Thanks, I missed the footnote. My best shot at a principled answer: when someone says “0%” they are more precisely saying “a number that rounds to 0%”, just as when someone says a distance is 6.0m they are saying a distance between 5.95m and 6.05m. So very naively we can treat this answer as 0.25% when adding it to the geometric mean.
Another issue is a poll question like “what percentage of French citizens are proficient in French”, where most answers are close to 100%. The geometric mean of 90%, 99%, and 99.9% is about 96%, whereas the geometric mean of 10%, 1%, and 0.1% is 1%. The right algorithm should be symmetric.
Thanks, I missed the footnote. My best shot at a principled answer: when someone says “0%” they are more precisely saying “a number that rounds to 0%”, just as when someone says a distance is 6.0m they are saying a distance between 5.95m and 6.05m. So very naively we can treat this answer as 0.25% when adding it to the geometric mean.
Another issue is a poll question like “what percentage of French citizens are proficient in French”, where most answers are close to 100%. The geometric mean of 90%, 99%, and 99.9% is about 96%, whereas the geometric mean of 10%, 1%, and 0.1% is 1%. The right algorithm should be symmetric.
Yeah, I think in that case the best thing to do would be to use log-odds aggregation. That would be symmetric.