Saturday, October 15, 2011

The Rational Limits of the Human Brain






As intelligent humans (most of us) there is the underlying assumption that we are confident of our brains to sort the world out, analyze most of its problems as well as deal with assorted conundrums that appear each day: from work dilemmas, to financial decisions. The truth is that the human brain, given its evolutionary underpinning, falls far short of even optimal rational function - never mind perfection- most of the time.

A simple question can actually demonstrate this nicely:

A bat and a baseball cost a total of $1.10. If the bat costs $1 more than the ball then what is the price of the ball?

Nearly everyone who attempts this gives the answer of 10 cents, then asks what the hell was he thinking asking such a stupidly easy question. But they'd be quite wrong, even as more than 50% of Harvard, Princeton and MIT students were when asked the same question, according to psychologist Daniel Kahneman, a Nobel laureate based at Princeton.

The actual answer is $1.05 for the bat and 5 cents for the ball.

The most direct way to show it is just converting the problem into a basic algebra problem. Then let x = $y + 1 for the bat and assign y for the ball

We have the total cost:

x + y = 1.10

and substituting for x:

(y + 1) + y = 1.10

and solving for y (the ball cost):

2y + 1 = 1.10

2y = 1.10 -1 = 0.10

yielding the actual price of the ball:

y = 0.10/2 = 0.05

or 5 cents!


This is only one of the most glaring demonstrations of how our brains can be fooled into giving answers we intuitively feel are correct, but which when more deeply analyzed are not. In this case, the deeper analysis meant actually converting the verbal problem into one of basic algebraic symbols then solving for one (the ball price) in this case.

Another reason for the slapdash answer is a characteristic human hubris and over confidence. We think on hearing a problem we believe to be simple, we can offer or find a simple answer, when deeper thought shows this isn't so.

A perfect example is the casino slots player who wins a pile - say $100- but believes she can keep going and turn it into $200. This egregious error usually means losing everything, since more and more coins are fed into the machines to make up for what's already lost.

The stock market is another example. People - especially males- often believe they know more than most (usually their wives) about investing so approach it with hubris. Never mind the stock market is the classic process of randomness in which - as one study once showed - a monkey firing darts at a giant page full of blocked stock names stands a better chance of picking a winner than a human.

In a way this isn't surprising because - as Dr. Kahneman has noted - the year to year correlation between the performance of the vast majorituy of funds is barely above 0. Thus, most stock or fund managers are relying on luck, not talent. In a way they are not much better off than our slots player.

Hubristic bias and over-confidence in pattern thinking and belief can be seen in other areas of human endeavor as well. Take baseball and specifically the National League Championship Series betwen the St. Louis Cardinal and Milwaukee Brewers.

By a study of actual baseball statistics based on empirical data, one saw in looking at the Brewers' pitching rotation, that Shaun Marcum had fallen off a cliff, literally, since shoulder surgery some months ago. He was 3-6 after the surgery with an ERA of over 5.00.

Nonetheless, Brewer manager Ron Roenicke pitched him in the second of two initial home games in Milwaukee (where the Brewers were dominant with the best record in baseball the whole year) as opposed to his other ace - Yovani Gallardo - who he was saving for Game 3 in St. Louis where Gallardo had a 1-3 record and ERA over 5.70. Roenicke here was going with his usual rotation order, and pitching Marcum in his normal position, despite the fact that rational analaysis disclosed this was a lousy decision and Marcum would be better used as a sacrificial lamb for Game 3 in St. Louis, and pitching Gallardo would give the Brewers a 2-0 series lead before going there.

This analysis turned out to be correct, as Marcum was shelled in a 12-3 howler, while Gallardo also lost in St. Louis. To make matters worse, Roenicke still clung to his normal rotation order pitching Zack Greinke in Game 5 despite the fact he'd never won in St. Louis. Greinke - by rational analysis - would have been better saved for Game 6 in Milwaukeee - where he was undefeated. Then having Yovani Gallardo go in Game 7 for a back to back putative Brewers' clinching of the NL pennant.

This also turned out correct, as Greinke lost 7-1 in the fifth game and the Cards took a 3-2 game edge going back to Milwaukee.

So who is Roenicke going to pitch tomorrow for Game 6? (The critical game which is win or go back home for the off season, for the Brew Crew).

Why he's going with Shaun Marcum! He has still not budged from believing his normal rotation will work when the numbers from rational analysis (including sabermetrics) show they won't!

In a more general sense, the edifice of human irrationality shows that even certain assumptions - say of modern economic theory - may have to be turned on their heads. The basic assumption is that humans are rational agents and, when offered a set of choices - say for a product- will end up making the optimum one. But in an excellent book entitled The Paradox of Choice, the author showed this isn't the case and when humans are offered a surfeit of choice they punt! They either don't make any purchase, or they opt for the first one that comes to mind or in their field of vision.

This miasma of choice has been found to carry over to Medicare and its beneficiaries who each year must confront more than 500 different plan choices for Medicare Part B, C , D, and F and often make choices that end up being extremely costly! Worse, the whole Medicare system is contrived of constantly moving parts which change prices, benefits year to year - especially Part D - the Prescription Drug Plan. The situation has become so intractable for many seniors, they are having to hire special services to wade through all the issues and make a decision!

We pride ourselves on being rational beings, but we may not be as rational as we think!

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