A better statement of this idea would be “If the probability of X is p(X), I want the proportion of people who tell me X is true to be p(X)”.
Er… if p(anthropogenic global warning is occurring | all publicly available evidence) is 85%, I’m not sure what I want is 85% of the people to tell me anthropogenic global warning is occurring and 15% of the people to tell me it’s not.
Of course, the best proportion would be 100% of people telling me that p(the_warming)=85%;
but if we limit the outside opinions to simple yes/no statements, then having 85% telling ‘yes’ and 15% telling ‘no’ seems to be far more informative than 100% of people telling ‘yes’ - as that would lead me to very wrongly assume that p(the_warming) is the same as p(2+2=4).
Er… if p(anthropogenic global warning is occurring | all publicly available evidence) is 85%, I’m not sure what I want is 85% of the people to tell me anthropogenic global warning is occurring and 15% of the people to tell me it’s not.
Why not?
Of course, the best proportion would be 100% of people telling me that p(the_warming)=85%; but if we limit the outside opinions to simple yes/no statements, then having 85% telling ‘yes’ and 15% telling ‘no’ seems to be far more informative than 100% of people telling ‘yes’ - as that would lead me to very wrongly assume that p(the_warming) is the same as p(2+2=4).
Why?