This resulted in a mean moral weight of poultry of 2 QALY/pQALY[14], which implies that 1 year of fully healthy poultry life is 2 times as valuable as 1 QALY.
Unless I'm confused about what you're saying here, this is an unusual enough view that it's worth highlighting. You're saying that we're indifferent been giving a human a year of healthy life, or giving a chicken six months, right?
(I expect most people would give very different numbers than this, at the very least valuing a marginal human year above that of a chicken year.)
Ya, it's better not to take expected values over moral weights, to avoid two envelopes-like problems. The results with moral weight point estimates are much more informative.
Chicken's moral weight 17x human's also seems high to me for the top 5%, although it is conceivable that chickens have greater moral weight. The results for each power of 10 between 1/10,000 and 10 would be most informative to me, although the tables might be pretty cluttered, and I think it would be a pain to get all that from Guesstimate (there are a calculator function and some more advanced things that can help, though).
Thanks for the comment, and introducing me to that post some weeks ago!
1- Note that I only made the Guesstimate model for illustration purposes, and to allow people to choose their own inputs. I am only using the Google Colab program and this Sheets to obtain the post results.
2- I do not find it odd that the moral weight of poultry birds relative to humans is as likely to be smaller than 2*10^-5 (5th percentile) as to be larger than 20 (95th percentile).
3- I tend to think distributions are more informative because they allow us to calculate the expected (mean) results. It would be possible to compute the mean moral weight from point estimates, but I think it makes more sense to assume a continuous probability density function.
4- I do not understand why calculating the expected value of moral weights is problematic. Brian mentions that:
We could naively try to compute expected utility and say that the expected value of creating two elephants is 50% * f1(two elephants) + 50% * f2(two elephants) = 50% * 1/2 + 50% * 2 = 1.25, which is greater than the expected value of 1 for creating the human. However, this doesn't work the way it did in the case of a single utility function, because utility functions can be rescaled arbitrarily, and there's no "right" way to compare different utility functions. For example, the utility function 1000 * f1 is equivalent to the utility function f1, since both utility functions imply the same behavior for a utilitarian. However, if we use 1000 * f1 instead of f1, our naive expected-value calculation now favors the human
I do not see why "utility functions can be rescaled arbitrarily". For the above case, I would say replacing f1 by 1000 f1 is not reasonable, because it is equivalent to increasing the weight of f1 from 50% (= 1/(1 + 1)) to 99.9% (= 1000/(1000 + 1)).
If we had started with 1000 f1 rather than f1 in the first place, then switching it to f1 would seem to give f1 (or 1000 f1, or whatever) too little weight relative to f2, right?
Right, for f3 = 1000 f1, we would need some kind of information to change the weight of f3 from 50% (= 1/(1 + 1)) to 0.1% (= 0.001/(0.001 + 1)).
Note that I do not think the starting functions are arbitrary. For the analysis of this post, for example, each function would represent a distribution for the moral weight of poultry birds relative to humans in QALY/pQALY, under a given theory.
In addition, to determine an overall moral weight given 2 distributions for the moral weight, MWA and MWB, I would weight them by the reciprocal of their variances (based on this analysis from by Dario Amodei):
Ya, we can have different intuitions about how large the chicken's relative moral weight can be. 20 is probably about the maximum I would allow, so the tail would go to more extreme values than I would personally use, and that skews the EV.
My bottom ~5% for chickens would probably be for chickens not being conscious, so 0 moral weight.
I agree. That being said, I think most informed intuitions will imply the mean negative utility of poultry living time is at least comparable to that of human life.
For example, your intuitions about the maximum moral weight might not significantly change the mean moral weight (as long as your intuitions about the intermediate quantiles are not too different from what I considered). Giving 5% weight to null moral weight, and 95% weight to the moral weight following a loguniform distribution whose minimum and maximum are the 5th and 95th percentiles I estimated above, the mean moral weight is 1.
I am also curious about your reasons for setting the maximum moral weight to 20. My distribution implies a maximum of 46, which is not much larger than 20 having in mind that my 95th percentile is 1 M times as large as my 5th percentile.
Ah, sorry, my misunderstanding about your use of Guesstimate.
One reason that taking expectations over moral weights can be misleading is that the cases where chickens matter much less than humans may be because the human's absolute moral weight is much higher than it is in the cases where chickens have closer to average moral weight to humans. Taking expected values of the ratio with human moral weight in the denominator treats human moral weight as fixed, and not allowed to be larger than otherwise in absolute terms. So you could be underweighting cases where humans matter much more, because those have little influence on the expected value of the ratio. I think Brian's article illustrates this, but you could also see the Felicifia thread discussion he references for more.
Another reason is that this involves genuine uncertainty over different theories of consciousness, each of which may define its own hedonic/value scale, and these scales may not be intertheoretically comparable (I expect them not to be). So it's really moral/normative uncertainty, and you need to justify intertheoretic comparisons and the units you normalize by to take expected values over moral uncertainty this way. I haven't found any such attempts persuasive, and I think they can lead to unresolvable disagreements if two groups of beings (humans and intelligent conscious aliens or conscious AI, say) fix their own moral weight and treat the other's as uncertain and relative to their own.
A priori, I would expect any theory of consciousness to produce a mean moral weight of poultry birds relative to humans in pQALY/QALY.
Subsequently (and arguably "naively", according to Brian, Luke and probably you), I would give weights to each of the theories of consciousness, and then determine the weighted expected moral weight (the rest of this sentence was added after this reply) overall moral weight distribution from the weighted mean of the moral weight distributions of the various theories of consciousness (see here).
If I understand you correctly, you do not expect the above to be possible. I would very much welcome any sources explaining why that might be the case!
A priori, I would expect any theory of consciousness to produce a mean moral weight of poultry birds relative to humans in pQALY/QALY.
I think this is probably right, as long as the theory is sufficiently quantitatively precise.
Subsequently (and "naively", according to Brian, Luke and probably you), I would give weights to each of the theories of consciousness, and then determine the weighted expected moral weight.
