Regarding the choice of means, I personally think that the arithmetic mean may make more sense in this case. Suppose you had 3 respondents who gave responses of 0.1, 0.001, and 0.001 as their DALYs from full banning of sugary drinks. If we assume that the individuals are accurately responding regarding their views and (as you are though the rest of this analysis) that utility gains and losses can be linearly aggregated across different individuals, and then the total harm that occurs to the three individuals in the case of a drink ban is 0.102 DALYs. If you had used the geometric mean instead, you would estimate that the total harm from a drink ban was just 0.014 DALYs.
It seems that an arithmetic mean would make more sense if one thinks that differences between the survey respondents’ views reflected true underlying differences in preferences, whereas a geometric mean would make more sense if one thinks that differences between the survey respondents’ views reflected noise in estimates of similar underlying preferences.
As mentioned to Daniel in the other thread: I think both of you are right on the averaging issue—in a number of other areas (e.g. calculating probabilities from a bunch of reference classes), we’ve tended to use the geomean, but that’s for extrapolating from estimates to the true value, as opposed to true individual means to the true population means. The other related issue, however, is whether the sample is representative, and whether we think that highly educated people are more likely to report caring about abstract concerns. Again, will have to think about this, but grateful for the feedback!
Regarding the choice of means, I personally think that the arithmetic mean may make more sense in this case. Suppose you had 3 respondents who gave responses of 0.1, 0.001, and 0.001 as their DALYs from full banning of sugary drinks. If we assume that the individuals are accurately responding regarding their views and (as you are though the rest of this analysis) that utility gains and losses can be linearly aggregated across different individuals, and then the total harm that occurs to the three individuals in the case of a drink ban is 0.102 DALYs. If you had used the geometric mean instead, you would estimate that the total harm from a drink ban was just 0.014 DALYs.
It seems that an arithmetic mean would make more sense if one thinks that differences between the survey respondents’ views reflected true underlying differences in preferences, whereas a geometric mean would make more sense if one thinks that differences between the survey respondents’ views reflected noise in estimates of similar underlying preferences.
As mentioned to Daniel in the other thread: I think both of you are right on the averaging issue—in a number of other areas (e.g. calculating probabilities from a bunch of reference classes), we’ve tended to use the geomean, but that’s for extrapolating from estimates to the true value, as opposed to true individual means to the true population means. The other related issue, however, is whether the sample is representative, and whether we think that highly educated people are more likely to report caring about abstract concerns. Again, will have to think about this, but grateful for the feedback!