Here's another installment of rationality quotes. The usual rules apply:
- Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself.
- Do not quote from Less Wrong itself, Overcoming Bias, or HPMoR.
- No more than 5 quotes per person per monthly thread, please.
If I throw a die once and it comes up heads I'm going to be confused. Now, assuming you meant "toss a coin and it comes up heads six times out of ten".
What is your intended 'correct' answer to the question? I think I would indeed hesitantly update a very (very) tiny bit in the direction of the coin being biased but different priors regarding the possibility of the coin being biased in various ways and degrees could easily make the update be towards not-biased. I'd significantly lower p(the coin is biased by having two heads) but very slightly raise p(the coin is slightly heavier on the tails side), etc.
My intended correct answer is that, on this data, you technically can adjust your belief very slightly; but because the prior for a biased coin is so tiny, the update is not worth doing. The calculation cost way exceeds any benefit you can get from gruel this thin. I would say "Null hypothesis [ie unbiased coin] not disconfirmed; move along, nothing to see here". And if you had a political reason for wishing the coin to be biased towards heads, then you should definitely not make any such update; because you certainly wouldn't have done so, if ta... (read more)