from the air, the inhabitants driven out into the countryside, the cattle machine-gunned, the huts set on fire with incendiary bullets: this is called pacification. Millions of peasants are robbed of their farms and sent trudging along the roads with no more than they can carry: this is called transfer of population or rectification of frontiers. People are imprisoned for years without trial, or shot in the back of the neck or sent to die of scurvy in Arctic labor camps: this is called elimination of unreliable elements. Such phraseology is needed if one wants to name things without calling up mental pictures of them.

By comparison “campaign finance reform” is not very serious, and if Orwell were alive he would laugh. Yet the mental fog that surrounds it is very serious indeed. Easy to sneer at “People’s Republics”; harder to put one’s own lingustic house in order.

Greville’s Long Night

 Poetry  7 Responses »
Feb 012004
 

In night when colors all to black are cast,
Distinction lost, or gone down with the light;
The eye a watch to inward senses placed,
Not seeing, yet still having powers of sight,

Gives vain alarums to the inward sense,
Where fear stirred up with witty tyranny,
Confounds all powers, and thorough self-offense,
Doth forge and raise impossibility:

Such as in thick depriving darknesses,
Proper reflections of the error be,
And images of self-confusednesses,
Which hurt imaginations only see;
And from this nothing seen, tells news of devils,
Which but expressions be of inward evils.

Fulke Greville, Lord Brooke (1554-1628), author of this somber performance, was a minister to Elizabeth and James I and friend to and biographer of Sir Philip Sidney. His elegy on Sidney’s death is well worth reading. (This text is inferior but it’s the only link I can find. The poem ends “Salute the stones, that keep the limbs, that held so good a mind” — “keep the bones” jingles.) Greville died one of the richest men in England, stabbed by a servant who believed, mistakenly, that he was to be cheated of a bequest. He was also one of the greatest poets of one of the greatest eras in English poetry.

I have expostulated on tenor and vehicle in poetry, but this sonnet makes me doubt that the distinction is as simple as I made it out. It operates at three levels at least. At the literal level, night is simply night and the eye the eye. By “witty tyranny” Greville means tyranny of the wit, or the imagination. Anyone who has been startled by a shadow on a deserted street at night will understand “forge and raise impossibility.” The precision of those two verbs characterizes all of Greville’s verse.

The first quatrain contains a miniature treatise on epistemology. True perception, for Greville, requires both an external reality to perceive and an observer to do the perceiving. At night “distinction” (external reality) only appears to be lost; it has “gone down with the light” but remains, though hidden. Similarly the eye’s powers are unabated, but with “distinction” hidden they are useless, in fact worse than useless, for the perceiver turns them inward, projecting his own doubts, fears, and errors on a world he can no longer see.

Greville here begins to write at a second level, somewhere between tenor and vehicle. He has in mind much more than mere sight. Everyone, especially writers, who spend so much time cloistered with their own thoughts, knows how easy it is to promote a fancy to a theory, a preference to a dictum. (Of course I’m talking about the rest of you. I never do that.) Greville speaks of “proper reflections of the error” and in another poem of “the error’s ugly infinite impression,” the way it mirrors or ripples outward indefinitely. In his introduction to Greville’s poems, Thom Gunn remarks acutely that “the vowel-alliteration [of ‘ugly infinite impression’] makes it easy to say quickly; the error’s ‘impression’ spreads, similarly, with the ease and speed of a stain on water.”

Finally, as we ascend to the tenor, the poem is theological. The “evils” and “devils” of the closing couplet belong to Christian vocabulary, along with, less obviously, “depriving” and “error.” Gunn identifies night, at this level, with Hell. More precisely, it is man’s state deprived of divine Grace — “thick depriving darknesses.” Here reality is God. Life on earth is vanity, “self-confusednesses,” “self-offense,” and error, from which there is no escape but Grace. Whether the reader objects to the sentiment is beside the point. Greville knows perfectly well that the human mind can “distinguish” on its own, in some circumstances, and says so, in the same poem, and in the same words. The poem shows a great mind wrestling with an impossible intellectual situation.

To a modern sensibility Greville has no obvious appeal. The verse movement in Campion and Morley is sprightly: in Greville it is stately, even ponderous. Ralegh despairs cynically: Greville hopes, but realistically. Donne imposes and dramatizes his personality: Greville submerges his. Spenser rhapsodizes: Greville analyzes. Sidney was a dashing soldier who died young on the battlefield: Greville rendered greater service to the state by surviving to old age. His poetry was obscure in his own time, and its qualities guarantee its continued obscurity. He is only the subtlest, most precise intellect of all the Elizabethan poets. Intellect was not popular then, and it is less popular now.

(Update: Here is a portrait of Greville in which he looks very like what he was.)