This is an interesting exercise. I imagine that Luke’s estimates were informed by his uncertainty about multiple incompatible theories / considerations and so any smooth distribution won’t properly reflect the motivations that lead to those estimates. Do you think these results suggest anything about what a lumpy distribution would say?
If the moral weight distribution is based on 2 theories A and B which produce distributions (lumps) MWA and MWB, and we think A and B are equally valid, the moral weight and expected moral weight would be:
MW = 0.5 MWA + 0.5 MWB.
E(MW) = 0.5 E(MWA) + 0.5 E(MWB)
It is unclear whether this expected moral moral weight would be smaller/larger than the one of the continuous case. Luke only provides 2 quantiles, but MWA and MWB are defined by 4 parameters (assuming 2 for each).
Eventually, to derive the 4 paramers, one could further assume that the variance of MWA equals that of MWB, and that the median of MW equals the arithmetic/geometric mean between Luke’s lower and upper bound. However, I do not know whether these assumptions make sense.
This is an interesting exercise. I imagine that Luke’s estimates were informed by his uncertainty about multiple incompatible theories / considerations and so any smooth distribution won’t properly reflect the motivations that lead to those estimates. Do you think these results suggest anything about what a lumpy distribution would say?
Thanks for commenting!
If the moral weight distribution is based on 2 theories A and B which produce distributions (lumps) MWA and MWB, and we think A and B are equally valid, the moral weight and expected moral weight would be:
MW = 0.5 MWA + 0.5 MWB.
E(MW) = 0.5 E(MWA) + 0.5 E(MWB)
It is unclear whether this expected moral moral weight would be smaller/larger than the one of the continuous case. Luke only provides 2 quantiles, but MWA and MWB are defined by 4 parameters (assuming 2 for each).
Eventually, to derive the 4 paramers, one could further assume that the variance of MWA equals that of MWB, and that the median of MW equals the arithmetic/geometric mean between Luke’s lower and upper bound. However, I do not know whether these assumptions make sense.