Does the table in section 3.2 take the geometric mean for each of the 6 components?
From footnote 7 it looks like it does, but if it does then I don’t see how this gives such a different bottom line probability from the synthetic method geomean in section 4 (18.7% vs. 1.65% for all respondents). Unless some probabilities are very close to 1, and those have a big influence on the numbers in the section 3.2 table? Or my intuitions about these methods are just off.
That’s correct—the table gives the geometric mean of odds for each individual line, but then the final line is a simple product of the preceding lines rather than the geometric mean of each individual final estimate. This is a tiny bit naughty of me, because it means I’ve changed my method of calculation halfway through the table—the reason I do this is because it is implicitly what everyone else has been doing up until now (e.g. it is what is done in Carlsmith 2021) , and I want to highlight the discrepancy this leads to.
Does the table in section 3.2 take the geometric mean for each of the 6 components?
From footnote 7 it looks like it does, but if it does then I don’t see how this gives such a different bottom line probability from the synthetic method geomean in section 4 (18.7% vs. 1.65% for all respondents). Unless some probabilities are very close to 1, and those have a big influence on the numbers in the section 3.2 table? Or my intuitions about these methods are just off.
That’s correct—the table gives the geometric mean of odds for each individual line, but then the final line is a simple product of the preceding lines rather than the geometric mean of each individual final estimate. This is a tiny bit naughty of me, because it means I’ve changed my method of calculation halfway through the table—the reason I do this is because it is implicitly what everyone else has been doing up until now (e.g. it is what is done in Carlsmith 2021) , and I want to highlight the discrepancy this leads to.