## Saturday, July 17, 2010

### Cognitive Dissonance, Monty Hall, and the nature of science.

Back in 2007, a study attempted to apply the theory of Cognitive Dissonance to monkeys. It lead to a good number of comments, made the NY Times, and got a good amount of comments on Slashdot.

Once a monkey was observed to show an equal preference for three colors of M&M’s — say, red, blue and green — he was given a choice between two of them. If he chose red over blue, his preference changed and he downgraded blue. When he was subsequently given a choice between blue and green, it was no longer an even contest — he was now much more likely to reject the blue.

So a monkey was shown to eat M&Ms pretty much equally and not much care. But, when forced to make a choice between two different M&Ms say red and blue, the rejected M&M when placed against green would be rejected at greater than the expected 1/2 outcome and was rejected closer to 2/3rds of the time. Thus proving the theory that they must have needed to rationalize the rejection and therefore valued the given item less than previously. When offered another choice, they were much less likely to chose that M&M which they rationalized themselves into not wanting anyway. Much like the Aesop Fable of the Fox and the Grapes who after thinking about it and realizing the grapes were unreachable, decided that they were also unripe and bitter.

Why do I bring this silly story up? Well, it has to do with the Monty Hall riddle. By the way, if you noticed the problem with the study, mad kudos to you. If you want, try to stop reading and figure it out (if you're well versed on the Monty Hall Riddle).

Well, it turns out that the odds for the second choice aren't 1/2, they are actually 1/3rds for the rejected and 2/3rds for the other. If there's a preference hierarchy at all there are a total of 6 different ways to rank the M&Ms.

RGB, RBG, BGR, BRG, GRB, GBR

If you are asked which you'd prefer red vs blue and you take the red, there are three possible hierarchies which could exist.

RGB, RBG, GRB - These are the only times that red is better liked than blue. And in these when offered B vs G, we find that 2 rank green > blue:

RGB, GRB. So the odds really are 1/3 that they should accept the rejected M&M if we go by pure raw statistics. The Social Psychologists who ran the experiment as well as the slashdot thread about it, which had highly rated comments about color vision in monkeys and possible flaws in methodology, etc. But, they like generations of social psychologists failed to spot this mistake. However, the flaw in the study was noticed by an economist, Dr. Keith Chen who subsequently published a paper about the flaw and the series of similar flaws that are seen throughout the field of Cognitive Dissonance all the way back to the early studies in the 1950s. And that the paradigm of "Rank, Choice, Rank" is always going to skew things because the choice changes the odds, even without any rationalization at all the first choice means the odds for the second question are different.

In fact, this same research is still going on. Supposing that if you could make the choice arbitrary enough, that it should somehow prove the point, and still it holds that if you use any metric at all (in that you don't simply flip a coin, or that if given the first choice again would more often than not choose the same way), you will find that if given and choice and then made to "chose between the rejected object and a third similar object." -- anything will prefer the third similar object 2/3rds of the time and studies with amazing datapoints like: "Both children and monkeys preferred the third object" are moot and expected by random chance and statistics.

So, an economist without any formal training in Social Psychology, Psychology, Cognitive Dissonance, or the various fields thereof offered a rather stunning rebuttal that properly refuted a fair amount of research from the 1950s to the present, and is undoubtedly correct. An economist offered a scientific refutation and demolished literally thousands of studies as an outsider. Think about this next time you hear anybody claim that atheists should study religion before trying to refute it. Or that science is simply dogmatic. It really is possible for somebody from the sidelines to kick the wall and destroy an entire house of cards. Science loves this! It doesn't matter who you are, you could be a 11 year old girl disproving therapeutic touch, or a balloonist explaining geophysics. The right answer wins. Sometimes it takes a few decades, sometimes it doesn't, but if you have the right answer then everybody else be damned. This is the debunking spirit atheists are accused of applying to religion and being wrong to do so. But, really it doesn't work that way. It doesn't matter how many texts you have on the bristliness of God's beard, if he's fictional then he's fictional.

"Any man more right than his neighbor constitutes a majority of one already." - Henry David Thoreau.

It doesn't take much to overthrow lies, it takes one boy to point and laugh and say that "the Emperor has no clothes". This is the nature of not only science but of truth. Lies cannot take the heat and it only takes a gentle wind to collapse a house of cards, so why should atheists be told to not go around blowing at the cherished beliefs of others? Are we to value the belief as worth more than the truth? In reality this is exactly what we are told. And ultimately this is the bane of skepticism and the birth of dogma. If one believes that wanting something to be true, makes it one iota more likely, then that is the only step you need to take in the wrong direction and suddenly any belief becomes acceptable because we are inclined to accept it. Restricting ones beliefs to those which are true, demands that we discount a lot of nonsense the chief-most being religion.

Those who would give up Essential Truth to purchase a little Temporary Comfort, deserve neither Truth nor Comfort.

Tracy said...

Brilliant Post David. One of my professors at the U of A was doing research on decision making processes such as those in your blog post. She gave us many examples of common lines of thought that lead to very bad decision making. Many of these examples were very surprising when you find out that they were very bad or faulty. Often what seems to be intuitively the correct or best decisions is not the best one at all.

magx01 said...

I'm not quite grasping this. How can the odds be 2/3 in favour of a non rejected colour if the red is not offered in the second scenario? The only way I can see the odds being anything other than 1/2 is if 'none' is a choice.

I know I'm wrong, I just don't see where.

Tatarize said...

Because if you are to rank things by any criteria and you rank 3 things then there are only 6 order they could be in.

123, 132, 213, 231, 312, 321

If you express that you like one thing more than another thing, you have ruled out half of the possibilities regardless which thing you liked better.

Say you liked thing 1 more than thing 2. Well that means you only have three remaining orders the items could be in.

123, 132, 312

Because if you like 1 more than 2 (or measure on any criteria) then these are the only remaining orders. In two out of three of them, 3 is going to be liked better than 2. Namely, 132, 312 and only in one of them is 3 still liked less: 123.

It seems really really odd that a choice between two seemingly equal choices should have anything other than even odds, but the previous choice gives us information which changed the odds. The fact that it's counter-intuitive is exactly why people missed it for so long.

magx01 said...

Ah, that is rather counterintuitive, but I get it now. Thanks for the explanation :)