This treats human moral weight like it's fixed and the same across theories. That needs justification to me, since I don't see why there would be any fact of the matter for such intertheoretic comparisons, and since there are alternative choices to fix that would make different recommendations in practice, e.g. chicken moral weight, alien moral weight, sentient AI moral weight, human toe stubs, chicken torture, an ant eating sugar, and so on. I think what you're proposing is the maximizing expected choice-worthiness/choiceworthiness approach to moral uncertainty, so you could look for discussions and critiques of that. Or, just more general treatments of moral uncertainty.
Which of these do you think is problematic (I have clarified above what I would do; see 2nd bullet)?
Giving weights to each of the theories of consciousness (e.g. as I described here).
Determining the overall moral weight distribution from the weighted mean of the moral weight distributions of the various theories of consciousness.
I might not have been clear about it (if that was the case, sorry!), but:
I actually agree I cannot use expected moral weights to determine the expected negative utility of poultry living time as a fraction of the utility of human life.
I think what you're proposing is the maximizing expected choice-worthiness/choiceworthiness approach to moral uncertainty, so you could look for discussions and critiques of that. Or, just more general treatments of moral uncertainty.
Which of these do you think is problematic (I have clarified above what I would do; see 2nd bullet)?
Giving weights to each of the theories of consciousness (e.g. as I described here).
Determining the overall moral weight distribution from the weighted mean of the moral weight distributions of the various theories of consciousness.
I think the first probably makes some unverifiable and unjustified assumptions. Why normalize by the variance in particular?
It seems similar to variance voting, although variance voting normalizes by the standard deviation instead of the variance, to ensure each has variance 1 (Var(aX)=a2Var(X), so Var(X/√Var(X))=Var(X)/Var(X)=1). It is one approach to moral uncertainty, but there are others, like the parliamentary approach. Why normalize by the variance or standard deviation and not some other measure, for example?
You are taking expected values over products of values, one of which is the moral weight, though, right?
Here is how I would think about it, with variables with units.
Mh = measured units of human welfare from the intervention, in QALYs (total, not per year or per capita, for simplicity)
Mc = measured units of chicken welfare from the intervention, in pQALYs (total, not per year or per capita, for simplicity)
Vh,t = value per measured unit of human welfare on the theory of consciousness t, in units valt/QALY
Vc,t = value per measured unit of chicken welfare on the theory of consciousness t, in units valt/pQALY
Vh,t/Vc,t, basically the relative moral weight of chickens wrt humans humans wrt chickens, in units pQALY/QALY
Vc,t/Vh,t, basically the relative moral weight of humans wrt chickens chickens wrt humans, in units QALY/pQALY
You're trying to calculate, where T is a random variable for the theory of consciousness,
E[Vc,TMc+Vh,TMh]=E[Vc,TMc]+E[Vh,TMh]
but first, the above means taking expectations over values with units valt for different t, like adding values in Fahrenheit and values in Celsius (or grams), so you need to condition on a theory of consciousness T=t first. So, let's look at, for each theory t,
E[Vc,TMc|T=t]+E[Vh,TMh|T=t]=E[Vc,tMc]+E[Vh,tMh]
Then, I think you're effectively assuming Vh,t=1 and that it's unitless, and so you infer the following:
Vc,t=Vc,t/Vh,tVc,tMc=Vc,t/Vh,tMc
But even on a fixed theory of consciousness, there could still be empirical uncertainty about Vh,t, so you shouldn't assume Vh,t is fixed.
I mainly wanted to understand whether you tought the simple fact of attributing weights and then calculating a weighted mean might be intrinsically problematic. Weighting the various moral weight distributions by the reciprocal of their variances is just my preferred solution. That being said:
It is coherent with a bayesian approach (see here).
It mitigates Pascal's Mugging (search for "Pascal’s Mugging refers" in this GiveWell's article). This would not be the case if one used the standard deviation instead of the variance. For a distribution k X:
The mean E(k X) is k E(X).
The variance V(k X) is k^2 V(X).
Therefore the ratio between the mean and standard deviation is inversely proportional to k.
The standard deviation V(k X)^0.5 is k V(X)^0.5.
Therefore the ratio between the mean and standard deviation does not depend on k.
It facilitates the calculation of the weights (as they are solely a function of the distributions).
You are taking expected values over products of values, one of which is the moral weight, though, right?
I am calculating the mean of R = "negative utility of poultry living time as a fraction of the utility of human life" from the mean of R_PH, which is defined here.
Vh,t/Vc,t, basically the relative moral weight of chickens wrt humans, in units pQALY/QALY
I think you meant "humans wrt chickens" (not "chickens wrt humans"), as "h" is in the numerator.
Vc,t/Vh,t, basically the relative moral weight of humans wrt chickens, in units QALY/pQALY
I think you meant "chickens wrt humans" (not "humans wrt chickens"), as "c" is in the numerator.
But even on a fixed theory of consciousness, there could still be empirical uncertainty about Vh,t, so you shouldn't assume Vh,t is fixed.
Let me try to match my variables to yours, based on what I defined here:
R_PH (= R_HP), which is what I am trying to calculate, is akin to (Vc,tMc)/(Vh,tMh), not Vc,tMc+Vh,tMh.
Mc is akin to T*Q, where:
T = "poultry living time per capita (pyear/person/year)".
Q = "quality of the living conditions of poultry (-pQALY/pyear)".
Mh is akin to H = "utility of human life (QALY/person/year)".
PH = "moral weight of poultry birds relative to humans (QALY/pQALY)" is Vc,t/Vh,t.
I did not set Vh,t to 1, because my PH represents Vc,t/Vh,t, not Vc,t.
Note that if you divide a random variable with units by its variance, the result will not be unitless (it'll have the reciprocal units of the random variable), and so you would need to make sure the units match before adding. In this case, with the notation I introduced, you'd have different theory-specific units you're trying to sum across, and this wouldn't work. Dividing by the standard deviation or the range or some other statistics with the same units as the random variable would work.
I think you meant "humans wrt chickens" (not "chickens wrt humans"), as "h" is in the numerator.
(...)
I think you meant "chickens wrt humans" (not "humans wrt chickens"), as "c" is in the numerator.
Woops, yes, good catch.
