Look Before You Leap

Even the best of us get to make ourselves look silly once in a while, and today it appears to be Bob Somerby's turn. Bob writes the Daily Howler, which you'll find in my list of links, and I highly respect his work. Most of the time. But today he's come up with this, well, you know . . . howler:

Good God! Kaplan and Kaplan spent some time writing a book on “adventures in probability.” For their trouble, they get to read this, from William Grimes’ review in the Times:

GRIMES (3/31/06): Before scoffing, chew on the now famous Monty Hall problem, named after the host of ''Let's Make a Deal.'' A contestant knows that concealed behind three doors there are two goats and one new car. The contestant chooses Door No. 1. The beaming host opens Door No. 3 to reveal a goat, and then asks the contestant if he would like to change his choice to Door No. 2. Two doors add up to a 50-50 proposition, obviously. So why bother? Because the odds have actually shifted. The chances are now two out of three that changing to Door No. 2 will obtain the car.

Say what? We don’t know what the Kaplans wrote to provoke that highlighted sentence. But for the record: If the contestant changes to Door No. 2, he’ll obtain the car half the time—and “half the time” is not “two out of three.” . . .

Numbers, dear friends, are hard work.

Sometimes harder than they look. For the record: Bob's entirely wrong.

To see why this is so, consider the initial choice of a door. There are three doors, each with an object behind it. Two of these objects are goats; the third is a car. If you pick randomly (and there's no reason to think you won't), you have a 1 in 3 chance of choosing the door concealing goat A, a 1 in 3 chance of choosing the door concealing goat B, and a 1 in 3 chance of choosing the door concealing the car.

So far, so clear. Now Monty shows you a goat. At this point, what happens if you stick? If you started out choosing a goat, there's no chance that you'll switch to the other goat; that goat has been revealed and is hors de combat. You'll get the car. On the other hand, if you started out with the car, you will switch to the still-hidden goat. It looks like this:

• If you started with goat A, you'll get the car if you switch
• If you started with goat B, you'll get the car if you switch
• If you started with the car, you'll get the remaining goat if you switch

As we saw, each of the initial choices had a probability of 1/3, so switching will pay off 2/3 of the time. Sticking with your original door is the right thing to do if you chose the car to begin with, but there's only a 1 in 3 chance of that.

Bob's mistake is to assume that after Monty opens up door #3, the fact that two doors remain in play makes the odds of finding the car behind either one of them exactly 50:50. But this is magic. The probability that the car is behind door #1 (the one you've chosen) has not changed; it's still 1 in 3. (Grimes is wrong when he says "the odds have shifted"). What has changed is that you don't have to pick between the other two doors if you decide to abandon your initial door. Monty has effectively now given you the chance to exchange what's behind your door for what's behind both other doors. Remember, he didn't choose to open door #3 at random; he chose a door that he knew harbored a goat. The aggregate probability of finding a car behind either door #2 or door #3 is still 2 in 3, but now you know which of these doors not to pick.

This knowledge yields a simple set of equations (where P(doorX) is the probability of finding a car behind door X):

• P(door1) = 1/3
• P(door1) + P(door2) + P(door3) = 1
• therefore P(door2) + P(door3) = 1 - 1/3 = 2/3
• but we now know P(door3) = 0
• therefore P(door2) = 2/3 - 0 = 2/3

That is, switching will get you the car 2/3 of the time. QED.

[For those of you with an aversion to equations, there's a simulation of this problem here. Just play it a few times and keep track of how often you win the car by switching (or win a goat by sticking).]

The only thing that could alter these odds would be some sort of unfairness on Monty's part. And in fact you wouldn't expect Monty to play fair in real life. For example, he might show the goat and offer a switch only when the contestant has chosen the car, which would reduce the chance of getting the car by switching all the way to zero. You could imagine other behavior on Monty's part that would produce other probabilities, including Bob's answer of 50%. But that 50% doesn't follow necessarily from any of the premises of the problem; it would be an arbitrary importation by the host. And it wouldn't be, as Bob thinks, the one and only answer to the problem.

