I still disagree with your belief that the accuracy of the iterated questions format was lower than the accuracy of the fraction of income format—both questions had standard deviations that were approximately the same multiple of their means.
I think your original strategy of aggregating across the population using the arithmetic mean made sense, and don’t understand what the justification is supposed to be for replacing it with a geometric mean [1]. Concretely, imagine a decision that affects two friends lives, making one 50% worse, and the other 0.005% worse. Presumably you wouldn’t take the geometric mean and say “this basically makes both your lives 0.5% worse, which is not very much”. Instead you might conclude that your friends are different in some way. Similarly, it seems like probably some people like sugary drinks and others don’t, causing significant variation in how much they care about sugary drinks being banned.
As DMR said, that curve seems kind of weird to me—it seems like an unjustified assumption is being used to cut a BOTEC by a factor of 50, which strikes me as suspicious. The real curve is presumably not linear (because otherwise people would buy more sugary drinks on the margin), but intuitively I feel like a factor of 5 adjustment makes way more sense than a factor of 50.
By my analysis of your sheet, if you use a factor of 5 rather than 50 for the decreasing marginal utility, and use the arithmetic mean rather than the geometric mean to aggregate across participants, you get the disutility of freedom as 500% higher than the gains. If you also weight both estimation methods equally, it goes up to 1,100% - which is bigger enough than my BOTEC that I worry you might be making some errors in the opposite direction?
[1] Consider that this analysis is done in the genre of a utilitarian calculation, which usually uses the arithmetic mean of welfare rather than the geometric mean, as is used implicitly in the disease reduction component.
I still disagree with your belief that the accuracy of the iterated questions format was lower than the accuracy of the fraction of income format—both questions had standard deviations that were approximately the same multiple of their means.
I think your original strategy of aggregating across the population using the arithmetic mean made sense, and don’t understand what the justification is supposed to be for replacing it with a geometric mean [1]. Concretely, imagine a decision that affects two friends lives, making one 50% worse, and the other 0.005% worse. Presumably you wouldn’t take the geometric mean and say “this basically makes both your lives 0.5% worse, which is not very much”. Instead you might conclude that your friends are different in some way. Similarly, it seems like probably some people like sugary drinks and others don’t, causing significant variation in how much they care about sugary drinks being banned.
As DMR said, that curve seems kind of weird to me—it seems like an unjustified assumption is being used to cut a BOTEC by a factor of 50, which strikes me as suspicious. The real curve is presumably not linear (because otherwise people would buy more sugary drinks on the margin), but intuitively I feel like a factor of 5 adjustment makes way more sense than a factor of 50.
By my analysis of your sheet, if you use a factor of 5 rather than 50 for the decreasing marginal utility, and use the arithmetic mean rather than the geometric mean to aggregate across participants, you get the disutility of freedom as 500% higher than the gains. If you also weight both estimation methods equally, it goes up to 1,100% - which is bigger enough than my BOTEC that I worry you might be making some errors in the opposite direction?
[1] Consider that this analysis is done in the genre of a utilitarian calculation, which usually uses the arithmetic mean of welfare rather than the geometric mean, as is used implicitly in the disease reduction component.