The question is whether the likelihood that the 21st experiment will validate the best theory constructed from 20 data points and invalidate the best theory constructed from 10 data points, when that theory also fits the other ten, is greater than the likelihood scientist B is just being dumb.
The likelihood of the former is very hard to calculate, but it’s definitely less than 1⁄11, in other words, over 91% of the time the first theory will still be, if not the best possible theory, good enough to predict the results of one more experiment. The likelihood that a random scientist, who has 20 data points and a theory that explains them, will come up with a different theory which is total crap, is easily more than 1 in 10.
The question is whether the likelihood that the 21st experiment will validate the best theory constructed from 20 data points and invalidate the best theory constructed from 10 data points, when that theory also fits the other ten, is greater than the likelihood scientist B is just being dumb.
The likelihood of the former is very hard to calculate, but it’s definitely less than 1⁄11, in other words, over 91% of the time the first theory will still be, if not the best possible theory, good enough to predict the results of one more experiment. The likelihood that a random scientist, who has 20 data points and a theory that explains them, will come up with a different theory which is total crap, is easily more than 1 in 10.
Ergo, we trust theory A.