In Bob's defense, he's by no means alone in this error. When the Monty Hall problem appeared years ago in Marilyn vos Savant's Sunday supplement column Ask Marilyn, and Marilyn gave the correct answer, she was deluged with complaints. Some pointed out, quite reasonably, that the answer depends on whether Monty offers the same choice to all contestants. But there were others, including some with serious math credentials, who got it wrong in just the same way that Bob has, and made no secret of their scorn (sometimes sexist) at Marilyn for coming up with a different answer.

Yes, dear friends, numbers are hard work.

Maverick No More

I had intended to post a much longer comment on John McCain's recent activities, but there's just no time. Suffice it to say that I'm very, very disappointed. Although we differ on a whole raft of issues, during the 2000 campaign I admired his independence, his forthrightness, and even his occasional (at least apparent) unscriptedness. He called his campaign the "Straight Talk Express" and the name seemed to fit. It was gratifying to hear a conservative Republican speak out against Jerry Falwell and Pat Robertson as "agents of intolerance" (a remark that, though both honest and accurate, was also grossly impolitic and may have cost him the nomination), and again later to stand up to his party's disastrous tax cuts:

I cannot in good conscience support a tax cut in which so many of the benefits go to the most fortunate among us.

That was then.

As E. J. Dionne writes, "McCain has decided the only way he'll ever be president is as the Republican nominee." This means that he has to play nice with the powers that be in a party controlled by agents for monied interests and the Religious Right. His maverick days are over.

The one-time opponent of tax cuts for the wealthy voted last month to extend cuts on dividends and capital gains taxes.

Now we hear that he's accepted an invitation to speak at this year's commencement ceremonies at Jerry Falwell's Liberty University. I'm guessing he won't be calling Falwell an "agent of intolerance" this time around.

Falwell, of course, hasn't changed. But McCain has.

Annals of Delusion

Newsweek:

Julie Scheving, a 46-year-old resident of Holland, Mich., doesn't believe the decision to open "The Da Vinci Code" on May 19 happened by chance—she believes it was an act of God. The movie opens on her birthday, and Scheving, a born-again Christian, is planning on using the occasion to buy tickets for at least a dozen of her "unchurched" friends. Though the movie's claims about Christianity run contrary to Scheving's beliefs, she's looking forward to initiating a discussion about the true nature of Jesus Christ.

. . . including, presumably, the fact that He arranges movie openings to suit her personal convenience. What a Guy.

I do feel sorry for all the born-again Christians whose birthdays don't fall on May 19. How sad that God has deprived them of their chance at evangelism.

Trends

A quick Google blog search shows a surge of good feeling on the left regarding the latest Pew Research Center survey involving, among other things, attitudes towards gay marriage. And certainly some of the numbers look good.

For example, opposition to gay marriage is off 10 percentage points, from 61% to 51%, since December, 2004; strong opposition is also off over the same period, from 38% to 28%. Outright support for gay marriage doesn't look to have risen by quite this much, but it's still up, from 32% in December, 2004 to 39% today. (The margin of error is 3 or 4%.) If this is a trend, we might actually look forward to a day reasonably soon when a gay-marriage ban loses at the ballot box.

But I wonder. The poll numbers also show that, for all the apparent progress in the last year and a half, we're still right around where we were in July, 2003, when Pew found 38% in favor of gay marriage and 53% opposed—margin-of-error-wise, numbers pretty much indistinguishable from today's results. A graph of poll results since then shows two spikes in opposition—one in late 2003-early 2004, around the time the Massachusetts Supreme Judicial Court ruled in favor of gay marriage, and another in late 2004, around the time that gay-marriage bans appeared on 11 state ballots across the country (and passed in all of them). In between these spikes, opposition had fallen by seven percentage points. If you'd identified the Pew numbers from early 2004 as representing a trend (63% opposed in February, 59% in March, and 56% in June) you'd have been sorely mistaken, for by the end of the year opposition was up to 61% again.

