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.
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.