(1) One issue weāve had issues with is large variance in estimatesāand we typically try to use the geometric (rather than arithmetic mean) to better capture the differences in magnitudes. Our previous average of different peopleās estimates used a pure arithmetric mean (because of the presence of zeroesāpeople didnāt value drinking sugary drinks at all, I guess).
Partly because of our discussion on weighing, I tried a different approach of getting a geomean of the non-zeroes, and then creating a weighted average with the zeroes. The results are pretty sensitive ā 0.0002 with this mixed method vs 0.001 with a pure arithmetric mean. I do think the former is probably the better method, insofar as arithmetric means are too sensitive to the high-end number, and have updated accordinglyābut Iām not sure if thereās a good answer one way or another!
(2) For diminishing marginal returnsāI basically think of it in terms of a graph (x axis is number of sugary drinks you can buy with your current income, y-axis is āfreedom of choiceā), and I take the relationship to be y=x^0.1. The proportional reduction in the number of sugar drinks you can buy is estimated like this: (a) calculating how much you can buy without the tax (an arbitrary USD 1000, divided by prevailing prices sourced from Walmart), (b) calculating how much you can buy after the tax (USD 1000, divided by prices subject to 20% tax), and then (c) taking ABS((b-a)/āa) to get the proportional reduction (0.17, for a 20% price rise). (d) 1-c then gives how much you can still buy, proportionally (0.83). (d) Then, using the y=x^0.1 formula, we take (1-d)^0.1 to find that 98% of āfreedom of choiceā still remains, and correspondingly, there was a 2% reduction.
Obviously, a whole bunch of assumptions are made, most significantly about the curve and DMRāany thoughts you have would be welcome!
Then, using the y=x^0.1 formula, we take (1-d)^0.1 to find that 98% of āfreedom of choiceā still remains, and correspondingly, there was a 2% reduction.
The number in the sheet is a 0.2% reduction, not a 2% reduction. [EDIT: my bad, itās a 2% reduction, thereās just another factor of 10 reduction that I mistakenly lumped into that]
I still disagree with your belief that the accuracy of the iterated questions format was lower than the accuracy of the fraction of income formatāboth 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 donāt 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 wouldnāt take the geometric mean and say āthis basically makes both your lives 0.5% worse, which is not very muchā. Instead you might conclude that your friends are different in some way. Similarly, it seems like probably some people like sugary drinks and others donāt, causing significant variation in how much they care about sugary drinks being banned.
As DMR said, that curve seems kind of weird to meāit 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.
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 respondentsā views reflected true underlying differences in preferences, whereas a geometric mean would make more sense if one thinks that differences between the survey respondentsā 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 issueāin a number of other areas (e.g. calculating probabilities from a bunch of reference classes), weāve tended to use the geomean, but thatās 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!
Very interesting, thanks for the detailed explanation! Iāll be curious to see what Daniel says, but my intuition is that y=x^0.1 is a generous assumption for the shape of the freedom of choice utility curve. I do agree that Iād expect utility losses from freedom of choice to be nonlinear, but the function youāre using would imply that 80% of freedom of choice is preserved when sugary drink consumption has been cut by 90%. Moreover, my intuition is that the welfare losses due to reduced sugary drink consumption are also partially due to not getting tasty drinks anymore (thinking for myself, I wouldnāt really mind not having sugary drinks, but I would definitely be sad in the similar case of not having sugary foods). That component of the utility losses seems like it would be closer to linear.
Hi Danielāthanks for all the previous feedback. I did a tentative update to the CEA (https://āādocs.google.com/āāspreadsheets/āād/āā1kdnvaeP5iAUAF_Fgcf_ZgZDci2cYV02M51N7HMTMOBQ/āāedit#gid=1248986269), taking into account the points you raised plus some other considerations. I also separated out the analysis into its own tab, hopefully for better clarity.
(1) One issue weāve had issues with is large variance in estimatesāand we typically try to use the geometric (rather than arithmetic mean) to better capture the differences in magnitudes. Our previous average of different peopleās estimates used a pure arithmetric mean (because of the presence of zeroesāpeople didnāt value drinking sugary drinks at all, I guess).
Partly because of our discussion on weighing, I tried a different approach of getting a geomean of the non-zeroes, and then creating a weighted average with the zeroes. The results are pretty sensitive ā 0.0002 with this mixed method vs 0.001 with a pure arithmetric mean. I do think the former is probably the better method, insofar as arithmetric means are too sensitive to the high-end number, and have updated accordinglyābut Iām not sure if thereās a good answer one way or another!
(2) For diminishing marginal returnsāI basically think of it in terms of a graph (x axis is number of sugary drinks you can buy with your current income, y-axis is āfreedom of choiceā), and I take the relationship to be y=x^0.1. The proportional reduction in the number of sugar drinks you can buy is estimated like this: (a) calculating how much you can buy without the tax (an arbitrary USD 1000, divided by prevailing prices sourced from Walmart), (b) calculating how much you can buy after the tax (USD 1000, divided by prices subject to 20% tax), and then (c) taking ABS((b-a)/āa) to get the proportional reduction (0.17, for a 20% price rise). (d) 1-c then gives how much you can still buy, proportionally (0.83). (d) Then, using the y=x^0.1 formula, we take (1-d)^0.1 to find that 98% of āfreedom of choiceā still remains, and correspondingly, there was a 2% reduction.
Obviously, a whole bunch of assumptions are made, most significantly about the curve and DMRāany thoughts you have would be welcome!
The number in the sheet is a 0.2% reduction, not a 2% reduction. [EDIT: my bad, itās a 2% reduction, thereās just another factor of 10 reduction that I mistakenly lumped into that]
I still disagree with your belief that the accuracy of the iterated questions format was lower than the accuracy of the fraction of income formatāboth 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 donāt 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 wouldnāt take the geometric mean and say āthis basically makes both your lives 0.5% worse, which is not very muchā. Instead you might conclude that your friends are different in some way. Similarly, it seems like probably some people like sugary drinks and others donāt, causing significant variation in how much they care about sugary drinks being banned.
As DMR said, that curve seems kind of weird to meāit 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.
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 respondentsā views reflected true underlying differences in preferences, whereas a geometric mean would make more sense if one thinks that differences between the survey respondentsā 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 issueāin a number of other areas (e.g. calculating probabilities from a bunch of reference classes), weāve tended to use the geomean, but thatās 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!
Very interesting, thanks for the detailed explanation! Iāll be curious to see what Daniel says, but my intuition is that y=x^0.1 is a generous assumption for the shape of the freedom of choice utility curve. I do agree that Iād expect utility losses from freedom of choice to be nonlinear, but the function youāre using would imply that 80% of freedom of choice is preserved when sugary drink consumption has been cut by 90%. Moreover, my intuition is that the welfare losses due to reduced sugary drink consumption are also partially due to not getting tasty drinks anymore (thinking for myself, I wouldnāt really mind not having sugary drinks, but I would definitely be sad in the similar case of not having sugary foods). That component of the utility losses seems like it would be closer to linear.