So although it's tempting to think that acceptance of same-sex marriage is on the rise, recent history suggests that something else may be going on. It may just be that people don't get as worked up over the issue as long as they haven't been thinking too much about it and it's not in the news every day. The next burst of publicity, the next round of ballot questions, could send opposition up once again.

This is not to say that things are hopeless, or that progress can't be made. The long-term trend is positive, and polls (even those commissioned by Faux) show that the younger you are, the more likely you are to support equal marriage rights. But it may be a longer slog than this week's numbers seem to indicate.

Sneer quotes

Speaking of censure, Andy McCarthy has this to say over at National Review Online:

On that score, it looks like Tuesday's [Senate Judiciary Committee] hearing will include testimony from some legal experts (including perhaps some past or present FISA court judges). Expect the program's opponents to try to glean from Tuesday's witnesses "expert" opinions that the program is illegal, which said opponents can then use at Friday's hearing as part of the argument that the President has committed crimes and could be impeached, therefore -- so the argument will go -- censure is an entirely reasonable middle ground.

An entirely acceptable analysis of opposition motives, as far as it goes. But why the pettiness? You would expect the testimony of legal experts to consist, more or less, of expert opinions. But no; not when such testimony might aid the other side. Then it's sneer-quoted "expert" opinion that must be gleaned (presumably with a magnifying glass and a sharp pair of tweezers).

Anyway, if the experts do testify that Bush has committed impeachable crimes, it won't be by virtue of any "argument" that censure becomes a middle ground, but rather by virtue of plain fact. And very exposed middle ground at that.

Bush to Congress: Drop Dead

Russ Feingold is right. There's significant evidence that George W. Bush broke the law when he authorized the NSA's program of warrantless wiretapping, and for that he deserves censure. Whether Feingold can persuade enough other Senators—even within his own party—is another question.

Even if Feingold's current proposal goes nowhere, however, perhaps he should already be gearing up for the next round, when Bush violates a law that he himself signed.

Earlier this month, after months of hard negotiation over the addition of civil liberties protections, Congress approved a renewal of the "USA PATRIOT" Act and sent it to the President's desk. Senate minority leader Harry Reid pronounced himself satisfied with "a better bill" that "does not mean a blank check for the president". Bush praised the new bill, which, he said, "will allow our law enforcement officials to continue to use the same tools against terrorists that are already used against drug dealers and other criminals, while safeguarding the civil liberties of the American people". He signed it on March 9th. He then turned around and officially repudiated one of those civil liberties safeguards. Maybe it is a blank check after all.

In a signing statement accompanying the PATRIOT Act extension, Bush declared that he would not consider himself bound to obey specific oversight provisions requiring the FBI to report to Congress on its use of PATRIOT Act powers, if he felt that to do so would "impair foreign relations, national security, the deliberative process of the executive, or the performance of the executive's constitutional duties."

In one fell swoop Bush has knocked Congress's deliberative function into a cocked hat. If the President can get away with this kind of maneuver, then the months of wrangling over the exact contents of the PATRIOT renewal were, it turns out, worth absolutely nothing.

The only question about censure would now seem to be, "now or later?" Remember that the President has sworn an oath to "preserve, protect and defend the Constitution of the United States". Either Bush believes that the reporting provision is unconstitutional, in which case signing the bill was inconsistent with his oath (censure him now), or he believes it is constitutional but plans to violate it if necessary (be ready to censure him when he does).*

Either way, Congress should be up in arms. Only Patrick Leahy (D-VT) has had anything to say about this publicly. Where are the rest of the Democrats?

Where, for that matter, is the Republican leadership? It was once possible, perhaps, for them to believe that party solidarity trumped all other considerations, even the safeguarding of their own Constitutional role. That should no longer be possible, now that presidential poll numbers are in the 30's. The Republicans won't always be in charge of the entire apparatus of government, and they're bound to be very sorry when the precedents set during this Presidency redound to their detriment.