R_PH (= R_HP), which is what I am trying to calculate, is akin to (Vc,tMc)/(Vh,tMh), not Vc,tMc+Vh,tMh.
I think this is the problem, then. You should not take and use the expected value of the ratio (Vc,tMc)/(Vh,tMh), for basically the reasons I gave previously that you should not in general (except when you condition on enough things or make certain explicit and justified assumptions) take expected values of relative moral weights. Indeed, these are moral weights, just aggregates. When you're interested in the impacts of an intervention on different individuals, you would sum the impacts over each individual, and then take the expected value (or sum expected individual impacts), i.e. E[Vc,tMc+Vh,tMh]. E[(Vc,tMc)/(Vh,tMh)] isn't generally useful for this unless, without further assumptions that are unjustified and plausibly wrong, e.g. (Vc,tMc)/(Vh,tMh) and Vh,tMh are independent.
(You could estimate E[Vc,tMc]/E[Vh,tMh] instead, though, and that could be useful, if you also have an estimate of E[Vh,tMh].)
Note that if you divide a random variable with units by its variance, the result will not be unitless (it'll have the reciprocal units of the random variable), and so you would need to make sure the units match before adding.
I agree, but I do not expect this to be a problem:
A priori, I would expect any theory of consciousness to produce a mean moral weight of poultry birds relative to humans in pQALY/QALY [or QALY/pQALY].
Moreover, if this is not the case, it seems to me that weighting the various moral weight distributions by the reciprocal of their standard deviations (or any other metric, with or without units) would also not be possible:
As you point out, the terms in the numerator would both be unitless, and therefore adding them would not be a problem.
However, the terms in the denominator would have different units. For example, for 2 moral weight distributions MWA and MWB with units A and B, the terms in the denominator would have units A^-1 and B^-1.
Dividing by the standard deviation or the range or some other statistics with the same units as the random variable would work.
As explained above, I do not see how it would be possible to combine the results of different theories if these cannot be expressed in the same units.
E[(Vc,tMc)/(Vh,tMh)] isn't generally useful for this unless, without further assumptions that are unjustified and plausibly wrong, e.g. (Vc,tMc)/(Vh,tMh) and Vh,tMh are independent.
In order to calculate something akin to (Vc,tMc)+(Vh,tMh) instead of (Vc,tMc)/(Vh,tMh), I would compute S_PH = T*PH*Q + H instead of R_PH = T*PH*Q/H (see definitions here), assuming:
All the distributions I defined in Methodology are independent.
All theories of consciousness produce a distribution for the moral weight of poultry birds relative to humans in QALY/pQALY.
PH represents the weighted mean of all these distributions.
Under these assumption (I have added the 1st to Methodology, and the 2nd and 3rd to Moral weight of poultry), E(R_PH) is a good proxy for E(S_PH) (which is what we care about, as you pointed out):
S_PH = (R_PH + 1) H.
I defined H as a constant.
Consequently, the greater is E(R_PH), the greater is E(S_PH).
Normalizing PH (or HP) by its variance on each theory could introduce more arbitrarily asymmetric treatment between animals, overweight theories where the variance is lowest for reasons unrelated to the probability you assign to them (e.g. on aome theories, capacity for welfare may be close to constant), and is pretty ad hoc. I would recommend looking into more general treatments of moral uncertainty instead, and just an approach like variance voting or moral parliament, applied to your whole expected value over outcomes, not PH (or HP).
As I discussed in other comments and the other links discussing the two envelopes problem, H should not be defined as constant (or independent from or uncorrelated with PH) without good argument, and on any given theory of consciousness, it seems pretty unlikely to me, since we still have substantial empirical uncertainty about human (and chicken) brains on any theory of consciousness. You can estimate the things you want to this way, but the assumptions are too strong, so you shouldn't trust the estimates, and this is partly why you get the average chicken having greater capacity for welfare than the average human in expectation. Sometimes PH is lower than on some empirical possibilities not because P is lower on those possibilities, but because H is greater on them, but you've assumed this can't be the case, so may be severely underweighting human capacity for welfare.
If you instead assumed P were constant (although this would be even more suspicious), you'd get pretty different results.
I would recommend looking into more general treatments of moral uncertainty instead, and just an approach like variance voting or moral parliament, applied to your whole expected value over outcomes, not PH (or HP).
I will do, thanks!
You can estimate the things you want to this way, but the assumptions are too strong, so you shouldn't trust the estimates, and this is partly why you get the average chicken having greater capacity for welfare than the average human in expectation.
Note that it is possible to obtain a mean moral weight much smaller than 1 with exactly the same method, but different parameters. For example, changing the 90th percentile of moral weight of poultry birds if these are moral patients from 10 to 0.1 results in a mean moral weight of 0.02 (instead of 2). I have added to this section one speculative explanation for why estimates for the moral weight tend to be smaller.
If you instead assumed P were constant (although this would be even more suspicious), you'd get pretty different results.
I have not defined P, but I agree I could, in theory, have estimated R_PH (and S_PH) based on P = "utility of poultry living time (-pQALY/person/year)". However, as you seem to note, this would be even more prone to error ("more suspicious"). The two methods are mathematically equivalent under my assumptions, and therefore it makes much more sense to me as a human to use QALY (instead of pQALY) as the reference unit.
Michael, once again, thank you so much for all these comments!
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.
In the 3rd point of Summary, I mention that that "The conclusions are very sensitive to the moral weight of poultry birds relative to humans, and the quality of their living conditions in factory farms relative to fully healthy life".
"You're saying that we're indifferent been giving a human a year of healthy life, or giving a chicken six months, right?" Yes, assuming the "six months" would correspond to fully healthy poultry life (in reality, you might need more than 1 chicken).
I am also thinking about writing a short separate post about the mean moral weight, under various distributions, of the animals mentioned in section "Moral weights of various species" of the post from Luke Muehlhauser based on which I modelled the moral weight distribution.
It's one thing to say that it's sensitive, but it's another to base your mainline argument on a really unusual view without flagging that?
Does it really seem plausible to you that we should be indifferent between six months of a happy healthy pet chicken and a year of a happy healthy human?
