Regarding your 1st reason, you seem to be referring to a distinction between the following distributions:
PH = “moral weight of poultry birds relative to humans (QALY/pQALY)” (i.e. poultry birds in the numerator, and humans in the denominator).
HP = “moral weight of humans relative to poultry birds (pQALY/QALY)” (i.e. humans in the numerator, and poultry birds in the denominator).
However, I think both distributions contain the same information, as HP = PH^-1. E(PH) is not equal to E(HP)^-1 (as I noted here), but R = “negative utility of poultry living time as a fraction of the utility of human life” is the same regardless of which of the above metrics is used. For T = “poultry living time per capita (pyear/person/year)”, Q = “quality of the living conditions of poultry (-pQALY/pyear)”, and H = “utility of human life (QALY/person/year)”, the 2 ways of computing R are:
Using PH, i.e. with QALY/person/year in the numerator and denominator of R:
R_PH = (T*PH*Q)/H.
Using HP, i.e. with pQALY/person/year in the numerator and denominator of R:
R_HP = (T*Q)/(HP*H).
Since HP = PH^-1, R_PH = R_HP.
(I have skimmed the Felicifia’s thread, which has loads of interesting discussions! Nevertheless, for the reasons I have been providing here, I still do not understand why calculating expected moral weights is problematic.)
If you used E[HP] as a multiplicative factor to convert human welfare impacts into chicken welfare-equivalent impacts and measure everything in chicken welfare-equivalent terms, your analysis would give different results. In particular, E[HP]>1, which would tell you humans matter more individually (per year) than chickens, but you have E[PH]>1, which tells you chickens matter more than humans. The tradeoffs in this post would favor humans more.
I agree that the following 2 metrics are different:
R_PH_mod = (T*E(PH)*Q)/H.
R_HP_mod = (T*Q)/(E(HP)*H).
However, as far as I understand, it would not make sense to use E(PH) or E(HP) instead of PH or HP. I am interested in determining E(R_PH) = E(R_HP), and therefore the expeced value should only be calculated after all the operations.
In general, to determine a distribution X, which is a function of X1, X2, …, and Xn, via a Monte Carlo simulation, I believe:
E(X) = E(X(X1, X2, …, Xn)).
For me, it would not make sense to replace an input distribution by its mean (as you seem to be suggesting), e.g. because E(A*B)E(A/B) is not equal to E(A)*E(B)E(A)/E(B).
For me, it would not make sense to replace an input distribution by its mean (as you seem to be suggesting), e.g. because E(A*B) is not equal to E(A)*E(B).
I agree in general, but I think you’re modelling A=PH as independent from T, Q and H, so you can get the expected value of the product as equal to the product of expected values. However, I also don’t think you should model PH as independent from the rest.
I gave a poor example (I have now rectified it above), but my general point is valid:
The expected value of X should not be calculated by replacing the input distributions by their means.
For example, for X = 1/X1, E(1/X1) is not equal to 1/E(X1).
As a result, one should not use (and I have not used) expected moral weights.
I agree that the input distributions of my analysis might not be independent. However, that seems a potential concern for any Monte Carlo simulation, not just ones involving moral weight distributions.
Regarding your 1st reason, you seem to be referring to a distinction between the following distributions:
PH = “moral weight of poultry birds relative to humans (QALY/pQALY)” (i.e. poultry birds in the numerator, and humans in the denominator).
HP = “moral weight of humans relative to poultry birds (pQALY/QALY)” (i.e. humans in the numerator, and poultry birds in the denominator).
However, I think both distributions contain the same information, as HP = PH^-1. E(PH) is not equal to E(HP)^-1 (as I noted here), but R = “negative utility of poultry living time as a fraction of the utility of human life” is the same regardless of which of the above metrics is used. For T = “poultry living time per capita (pyear/person/year)”, Q = “quality of the living conditions of poultry (-pQALY/pyear)”, and H = “utility of human life (QALY/person/year)”, the 2 ways of computing R are:
Using PH, i.e. with QALY/person/year in the numerator and denominator of R:
R_PH = (T*PH*Q)/H.
Using HP, i.e. with pQALY/person/year in the numerator and denominator of R:
R_HP = (T*Q)/(HP*H).
Since HP = PH^-1, R_PH = R_HP.
(I have skimmed the Felicifia’s thread, which has loads of interesting discussions! Nevertheless, for the reasons I have been providing here, I still do not understand why calculating expected moral weights is problematic.)
If you used E[HP] as a multiplicative factor to convert human welfare impacts into chicken welfare-equivalent impacts and measure everything in chicken welfare-equivalent terms, your analysis would give different results. In particular, E[HP]>1, which would tell you humans matter more individually (per year) than chickens, but you have E[PH]>1, which tells you chickens matter more than humans. The tradeoffs in this post would favor humans more.
I agree that the following 2 metrics are different:
R_PH_mod = (T*E(PH)*Q)/H.
R_HP_mod = (T*Q)/(E(HP)*H).
However, as far as I understand, it would not make sense to use E(PH) or E(HP) instead of PH or HP. I am interested in determining E(R_PH) = E(R_HP), and therefore the expeced value should only be calculated after all the operations.
In general, to determine a distribution X, which is a function of X1, X2, …, and Xn, via a Monte Carlo simulation, I believe:
E(X) = E(X(X1, X2, …, Xn)).
For me, it would not make sense to replace an input distribution by its mean (as you seem to be suggesting), e.g. because
E(A*B)E(A/B) is not equal toE(A)*E(B)E(A)/E(B).I agree in general, but I think you’re modelling A=PH as independent from T, Q and H, so you can get the expected value of the product as equal to the product of expected values. However, I also don’t think you should model PH as independent from the rest.
I gave a poor example (I have now rectified it above), but my general point is valid:
The expected value of X should not be calculated by replacing the input distributions by their means.
For example, for X = 1/X1, E(1/X1) is not equal to 1/E(X1).
As a result, one should not use (and I have not used) expected moral weights.
I agree that the input distributions of my analysis might not be independent. However, that seems a potential concern for any Monte Carlo simulation, not just ones involving moral weight distributions.