I read with sympathy your lament on the difficulties of persuasion, as illustrated by lingering contention over the Monty Hall problem. This problem of persuasion afflicts many areas of science, notably including the creation/evolution debate, where stout fundamentalists insist the world is 6000 years old, as made by godly fiat. Their source is the same ancient text that describes the earth as flat.
But I digress. The Monty Hall problem seems to me to be an instance of a broader debate in statistics, between the classicists and the Bayesians. Classicists approach each statistical question as fresh, discounting history. With that mindset, and Monty having made his choice, they are confronted with two doors and, finding no reason to discriminate, hold that either one is equally likely to conceal the car (my wife, an animal lover, would rather have the goat).
A Bayesian on the other hand would take history into account. Monty's choice would signal--assuming he had advance knowledge of the goods behind the doors-- that switching doors would double the odds of winning (assuming one prefers the car).
This debate among statisticians has consequences. Classical statistics still dominates education, with the Bayesian approach taught, if at all, as an afterthought. This classical dominance explains why Marilyn vos Savant received so many angry responses from PhDs to her original Parade article.
Education and statistics would be better served by a deep and thoughtful exploration of how problem history affects the abstract idea of probability.
posted by Richard LeVitt
August 16, 2008