To highlight better my view, I have moved the interpretation of the results regarding the moral weight and quality of the living condition of poultry from the Methodology to the Discussion.
Regarding your 2nd question, assuming that by "plausible" you mean likely, my answer is yes:
The mean and 82th percentile of the moral weight distribution are equal, which translates into a chance of 80% (20%) of the actual moral weight being smaller (larger) than the expected one.
That being said, I tend to think the focus should be on the expected moral weight, not on the quantile of the expected moral weight (although this is also relevant).
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This analysis estimates the negative utility of poultry living time as a fraction of the utility of human life, under total hedonic utilitarianism (classical utilitarisnism).
The results are presented by country in this spreadsheet (see tab "TOC").
The conclusions are very sensitive to the moral weight of poultry birds relative to humans, and the quality of their living conditions in factory farms relative to fully healthy life. However:
In expectation, the (mean) negative utility of poultry living time seems much larger than that of human life.
Realistically, the (median) negative utility of poultry living time seems comparable to that of human life.
You can use this Guesstimate model to select your preferred inputs.
Acknowledgements
Thanks to Cynthia Schuck-Paim, Jason Schukraft, Lewis Bollard, Matt Sharp, Michael St. Jules and Scott Smith for feedback.
Methodology
The logic of the calculations is illustrated in this Guesstimate model. The tabs mentioned throughout the following sections refer to this spreadsheet.
All the distributions defined in the following sections were assumed to be independent.
Utility of human life
The utility of human life (QALY/person/year) was determined from the ratio between the healthy and full life expectancy. This is imperfect[1], but allows to estimate the utility of human life via a linear regression on life expectancy at birth[2]:
The utility of human life was calculated through the mean life expectancy at birth of the years between 2025 and 2100 (see tab "Future utility of human life").
Data about the future life expectancy at birth was taken from OWID, and is in tab "Future life expectancy".
The linear regression coefficients were calculated based on data about the healthy and full life expectancy at birth from 1990 to 2016 (see tabs "Utility of human life and life expectancy" and "Past utility of human life").
Data about the past healthy life expectancy at birth was taken from OWID, and is in tab "Past healthy life expectancy".
Data about the past life expectancy at birth was taken from OWID, and is in tab "Past life expectancy".
Utility of poultry living time
The utility of poultry living time per capita (-QALY/person/year) is the product of:
The poultry living time per capita[3] (pyear/person/year), which is the product between:
The poultry production per capita (kg/person/year).
The ratio between poultry living time and production (pyear/kg).
Quality of the living conditions of poultry[5] (-pQALY/pyear).
The factors defining the poultry living time per capita were modelled as constants, and the ones regarding the moral weight and quality of the living conditions of poultry as distributions. The following sections provide further details.
The calculations of the utility of poultry living time per capita by country were performed in this Google Colab program[6], and the respective results uploaded to the tab "Utility of poultry living time per capita".
Poultry production per capita
The poultry production per capita between 2025 and 2100 (kg/person/year) was determined from the time-weighted average of those of the following periods[7]:
2025 to 2050: mean between the poultry production per capita in 2025 and 2050[8].
2050 to 2100: half of the poultry production per capita in 2050[9].
The poultry production per capita in 2025 and 2050 was estimated from the ratio between the poultry production and population. The poultry production was calculated considering:
The poultry production by country in 2018 from OWID (see tab "Poultry production").
The poultry production annual growth rate by region, which was estimated by adding the following (see tab "Poultry production annual growth rate"):
Poultry population annual growth rate between 2005/2007 and 2050 from FAO 2012.
Poultry carcass mass annual growth rate between 2005/2007 and 2050, which was calculated based on the poultry carcass mass in 2005/2007 and 2050 from FAO 2012.
The poultry production annual growth rate of a given country equal to that of its respectinve FAO 2012 region (see tab "Regions by country").
Population data were taken from OWID (see tab "Population").
Ratio between poultry living time and production
This metric was estimated from the ratio between the number of poultry birds[11] (OWID; see tab "Poultry livestock counts") and poultry production by country in 2018. The calculations are in tab "Ratio between poultry living time and production".
Moral weight of poultry
The moral weight of poultry (QALY/pQALY) was modelled as the product between:
A loguniform distribution whose 10th and 90th percentiles were set to 5*10^-5 and 10. These are the lower and upper bounds of the "80 % prediction interval" guessed by Luke Muehlhauser here for the moral weight of chickens relative to humans conditional on the former being moral patients[13] (see "Moral weights of various species").
The distribution for the moral weight of poultry might depend on the theory of consciousness. The above product is implicitly assumed to represent the weighted mean of the moral weight distributions of the various theories of consciousness. These are, in turn, supposed to produce (summable) moral weight distributions in QALY/pQALY.
Quality of the living conditions of poultry
The quality of the living conditions of poultry (-pQALY/pyear) was modelled based on data from the Welfare Footprint Project (overviewed here). It was determined from the ratio between[14]:
The sum of the products between the time experiencing and utility of each type of pain.
The time a poultry bird experiences each type of pain (h) was defined as a lognormal distribution with 5th and 95th percentiles equal to the lower and upper bound of the 90 % confidence interval (see this) estimated for a conventional scenario[16]:
For annoying pain: 212.82 and 436.52.
For hurtful pain: 195.08 and 472.12.
For disabling pain: 33.01 and 67.53.
For excruciating pain: 8.830/3600 and 51.57/3600.
The utility of each type of pain experienced by a poultry bird (-pQALY/pyear) was defined as a lognormal distribution with 5th and 95th percentiles equal to[17]:
For annoying pain: 0.01 and 1.
For hurtful pain: 0.1 and 10.
For disabling pain: 1 and 100.
For excruciating pain: 100 and 10 k.
The quality of the living conditions of poultry in -QALY/pyear is the product between the moral weight of poultry (QALY/pQALY) and quality of the living conditions of poultry in -pQALY/pyear.
Results
The location of the results by country in the spreadsheet is as follows[18] (see tab "TOC"):
Utility of human life (QALY/person/year): tab "Future utility of human life".
Poultry living time per capita[19] (pyear/person/year): tab "Poultry living time per capita".