Finally, has anyone seen the "liberal media" lately? According to Google News, today's piece in the Boston Globe (link above) is the first mention of something that has been a part of the public record for, depending on how you look at it, either a week (Leahy statement) or two (Bush statement). Fie and for shame.

————
* A third possibility exists: that he has no idea whether it's constitutional or not, and/or he doesn't care. Maybe this is the likeliest of the three.

---

Perhaps it was inevitable: I've discovered that when I chose the title of this post, I was inadvertently channeling (not plagiarizing) another blogger, GUY2K at Capitoilette, who used the same title on a post nearly three months ago, discussing essentially the same topic. Three months ago? Yep: it turns out that the whole signing-statement dodge has a longstanding place in the Bush playbook. Among GUY2K's topics is the signing statement via which Bush opted out of the McCain anti-torture amendment to last December's defense appropriations bill. This instance, too, received some attention from the Boston Globe, and I missed it. Mea culpa.

Twisting reality

Physicist and staunch advocate for sound science education (i.e., teaching evolution) Lawrence M. Krauss makes an interesting observation—several, actually—in the April/May Free Inquiry (not yet available online, but I'll post a link if and when).

Krauss contrasts statements issued by two U.S. presidential administrations a mere 13 years apart:

Science, like any field of endeavor, relies on the freedom of inquiry. And one of the hallmarks of that freedom is objectivity. Now, more than ever, on issues ranging from climate change to AIDS research to genetic engineering to food additives, government relies on the impartial perspective of science for guidance.

This administration looks at the facts and reviews the best available science based on what's right for the American people.

The first of these was spoken by the first President Bush to the National Academy of Sciences in 1990; the second by Scott McClellan, his son's press secretary, in 2003.

Now, I wasn't a particular fan of George H. W. Bush, but here he had it exactly right. It's disheartening to see what's happened on his son's watch: instead of using science (that is, objectively developed knowledge about the world we live in) to evaluate policy, the Bush II White House wants to use policy to evaluate science. If you're looking for reasons why George W. Bush has gone so wrong on so many issues, this reversal of priorities is not a bad place to start.

Perhaps this is why, as reported by Bob Woodward in Plan of Attack, the President never consulted his own father, who might have been presumed to have useful things to say on the subject, about his decision to invade Iraq and depose Saddam Hussein:

He is the wrong father to appeal to for advice. The wrong father to go to, to appeal to in terms of strength. There's a higher Father that I appeal to.

You see, Bush I was a member of, or at least paid eloquent lip service to, the "reality-based community" that a Bush II aide so famously derided in a conversation with Ron Suskind. And a dose of reality is the last thing you want if you're bent on twisting reality to conform to your preconceptions.

Outright Lies and Distortion

A click here, a click there, and pretty soon (if you're not careful) you find yourself deep in the bowels of an alternate, and not entirely pleasant, reality.

At issue is whether military casualty (actually, fatality) figures used by the mainstream media misrepresent the severity of American losses in Iraq and Afghanistan. RedState.org's "Proud Kaffir" says they do: "This is all simlpy [sic] outright lies and distortion."

Which, of course, is in the eye of the beholder. Max at MaxSpeak.org aptly summarizes PK's argument this way: "U.S. deaths in Iraq are not so bad, when you demonstrate your innumeracy by comparing them to irrelevant numbers."

(I'll never understand, by the way, why people who claim to "support the troops" -- whatever that means -- will go out of their way to minimize the very real dangers our troops face in Iraq and Afghanistan and, implicitly but inevitably, their bravery and sacrifice in facing them. Brit Hume (search for "California"), refuted here, is another egregious example.)

By all means go to RedState and see for yourself. A number of comments on PK's post ably dissect what he's done wrong. It's instructive.

