Humans are Naturally Tone Deaf to Probabilities
michaelgr.com
michaelgr.com
I like this article because it gives a hypothesis that explains this. But how do you educate people?
When I make cost-benefit analyses involving probabilities, an expected value calculation is really important, and I don't think everyone knows how to do it. So teaching that seems to be valuable. But when people don't have hard probabilities to look at, as the author notes, they seem to overestimate risk. That's something that can't be helped by teaching a formula - you have to teach an intuition.
Strategic games have probably helped me develop this intuition. Starcraft and the board game Puerto Rico both require you to continually estimate risks and rewards of taking certain actions.
It's like learning about cognitive biases. You'll still have most of them, but just being aware that they are there is a good start.
Maybe this could actually be part of education - why should it have to be boring?
This is one of the downsides of democracy.
The answer to this problem, at every scale, is marketing. That's not what a roomful of rationalists wants to hear, of course, but it is the correct answer: Although it is wise to support proposals that are backed up by statistics (because those are the ones that are likely to work!) you also need a sales pitch. You must get people to associate the proposals with mom and apple pie, or with sexy people, or with Progress. Or you must convince them to follow the herd.
However, one thing that I have learned throughout this whole financial crisis is that people do care. And regardless of whether or not the underlying problem(s) are generally understood, the public wants solutions...and good ones.
Political stances are always under a lot of scrutiny from the university professors and media networks. So if the general public cannot analyze and understand the full situation they will instead rely on and digest the consensus of the intellectual community. I cannot see politicians (at least smart ones) worrying about having their their voters understanding their policies. They have bigger fish to fry. They have to be right, they have a record to defend, and they want to carry on a political career that can only advance with a record of retrospectively, good judgment. Matthew Arnold put it best with, "The freethinking of one age is the common sense of the next."
Nonetheless, it was amusing to read the wild-eyed diatribes in the user comments. You couldn't explain the problem in a clearer way, and yet plenty of people simply refuse to accept a result that seems counterintuitive.
http://en.wikipedia.org/wiki/Monty_hall_problem
The article is nearly 6000 words and includes diagrams, detailed mathematical explanations, a very detailed synopsis of the history of the problem, and links to like 50 sources.
All for a probability puzzle. Unbelievable.