Utility of poultry living time per capita (-QALY/person/year): tab "Utility of poultry living time per capita".
Negative utility of poultry living time as a fraction of the utility of human life: tab "Utility of human life and poultry living time".
Results are also presented below for:
The poultry living time per capita, for 2018, 2025 to 2050, 2050 to 2100, and 2025 to 2100.
The moral weight of poultry.
The quality of the living conditions of poultry.
The mean, 5th percentile, median and 95th percentile of the negative utility of poultry living time as a fraction of the utility of human life between 2025 and 2100, for the mean, 5th percentile, median and 95th percentile countries, relative to all countries and to GW countries[20].
It is worth analysing GW countries to better understand the meat-eater problem:
The concern that some interventions aimed at helping humans might increase animal product consumption and as a result increase farmed animal suffering, e.g. by increasing real income or human population.
Poultry living time per capita
All countries
Poultry living time per capita (pyear/person/year)
2018
2025 to 2050
2050 to 2100
2025 to 2100
Mean
3.78
4.57
2.62
3.27
5th percentile
0.39
0.51
0.29
0.36
Median
2.36
3.02
1.72
2.16
95th percentile
11.54
12.62
7.35
9.05
GW countries
Poultry living time per capita (pyear/person/year)
2018
2025 to 2050
2050 to 2100
2025 to 2100
Mean
1.53
1.97
1.15
1.42
5th percentile
0.33
0.41
0.24
0.3
Median
1.2
1.5
0.86
1.07
95th percentile
2.88
3.74
2.22
2.73
Moral weight of poultry
Moral weight of poultry (QALY/pQALY)
Mean
5th percentile
Median
95th percentile
2.41
1.86*10^-5
0.0179
17.2
Quality of the living conditions of poultry
Quality of the living conditions of poultry
Unit
Mean
5th percentile
Median
95th percentile
-pQALY/pyear
67.3
3.18
23.6
251
-QALY/pyear
162
3.26*10^-4
0.450
609
Negative utility of poultry living time as a fraction of the utility of human life
All countries
Negative utility of poultry living time as a fraction of the utility of human life between 2025 and 2100
Mean
5th percentile
Median
95th percentile
Mean
768
0.13%
178%
2,412
5th percentile
69
0.01%
18%
259
Median
402
0.08%
111%
1,507
95th percentile
2,176
0.37%
515%
6,970
GW countries
Negative utility of poultry living time as a fraction of the utility of human life between 2025 and 2100
Mean
5th percentile
Median
95th percentile
Mean
539
0.11%
150%
2,025
5th percentile
155
0.03%
43%
583
Median
351
0.07%
97%
1,317
95th percentile
1,347
0.27%
374%
5,056
Discussion
Moral weight of poultry
This resulted in a mean moral weight of poultry of 2 QALY/pQALY[21], which implies that 1 year of fully healthy poultry life is 2 times as valuable as 1 year of fully healthy human life. In addition, the mean equals the 82th percentile, which translates into a chance of 80% of the actual moral weight being smaller than the expected one.
Quality of the living conditions of poultry
The mean quality of the living conditions of poultry was estimated to be 60 -pQALY/pyear and 100 -QALY/pyear. These imply 1 h of a poultry bird living in conventional conditions neutralises one of the following:
70 h of fully healthy poultry life.
200 h of fully healthy human life.
This latter value can be contextualised via a comparison with the Weighted Animal Welfare Index of Charity Entrepeneurship (CE). According to this, the negative utility per unit time of "FF [factory-farmed] broiler chicken" is:
1 (= (0.7*56)/(0.99*32)) times the utility per unit time of a "human in a low middle-income country".
0.5 (= (0.7*56)/(0.99*82)) times the utility per unit time of a "human in a high-income country".
In other words, 1 h of a poultry bird living in conventional conditions neutralises 0.5 h (= 0.483/0.927) of fully healthy human life[22]. As a consequence, the moral weight and quality of the living conditions of poultry defined in Methodology imply the mean negative utility of poultry life is 300 (= 162/0.521) times that of the Weighted Animal Welfare Index.
One speculative explanation is that moral weight estimates tend to be underestimates because they respect the median rather than the mean. This might cause significant differences given the moral weight distribution is arguably heavy-tailed (see this note).
The mean quality of the living conditions of poultry in -QALY/year estimated here is 400 times as large as the median.
The median quality of the living conditions of poultry was estimated to be 0.4 -QALY/pyear, which is 90 % (= 0.450/0.521) of the value implied by the Weighted Animal Welfare Index.
Estimating the expected (mean) moral weight is arguably better than providing median values which are as likely to be underestimates as overestimates.
Negative utility of poultry living time as a fraction of the utility of human life
The above results suggests that the negative utility of poultry living time between 2025 and 2100 is:
For the mean country:
In expectation, much larger than that of human life: the mean fraction is 800.
Optimistically, much smaller than that of human life: the 5th percentile fraction is 0.1 %.
Realistically, comparable to that of human life: the mean fraction is 2.
Pessimistically, much larger than that of human life: the 95th percentile fraction is 2 k.
For the mean GW country:
In expectation, much larger than that of human life: the mean fraction is 500.
Optimistically, much smaller than that of human life: the 5th percentile fraction is 0.1 %.
Realistically, comparable to that of human life: the mean fraction is 1.
Pessimistically, much larger than that of human life: the 95th percentile fraction is 2 k.
Consequently, assuming that saving one life could be approximated as a unitary increase of the population size, which is unclear, the reduction of the cost-effectiveness of GiveWell's top life-saving charities caused by accounting for poultry welfare might be significant.
Further work
For better understanding the meat-eater problem, it would be important to:
Narrow the uncertainty regarding the moral weight and quality of the living conditions of poultry.
Define the quality of the living conditions of poultry as a function of the country, and model their future evolution.
1 QALY (quality-adjusted life year) equates to 1 year of a human in perfect health. For this analysis, I considered health as defined by the WHO: "a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity". However, as noted here, "there is considerable disagreement over what the QALY represents, and what it ought to represent". The meaning of 1 QALY is ultimately related to how it was assessed (e.g. whether non-physical health is included).