Also interesting is how they react to contrary views over there. Dissenters who post reasonably polite, factual comments (not noticeably in violation of RedState's posting rules) are told to "Go away. Now." and blocked from further posting. One RedStater even threatened, "if you post again we will inform the abuse office at your ISP." An interesting peek into a worldview that tolerates no intrusion by troublesome facts.

Bales and Bales of Straw

The Associated Press tells us that President Bush has been using straw-man arguments in his speeches. It's nice to see some mainstream news outlet finally cotton on to something that should have been obvious for years to any sentient human.

In a straw-man argument, for those not in the know, one constructs a flimsy caricature of an opponent's position -- the "straw man" -- and then noisily knocks it over, proclaiming victory. Nothing of substance has been achieved, because the real opposing position hasn't even been met, much less bested. It's deeply dishonest. But it can look impressive to the unwary.

I don't happen to know, and the AP article doesn't say, whether Bush is freer in his use of straw men than previous presidents or than his political opponents today, but my guess is that he is. In any event it would make an interesting subject for study.

But he certainly does do it a lot. He was at it again just yesterday. At a White House press conference, Carl Cameron of Faux News asked him about the move in the Senate to censure him over illegal NSA wiretapping:

The primary sponsor, Russ Feingold, has suggested that impeachment is not out of the question. And on Sunday, the number two Democrat in the Senate refused to rule that out pending an investigation. What, sir, do you think the impact of the discussion of impeachment and censure does to you and this office, and to the nation during a time of war, and in the context of the election?

(Incidentally, you have to wonder what the White House press office thought they were doing inviting faux newsman Jim "Jeff Gannon" Guckert from faux news organization "Talon News" into White House press briefings. Guckert, of course, achieved fame for such softball questions as "How are you going to work – you've said you are going to reach out to these people – how are you going to work with people [Senate Democratic Leaders] who seem to have divorced themselves from reality?" Clearly this was an unnecessary and risky undertaking, given that capital-F Faux News people such as Cameron are obviously willing to ask the same sort of might-have-been-written-in-Karl-Rove's-office questions.)

This was the signal for Bush to pull out one of his biggest straw men to date:

I did notice that nobody from the Democrat Party has actually stood up and called for getting rid of the terrorist surveillance program. You know, if that's what they believe, if people in the party believe that, then they ought to stand up and say it. They ought to stand up and say the tools we're using to protect the American people shouldn't be used. They ought to take their message to the people and say, vote for me, I promise we're not going to have a terrorist surveillance program. That's what they ought to be doing. That's part of what is an open and honest debate.

But Bush said it himself: nobody has actually stood up and said that. Not because they're afraid of the political ramifications, but because that's not the argument. Nobody thinks we shouldn't be listening in on terrorists. The argument is that the wiretapping was undertaken illegally, in defiance of the explicit requirement for judicial oversight enacted in the 1978 Foreign Intelligence Surveillance Act (FISA). That "vote for me and I promise we won't have a terrorist surveillance program" is straw through and through. The real argument is that we have a Constitution, and we have laws, and Bush has violated them.

What's more, Bush must know this. He must know that not a single Democrat has called, or would call, for ending all surveillance of known or suspected terrorists. In describing their position as he has, he is lying.

It's amusing to turn this around. I wouldn't mind at all seeing Republican candidates in the upcoming elections take to the stump and say:

The tools that the Founding Fathers devised to protect the American people from unbridled executive power shouldn't be used. Vote for me, and I promise you that we're not going to have Constitutional checks and balances or a Bill of Rights.

A straw man? Yeah, I suppose.

Really Bad Analogies 101

John Dunleavy, the chairman of New York's St. Patrick's Day parade, explaining why he prevented a group of gay Irish-Americans from marching this year:

If an Israeli group wants to march in New York, do you allow neo-Nazis into their parade? If African-Americans are marching in Harlem, do they have to let the Ku Klux Klan into their parade?

No, of course not. That would be like forcing the organizers of a Gay Pride celebration to let you into their parade.

If you get my drift.