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Sewing-Machine comments on Rationality Quotes September 2012 - Less Wrong
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In a world of uncertainty, numbers between 0 and 1 find quite a bit of use.
I understand what it means to believe that an outcome will occur with probability p. I don't know what it means to believe this very strongly.
It means that many kinds of observation that you could make will tend to cause you to update that probability less.
Concretely: Beta(1,2) and Beta(400,800) have the same mean.
I don't understand K to be arguing in favor of high-entropy priors, or T to be arguing in favor of low-entropy priors. My guess is that TimS would call a position a "strong position" if it was accompanied by some kind of political activism.
I think of a strong position as a low-entropy posterior, but rereading I am not confident that's what TimS meant, and I also don't see the connection to politics.
E.T. Jaynes' Probability Theory goes into some detail about that in the chapter about what he calls the A_p distribution.
A possible interpretation is that the "strength" of a belief reflects the importance one attaches to acting upon that belief. Two people might both believe with 99% confidence that a new nuclear power plant is a bad idea, yet one of the two might go to a protest about the power plant and the other might not, and you might try to express what is going on there by saying that one holds that belief strongly and the other weakly.
You could of course also try to express it in terms of the two people's confidence in related propositions like "protests are effective" or "I am the sort of person who goes to protests". In that case strength would be referring to the existence or nonexistence of related beliefs which together are likely to be action-driving.
They might also differ in just how bad an idea they think it is.