The coefficient of determination (R^2) for the mean and median country were 52 % and 57 %. Other regressions were tested, but these did not result in significantly better correlations (see tab "Utility of human life and life expectancy"):
The linear regression of the utility of human life on the logarithm of life expectancy at birth resulted in mean and median coefficients of determination of 53 % and 58 %.
The linear regression of the logartithm of the utility of human life on life expectancy at birth resulted in mean and median coefficients of determination of 52 % and 57 %.
The linear regression of the logartithm of the utility of human life on the logarithm of life expectancy at birth resulted in mean and median coefficients of determination of 52 % and 58 %.
1 poultry QALY (pQALY) refers to 1 year of a poultry bird in perfect health. As suggested here, this could be interpreted "as [a chicken] living with all needs met, no or minimal fear of predation and disease-free (e.g. perhaps the best moments on a very good farm animal sanctuary)".
1 -pQALY/pyear means 1 negative poultry QALY per year of poultry living time. The moral value of a poultry bird experiencing 1 negative pQALY (-pQALY) plus 1 year in perfect health is neutral.
The Monte Carlo simulations of Guesstimate rely on 5 k samples, which was not sufficient to stabilise the results. The Google Colab program facilitates the calculation of results by country, and was run with 10 M samples in about 1 min.
Analogous to assuming it decreases linearly between 2050 and 2100, and reaches 0 in 2100, which seems optimistic. The reduction could be caused by moral circle expansion or technological innovation of plant-based products.
Poultry birds could be chickens or turkeys, which could have different moral weights and living conditions. However, the difference does not appear to be significant. Based on the Weighted Animal Welfare Index of Charity Entrepeneurship, the welfare score (whose scale ranges from -100 to 100) of factory-farmed broiler chickens is -56, and that of factory-farmed turkeys is -57.
Choosing a lognormal distribution would lead to a moral weight of 2 kQALY/pQALY, which appears unreasonably high. As noted here, "it appears unlikely that evolution would select for animals with a non-contiguous range that was exclusively extraordinarily strong because extremely intense experiences are distracting in a way that appears likely to reduce fitness".
In addition, selecting a heavy-tailed distribution (e.g. loguniform instead of uniform) also seems more reasonable:
Negative moral weights are avoided.
Intuitively, moral weight seems to be a product (not a sum) of the dimensions of moral weight described here (clock speed of consciousness, unity of consciousness, and unity-independent intensity of valenced aspects of consciousness).
Neutral utility is implicitly assumed when poultry birds are not in pain, what agrees with the WFP modelling for sleeping. According to Box 3 of section "Conventional and Reformed Scenarios" of Chapter 1 of Quantifying pain in broiler chickens:
"We [Welfare Footprint Project] conservatively assume that pain is not felt when individuals are sleeping".
"The duration ranges assumed in the Pain-Tracks presented in this book therefore consider a wide range of hypotheses for the time broiler chickens spend fully awake per day, with minimum and maximum sleeping times of 4 and 10 hours, respectively".
"Since young chicks may sleep for longer periods, we assume minimum and maximum sleeping times of 8 and 14 hours, respectively, in the first two weeks of life".
According to Cynthia Schuck-Paim, "data on typical times of onset of the many welfare challenges affecting broilers is not available in the literature, but our guess would be something between 5% to 20% of the approximately 42 days of existence".
The values are given in the interactive chart "Total Time in Pain" of this page. The 4 types of pain are described in Box 1 of Chapter 1 of Quantifying pain in broiler chickens. Note that it is possible to experience multiple types of pain simultaneously.
The "conventional scenario" is represented by the use of "fast-growing breeds" (in contrast to "a slower-growing strain" of the "reformed scenario"; see section "Conventional and Reformed Scenarios").
The percentiles were defined based on my intuition and the description of the types of pain. The geometric mean of the defined percentiles implies null median utility for 1 h of fully healthy poultry life plus one of the below experiences:
Here, "GW countries" are the ones in 2022 GiveWell cost-effectiveness analysis — version 4 which concern GiveWell's top life-saving charities. These are AMF, Malaria Consortium, Helen Keller International, and New Incentives.
Note that this result refers to the mean moral weight of poultry birds relative to humans, which is not equal to the reciprocal of the mean moral weight of humans relative to poultry birds. This could be understood by noting that the mean of X is not equal to the reciprocal of the mean of 1/X (i.e. E(X) is not equal to 1/E(1/X)).
The total negative utility of the living time regarding factory-farmed fish and poultry might be similar:
Their populations contain a similar number of neurons (but note that this might not be relevant):
10 E neurons for factory-farmed fish: 1 T fish in traditional aquaculture times 10 M neurons of an adult zebrafish.
5 E neurons for factory-farmed broiler chickens: 21.41 G chickens times 221 M neurons of the red junglefowl.
The utility of their living time might be similar:
Based on the Weighted Animal Welfare Index of Charity Entrepeneurship, the welfare score (whose scale ranges from -100 to 100) of factory-farmed fish in traditional aquaculture is -44, and that of factory-farmed broiler chickens is -56.
Unless I'm confused about what you're saying here, this is an unusual enough view that it's worth highlighting. You're saying that we're indifferent been giving a human a year of healthy life, or giving a chicken six months, right?
(I expect most people would give very different numbers than this, at the very least valuing a marginal human year above that of a chicken year.)
Ya, it's better not to take expected values over moral weights, to avoid two envelopes-like problems. The results with moral weight point estimates are much more informative.
https://reducing-suffering.org/two-envelopes-problem-for-brain-size-and-moral-uncertainty/
Chicken's moral weight 17x human's also seems high to me for the top 5%, although it is conceivable that chickens have greater moral weight. The results for each power of 10 between 1/10,000 and 10 would be most informative to me, although the tables might be pretty cluttered, and I think it would be a pain to get all that from Guesstimate (there are a calculator function and some more advanced things that can help, though).
Thanks for the comment, and introducing me to that post some weeks ago!
1- Note that I only made the Guesstimate model for illustration purposes, and to allow people to choose their own inputs. I am only using the Google Colab program and this Sheets to obtain the post results.
2- I do not find it odd that the moral weight of poultry birds relative to humans is as likely to be smaller than 2*10^-5 (5th percentile) as to be larger than 20 (95th percentile).
3- I tend to think distributions are more informative because they allow us to calculate the expected (mean) results. It would be possible to compute the mean moral weight from point estimates, but I think it makes more sense to assume a continuous probability density function.
4- I do not understand why calculating the expected value of moral weights is problematic. Brian mentions that:
I do not see why "utility functions can be rescaled arbitrarily". For the above case, I would say replacing f1 by 1000 f1 is not reasonable, because it is equivalent to increasing the weight of f1 from 50% (= 1/(1 + 1)) to 99.9% (= 1000/(1000 + 1)).
Why is increasing the weight of f1 this much unreasonable?
In my view, the weights of f1 and f2 depend on how much we trust f1 and f2, and therefore they are not arbitrary:
If we had started with 1000 f1 rather than f1 in the first place, then switching it to f1 would seem to give f1 (or 1000 f1, or whatever) too little weight relative to f2, right?
Right, for f3 = 1000 f1, we would need some kind of information to change the weight of f3 from 50% (= 1/(1 + 1)) to 0.1% (= 0.001/(0.001 + 1)).
Note that I do not think the starting functions are arbitrary. For the analysis of this post, for example, each function would represent a distribution for the moral weight of poultry birds relative to humans in QALY/pQALY, under a given theory.
In addition, to determine an overall moral weight given 2 distributions for the moral weight, MWA and MWB, I would weight them by the reciprocal of their variances (based on this analysis from by Dario Amodei):
MW = (MWA/V(MWA) + MWB/V(MWB))/(1/V(MWA) + 1/V(MWB)).
Having this in mind, the higher is the uncertainty of MWA relative to that of MWB, the larger is the weight of MWA.
Ya, we can have different intuitions about how large the chicken's relative moral weight can be. 20 is probably about the maximum I would allow, so the tail would go to more extreme values than I would personally use, and that skews the EV.
My bottom ~5% for chickens would probably be for chickens not being conscious, so 0 moral weight.
I agree. That being said, I think most informed intuitions will imply the mean negative utility of poultry living time is at least comparable to that of human life.
For example, your intuitions about the maximum moral weight might not significantly change the mean moral weight (as long as your intuitions about the intermediate quantiles are not too different from what I considered). Giving 5% weight to null moral weight, and 95% weight to the moral weight following a loguniform distribution whose minimum and maximum are the 5th and 95th percentiles I estimated above, the mean moral weight is 1.
I am also curious about your reasons for setting the maximum moral weight to 20. My distribution implies a maximum of 46, which is not much larger than 20 having in mind that my 95th percentile is 1 M times as large as my 5th percentile.
Ah, sorry, my misunderstanding about your use of Guesstimate.
One reason that taking expectations over moral weights can be misleading is that the cases where chickens matter much less than humans may be because the human's absolute moral weight is much higher than it is in the cases where chickens have closer to average moral weight to humans. Taking expected values of the ratio with human moral weight in the denominator treats human moral weight as fixed, and not allowed to be larger than otherwise in absolute terms. So you could be underweighting cases where humans matter much more, because those have little influence on the expected value of the ratio. I think Brian's article illustrates this, but you could also see the Felicifia thread discussion he references for more.
Another reason is that this involves genuine uncertainty over different theories of consciousness, each of which may define its own hedonic/value scale, and these scales may not be intertheoretically comparable (I expect them not to be). So it's really moral/normative uncertainty, and you need to justify intertheoretic comparisons and the units you normalize by to take expected values over moral uncertainty this way. I haven't found any such attempts persuasive, and I think they can lead to unresolvable disagreements if two groups of beings (humans and intelligent conscious aliens or conscious AI, say) fix their own moral weight and treat the other's as uncertain and relative to their own.
Regarding your 2nd reason:
weighted expected moral weight(the rest of this sentence was added after this reply) overall moral weight distribution from the weighted mean of the moral weight distributions of the various theories of consciousness (see here).If I understand you correctly, you do not expect the above to be possible. I would very much welcome any sources explaining why that might be the case!
I think this is probably right, as long as the theory is sufficiently quantitatively precise.
This treats human moral weight like it's fixed and the same across theories. That needs justification to me, since I don't see why there would be any fact of the matter for such intertheoretic comparisons, and since there are alternative choices to fix that would make different recommendations in practice, e.g. chicken moral weight, alien moral weight, sentient AI moral weight, human toe stubs, chicken torture, an ant eating sugar, and so on. I think what you're proposing is the maximizing expected choice-worthiness/choiceworthiness approach to moral uncertainty, so you could look for discussions and critiques of that. Or, just more general treatments of moral uncertainty.
Which of these do you think is problematic (I have clarified above what I would do; see 2nd bullet)?
I might not have been clear about it (if that was the case, sorry!), but:
Thanks, I will have a look!
I think the first probably makes some unverifiable and unjustified assumptions. Why normalize by the variance in particular?
It seems similar to variance voting, although variance voting normalizes by the standard deviation instead of the variance, to ensure each has variance 1 (Var(aX)=a2Var(X), so Var(X/√Var(X))=Var(X)/Var(X)=1). It is one approach to moral uncertainty, but there are others, like the parliamentary approach. Why normalize by the variance or standard deviation and not some other measure, for example?
You are taking expected values over products of values, one of which is the moral weight, though, right?
Here is how I would think about it, with variables with units.
chickens wrt humanshumans wrt chickens, in units pQALY/QALYhumans wrt chickenschickens wrt humans, in units QALY/pQALYYou're trying to calculate, where T is a random variable for the theory of consciousness,
E[Vc,TMc+Vh,TMh]=E[Vc,TMc]+E[Vh,TMh]but first, the above means taking expectations over values with units valt for different t, like adding values in Fahrenheit and values in Celsius (or grams), so you need to condition on a theory of consciousness T=t first. So, let's look at, for each theory t,
E[Vc,TMc|T=t]+E[Vh,TMh|T=t]=E[Vc,tMc]+E[Vh,tMh]Then, I think you're effectively assuming Vh,t=1 and that it's unitless, and so you infer the following:
Vc,t=Vc,t/Vh,tVc,tMc=Vc,t/Vh,tMcBut even on a fixed theory of consciousness, there could still be empirical uncertainty about Vh,t, so you shouldn't assume Vh,t is fixed.
