This is definitely a major improvement in situations where people have mostly independent data to aggregate, but in real life independence seems to be fairly rare and using likelihood ratios would cause extremely unnatural updating. In the end you can’t get around sharing all your models and data to solve the independence issue.
I guess my real question is: in a low-bandwidth/low-effort setting like casual conversation what is the best single number to share? If you had to design discourse norms surrounding sharing probabilities in this setting, is likelihood ratio really the right norm?
Albert and Betty should share likelihood ratios, not posterior beliefs.
This is definitely a major improvement in situations where people have mostly independent data to aggregate, but in real life independence seems to be fairly rare and using likelihood ratios would cause extremely unnatural updating. In the end you can’t get around sharing all your models and data to solve the independence issue.
I guess my real question is: in a low-bandwidth/low-effort setting like casual conversation what is the best single number to share? If you had to design discourse norms surrounding sharing probabilities in this setting, is likelihood ratio really the right norm?