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Logic Eludes Eabra and Pain: Case Study Closing Remarks


By Steve Dayton
Apr. 21, 2007

Folks, I’d rather spend my time writing creatively, but it’s important for the readers of U-K to stay cautious when reading our conservative writers, Edward Abraham and Tom Pain chief among them, and hearing them claim “logic” as an inherent characteristic of their partisan arguments:

This is inverse logic that only a liberal would use. 
Ed Abraham

Two days ago, despite this clear boast as to the superiority of "conservative" logic, Edward Abraham flunked a proposed test of genuine logic skills.  Ed’s miserable performance certainly validates my recent criticism of him in this regard, but it is only one scientific data point on his chart, and besides: it’s still early in the spring quarter.  Ed may be able to improve his grade and possibly even pass logic class, if he continues to do his homework, and aces the final exam.  Furthermore, Ed’s befuddlement illustrates why The Monty Hall Problem has attained the fame it has:  it is a fairly simple probability exercise whose solution appears counterintuitive to average (and some very non-average) thinkers.  Brian Barbeito failed the test prior to Abraham, responding with the most popular (wrong) answer.  Ed followed Brian's attempt and barked up a completely different – and equally wrong -- tree, conjuring up cars and goats and "Expected Value" virtually out of thin air, and then used poor judgment by concluding his errant essay with a boorish insult:

A person like you, Steven, might have a good use for that old goat when it's dark and you're lonely, and you might feel that you're a winner whichever one you pick.

Tom Pain, a self-described sucker-fish, didn’t respond directly to the Monty Hall challenge, although some believe Eabra to be just another alias in Pain’s tired repetoire, and Eabra's rare and unfortunately-timed animal-husbandry joke seems to provide support to the theory. It might have been a clever retort, or even humorous, if Eabra had responded to the Monty Hall problem in any manner other than a completely wrongheaded one.  Pain could also be called a “counterpuncher,” in the mold of Gerry Cooney, and as soon as the folly of Abraham’s response was revealed, Pain began frantically searching for a “logical loophole” that he could exploit, in an effort to “rescue” his conservative comrade (alias?) Ed Abraham from further embarrassment in this unexpected debacle.  Although absolutely no reference was made to the “relative value” of the prizes behind the three doors in the original problem statement (or to cars and goats for that matter), Pain, like Abraham, blindly wanders down this alleyway:

The point is that there is an element of value to the "prize" which is subjective. So, you think the yak farmer is going to somehow drag the prized automobile down the side of the Andes to some small village in Peru? You just don't get it. Here, let me try again so your midget brain can begin to comprehend:

Let's say the contestant is stranded on a small desert island - no roads, no gas stations, barely room to turn the car around. You know, that stereotypical desert island of cartoon fame. As you would guess, that marooned contestant is kinda hungry - the palm tree takes months to grow a coconut. Do you think he would want a shiny new car to fall out of the sky, or would he prefer a nice goat that could produce milk daily or be barbequed for food?

If the contestant happened to hail from the Bay area of California, he might even want to tap that goat a couple of times a day.

The point is that your logical example set up a subjective scenario - which Ed appropriately pointed out. We can both come up with ridiculous scenarios all day, but that fact still remains. Heck, maybe the contestant hates materialism so that the idea of winning NOTHING is tremendously appealing.

In truth, there is no subjectivity whatsoever in the Monty Hall problem, and a truly logical person would easily comprehend this fact.

To prove my point, let’s recast the Monty Hall Problem in another form, as a simple shell game.  Three clamshells lie on a table top, and beneath one of them is a red marble.  The other two shells have nothing underneath.  To eliminate Pain’s strawman concern about “contestant materialism,” or the lack thereof, the object in the modified Monty Hall game becomes not which shell you’d prefer to own, but underneath WHICH shell resides the marble?  Guessing correctly wins the contestant a prize of his choosing out of a catalog of prizes.

The contestant begins the game by pointing at one of the three shells.  The host lifts up one of the other two shells, revealing only emptiness beneath it, and then asks the contestant if he would like to switch his original shell selection to the last remaining unselected shell.  In other words, “You picked a shell, I gave you a freebie by showing you a bogus shell, and now I’m asking you if you want to switch your choice to the other shell.”

The best, most logical decision, as mathematics proves, and which seems counterintuitive to many, is for the contestant to switch his choice.  In fact, the odds of winning a personally-selected prize from the catalog DOUBLES if the contestant switches his choice to the other shell.

This modified formulation of the Monty Hall Problem prevents fallacious “logical” arguments of the kind (above) that Tom Pain specializes in.  I suppose Tom could still say there are people who would prefer “nothing” over a prize of their choice out of a catalog, and being cognizant of the true logic behind the shell game, these sandal-footed Zen-master contestants would then stoically stand pat with their original selections, knowing full well they’ve halved their odds of winning.

As Pain-fully “logical” as this might sound, I would suggest to Pain that the Zen masters could be persuaded to donate any winnings to charity, and I would personally urge the mathematically-competent monks to remember their mission with the less fortunate people of the world, and ask them to thus unsheathe their logical swords and slay the Monty Hall dragon. Or maybe these monks just want to prove how smart they are, and to Christian Hell with the prize.

I'd be down with that.

With regard to Pain’s concern about the setting or “scenario” of the game, since we don’t want gold bars being tossed at coconut trees, and we certainly don’t want any goat farmers dragging new automobiles down Andean mountainsides, let’s assume the game takes place in a special, controlled place, like a street corner in New York City.  The game host has a table, 3 clamshells, a red marble, a satellite phone, and a catalog of prizes, every one of which the host has been previously authorized to purchase outright, and then deliver personally, via Lear jet and air-conditioned semi-truck, to a location of the winning contestant's choosing.

What should a logical person do?  There is only one choice, despite what some conservatives on U-K might imagine.



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About the author: Steve Dayton writes articles like he hits range balls: high, far-out, and sometimes even straight.

Email: stixus_steve@yahoo.com


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