Thanks for the reply!
I mainly wanted to understand whether you tought the simple fact of attributing weights and then calculating a weighted mean might be intrinsically problematic. Weighting the various moral weight distributions by the reciprocal of their variances is just my preferred solution. That being said:
I am calculating the mean of R = "negative utility of poultry living time as a fraction of the utility of human life" from the mean of R_PH, which is defined here.
I think you meant "humans wrt chickens" (not "chickens wrt humans"), as "h" is in the numerator.
I think you meant "chickens wrt humans" (not "humans wrt chickens"), as "c" is in the numerator.
Let me try to match my variables to yours, based on what I defined here:
Note that if you divide a random variable with units by its variance, the result will not be unitless (it'll have the reciprocal units of the random variable), and so you would need to make sure the units match before adding. In this case, with the notation I introduced, you'd have different theory-specific units you're trying to sum across, and this wouldn't work. Dividing by the standard deviation or the range or some other statistics with the same units as the random variable would work.
Woops, yes, good catch.
I think this is the problem, then. You should not take and use the expected value of the ratio (Vc,tMc)/(Vh,tMh), for basically the reasons I gave previously that you should not in general (except when you condition on enough things or make certain explicit and justified assumptions) take expected values of relative moral weights. Indeed, these are moral weights, just aggregates. When you're interested in the impacts of an intervention on different individuals, you would sum the impacts over each individual, and then take the expected value (or sum expected individual impacts), i.e. E[Vc,tMc+Vh,tMh]. E[(Vc,tMc)/(Vh,tMh)] isn't generally useful for this unless, without further assumptions that are unjustified and plausibly wrong, e.g. (Vc,tMc)/(Vh,tMh) and Vh,tMh are independent.
(You could estimate E[Vc,tMc]/E[Vh,tMh] instead, though, and that could be useful, if you also have an estimate of E[Vh,tMh].)
I agree, but I do not expect this to be a problem:
Moreover, if this is not the case, it seems to me that weighting the various moral weight distributions by the reciprocal of their standard deviations (or any other metric, with or without units) would also not be possible:
As explained above, I do not see how it would be possible to combine the results of different theories if these cannot be expressed in the same units.
In order to calculate something akin to (Vc,tMc)+(Vh,tMh) instead of (Vc,tMc)/(Vh,tMh), I would compute S_PH = T*PH*Q + H instead of R_PH = T*PH*Q/H (see definitions here), assuming:
Under these assumption (I have added the 1st to Methodology, and the 2nd and 3rd to Moral weight of poultry), E(R_PH) is a good proxy for E(S_PH) (which is what we care about, as you pointed out):
Normalizing PH (or HP) by its variance on each theory could introduce more arbitrarily asymmetric treatment between animals, overweight theories where the variance is lowest for reasons unrelated to the probability you assign to them (e.g. on aome theories, capacity for welfare may be close to constant), and is pretty ad hoc. I would recommend looking into more general treatments of moral uncertainty instead, and just an approach like variance voting or moral parliament, applied to your whole expected value over outcomes, not PH (or HP).
As I discussed in other comments and the other links discussing the two envelopes problem, H should not be defined as constant (or independent from or uncorrelated with PH) without good argument, and on any given theory of consciousness, it seems pretty unlikely to me, since we still have substantial empirical uncertainty about human (and chicken) brains on any theory of consciousness. You can estimate the things you want to this way, but the assumptions are too strong, so you shouldn't trust the estimates, and this is partly why you get the average chicken having greater capacity for welfare than the average human in expectation. Sometimes PH is lower than on some empirical possibilities not because P is lower on those possibilities, but because H is greater on them, but you've assumed this can't be the case, so may be severely underweighting human capacity for welfare.
If you instead assumed P were constant (although this would be even more suspicious), you'd get pretty different results.
I will do, thanks!
Note that it is possible to obtain a mean moral weight much smaller than 1 with exactly the same method, but different parameters. For example, changing the 90th percentile of moral weight of poultry birds if these are moral patients from 10 to 0.1 results in a mean moral weight of 0.02 (instead of 2). I have added to this section one speculative explanation for why estimates for the moral weight tend to be smaller.
I have not defined P, but I agree I could, in theory, have estimated R_PH (and S_PH) based on P = "utility of poultry living time (-pQALY/person/year)". However, as you seem to note, this would be even more prone to error ("more suspicious"). The two methods are mathematically equivalent under my assumptions, and therefore it makes much more sense to me as a human to use QALY (instead of pQALY) as the reference unit.
Michael, once again, thank you so much for all these comments!
Regarding your 1st reason, you seem to be referring to a distinction between the following distributions:
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:
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:
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:
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.
Thanks for the comment!
In the 3rd point of Summary, I mention that that "The conclusions are very sensitive to the moral weight of poultry birds relative to humans, and the quality of their living conditions in factory farms relative to fully healthy life".
"You're saying that we're indifferent been giving a human a year of healthy life, or giving a chicken six months, right?"
Yes, assuming the "six months" would correspond to fully healthy poultry life (in reality, you might need more than 1 chicken).
I am also thinking about writing a short separate post about the mean moral weight, under various distributions, of the animals mentioned in section "Moral weights of various species" of the post from Luke Muehlhauser based on which I modelled the moral weight distribution.
It's one thing to say that it's sensitive, but it's another to base your mainline argument on a really unusual view without flagging that?
Does it really seem plausible to you that we should be indifferent between six months of a happy healthy pet chicken and a year of a happy healthy human?
I have now contextualised in this section how unusual my results are, and proposed a speculative explanation.
Thanks for the feedback!
To highlight better my view, I have moved the interpretation of the results regarding the moral weight and quality of the living condition of poultry from the Methodology to the Discussion.
Regarding your 2nd question, assuming that by "plausible" you mean likely, my answer is yes: