## Monthly Archive for July, 2013

### Non-Hansonian Prediction Markets

Having a baby? Want to predict its gender? Amazon.com offers just the product:

Does it work? Well, check out the distribution of customer reviews:

A delighted hat tip to our reader Mark Westling of Inuvi.com, who remarks that

The most interesting comments are along the lines of “It was wrong so I only gave it three stars”.

and then goes on to propose a business model:

Offer baby sex prediction over the web, charge \$75 (so consumers know it’s good), and offer a full refund if you’re wrong (upon review of relevant documents).

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### Unclear on the Concept

Mike Rizzo at The Unbroken Window reports spotting these two bumper stickers next to each other — on the same car.

### A Bayesian Solution

There were many excellent comments on yesterday’s Bayesian Riddle. Here’s what I believe is the simplest and most natural analysis.

First, let’s recall the problem:

A murder has been committed. The suspects are:

• Bob, a male smoker.
• Carol, a female smoker.
• Ted, another male smoker.
• Alice, a female non-smoker.

You are quite sure that one (and only one) of these suspects is the culprit. Moreover, after carefully examining the evidence, you’ve concluded that the odds are 2-to-1 that the culprit is a smoker.

Now your crack investigative team, in which you have total confidence, reports that, on the basis of new evidence, they’ve determined that the culprit is definitely female.

Who’s the most likely culprit, and with what probability?

Notice that if you considered all the suspects equally likely, your estimate would have been three to one for a smoker. Since you estimated only 2-to-1, you must have believed that the individual smokers were less likely than average to be guilty. So when you find out the culprit is female, it’s the female non-smoker — that is, Alice — who is now your prime suspect.

### A Bayesian Riddle

A murder has been committed. The suspects are:

• Bob, a male smoker.
• Carol, a female smoker.
• Ted, another male smoker.
• Alice, a female non-smoker.

You are quite sure that one (and only one) of these suspects is the culprit. Moreover, after carefully examining the evidence, you’ve concluded that the odds are 2-to-1 that the culprit is a smoker.

Now your crack investigative team, in which you have total confidence, reports that, on the basis of new evidence, they’ve determined that the culprit is definitely female.

Who’s the most likely culprit, and with what probability?

### Fortune Comes a-Crawlin’

With great humility, I am honored to inform you that Eric Crampton of Offsetting Behavior has nominated me for sainthood.

Riffing off yesterday’s Acta Sanctorum post, Eric is asking for your help in making this a reality:

So, here’s the campaign for Saint Steven.

1. Any of you who have any kind of illness at all pray to Steven Landsburg for intervention.
2. If you do not receive divine Landsburgean intervention, don’t tell me about it.
3. If you do receive divine Landsburgean intervention, please leave a record of such in the comments. Preferably with a link to a doctor’s note saying that your recovery was unexpected and pretty remarkable. This should happen in maybe 1% of cases.
4. We submit the documented evidence of the successes, while ignoring the failures. Ta-dah! Saint Steven.

My hope is to beat John Paul II’s record of two reported cures, plus the toppling of one Evil Empire, or, at a minimum, the National Endowment for the Arts. Oh, and while I’m at it I have a couple of other worldly improvements in mind. Watch your step, Paul Krugman!

### Acta Sanctorum

So if I have this right, it is now the official position of the Catholic church that:

1. The late Pope John Paul II has the ongoing power to cure brain aneurysms.
2. As far as we know, he has chosen to employ this power exactly once. (He also once cured a case of Parkinson’s.)
3. While hundreds of thousands of others have suffered and/or died from brain aneurysms, John Paul has not been moved to intervene.
4. The one victim he troubled himself to save was selected not because she was particularly deserving or particularly valuable to society, but because she chose the right guy to pray to — sort of like having to suck up to the teacher to get a good grade.
5. All of this makes John Paul II particularly fit for veneration.

For God’s sake (you should pardon the expression), if you’re looking to make the case that John Paul II was capable of performing (or at least catalyzing) genuine miracles, isn’t the defeat of Soviet Communism good enough? That right there makes him a saint in my book — though if I ever come to believe that he can cure aneurysms and has been holding out on us, I might have to retract my endorsement.

Paul Krugman, having apparently received another of his divine revelations, proclaims that if we demand (somewhat) better working conditions in Third World countries (backed up, presumably, with boycott threats), “we can achieve an improvement in workers’ lives … And we should go ahead and do it.”

Don’t ask how he knows; the ways of the Oracle are mysterious and beyond human ken.

Look. A well designed policy of boycotts and boycott threats can certainly improve working conditions in the Third World. It can also lower either wages, employment or both. Whether or not that package amounts to “an improvement in worker’s lives”, as Krugman puts it, is an interesting and important question, and well worth thinking about. But apparently the last thing Krugman wants you to do is think about it, since he’s already told you the answer, and seems to presume you won’t have the slightest interest in where it came from.

Now, among the many differences between me and Paul Krugman, there are probably some that redound to his credit. But his propensity to hide all of his reasoning (if any) is not one of them. Compare, for example, my blog post of a few years ago on working conditions in 1911 New York City, when the Triangle Shirtwaist fire claimed 146 lives, most of them young women, partly because the fire exits were blocked to prevent pilfering. Would workers in 1911 have wanted safer working conditions (including unblocked fire exits)? This was my answer:

### Hi, Mom!

My mother, who reads this blog, reports that she’s lost a few nights’ sleep lately, tormented by thoughts of Knights, Knaves and Crazies. Serves her right. Once when she and I were very young, she tormented me with a geometry puzzler that I now know she must have gotten (either directly or indirectly) from Lewis Carroll; you can find it here. If she remembers the solution, she should be able to sleep tonight.

Herewith, a proof that a right angle can equal an obtuse angle. The puzzle, of course, is to figure out where I cheated.

But wait! Let’s do this as a video, since I’m starting to fool around with this technology and could use the practice. Consider this more or less a first effort. If you prefer the old ways, you can skip the video and read the (identical) step-by-step proof below the fold.

Get the Flash Player to see this content.

Or, if you prefer to skip the video, start here:

### Hard and Harder

If you failed to solve Wednesday’s problem on Knights, Knaves and Crazies, take comfort from the fact that this has circulated among philosophers under the title “The Hardest Logic Problem Ever”. MIT philosopher George Boolos discussed it in the Harvard Review of Philosophy back in 1996. In that version, Crazies are never silent. But Oxford philosopher Gabriel Uzquiano soon observed that this can’t be the hardest logic problem ever, because it gets harder if the Crazies can be silent. Uzquiano’s new “hardest logic problem ever” was solved by the philosophers Gregory Wheeler and Pedro Barahona — and then solved again, substantially more elegantly, I think, in Wednesday’s comments section right here.

A few more thoughts, on the problem, its solution, and how to make it harder:

### Knights, Knaves and Crazies

The best dozen or so puzzle books ever written are, without a doubt, the works of Raymond Smullyan. If you’ve never encountered these, stop right now and order yourself a copy of What is the Name of This Book?, which is brilliant on multiple levels. On the surface, it’s a book of particularly amusing little brain teasers. One level down, those brain teasers contain a proof of Godel’s Incompleteness Theorem — solve all the riddles and you’ll have painlessly understood the proof!

Smullyan’s books are heavily populated by Knights who always tell the truth, Knaves who always lie, and bewildered travelers trying to distinguish one from the other via their cryptic utterances. Today’s puzzle is Smullyan-like in its set-up but considerably more difficult than most. It’s been proposed and discussed in philosophy journals, but I’m suppressing the sources (and rewording the problem) to make it a little harder to Google. I’ll of course pay appropriate homage to the authors when I post solutions in the near future. Meanwhile, if you’ve seen this before, or if you’ve found the answer on line, please restrain yourself from posting spoilers. But do post whatever you manage to come up with on your own.

And now to the puzzle: