As for medians rather than means, our main concern there was just that means tend to be skewed toward extremes. But we can generate the means if itās important!
Do you think the extremes of your moral weight distributions are reasonable? If so, even if the mean is skewed towards them, it would become more accurate. Anyways, I would say sharing the mean would be important, such that people could see how much influence extremes have (i.e. how heavy-tailed is the moral weight distribution).
Sorry for the slow reply, Vasco. Here are the means you requested. My vote is that if people are looking for placeholder moral weights, they should use our 50th-pct numbers, but I donāt have very strong feelings on that. And I know you know this, but I do want to stress for any other readers that these numbers are not āmoral weightsā as that term is often used in EA. Many EAs want one number per species that captures the overall strength of their moral reason to help members of that species relative to all others, accounting for moral uncertainty and a million other things. We arenāt offering that. The right interpretation of these numbers is given in the main post as well as in our Intro to the MWP.
My vote is that if people are looking for placeholder moral weights, they should use our 50th-pct numbers, but I donāt have very strong feelings on that.
Are there concrete reasons for neglecting large welfare ranges which have not been considered in the estimation of the welfare range distributions? If not, why should one use the medians instead of the means? The mean welfare range of shrimp is 4.67 (= 0.21/ā0.045) times the median welfare range of shrimp, whereas the mean welfare range of chickens is 1.00 (= 0.368/ā0.368) times the median welfare range of chickens. So using medians instead of means makes the cost-effectiveness of helping chickens as a fraction of that of helping shrimp 4.67 times as high.
Hi Vasco, Thanks for the good question! I think itās important to note that there are (at least) 3 types of model choices and uncertainty at work: a) we have a good deal of uncertainty about each theory of welfare represented in the model, b) we donāt have a ton of confidence that the function we included to represent each theory of welfare is accurate (especially the undiluted experiences function, which partially drives the high mean results), a) we could have uncertainty that our approach to estimating welfare ranges in general is correct, but weāve not included this overall model uncertainty. For instance, our model has no āpriorā welfare ranges for each species, so the distribution output by the calculation entirely determines our judgement of the welfare range of the species involved. We also might be uncertain that simply taking a weighted mixture of each theory of welfare is a good way to arrive at an overall judgement of welfare ranges. Etc.
Our preliminary method used in this project incorporates model uncertainty in the form of (a) by mixing together the separate distributions generated by each theory of welfare, but we donāt incorporate model uncertainty in the ways specified by (b) or (c). I think these additional layers of uncertainty are epistemically important, and incorporating them would likely serve to ādampenā the effect that the mean result of the model affects our all-things-considered judgement about the welfare capacity of any species. Using the median is a quick (though not super rigorous or principled) of encoding that conservatism/āadditional uncertainty into how you apply the moral weight projectās results in real life. But there are other ways to aggregate the estimates, which could (and likely would) be better than using the median.
I think these additional layers of uncertainty are epistemically important, and incorporating them would likely serve to ādampenā the effect that the mean result of the model affects our all-things-considered judgement about the welfare capacity of any species.
I tend to agree.
But there are other ways to aggregate the estimates, which could (and likely would) be better than using the median.
I wondered whether it would be better for you to aggregate the results from the different models with the geometric mean of odds. For example, if models 1 and 2 implied a probability of 50 % and 90 % of the welfare range being smaller than 0.2, corresponding to odds of 1 (= 0.5/ā(1 ā 0.5)) and 9 (= 0.9/ā(1 ā 0.9)), the aggregated model would imply odds of 3 (= (1*9)^0.5) of the welfare range being smaller than 0.2, corresponding to a probability of 75 % (= 1/ā(1 + 1ā3)). There is some evidence for using the geometric mean of odds, so I believe an approach like this combined with using the means of the aggregated distributions would be better than your approach of using the medians of the final distributions at the end.
Thanks for clarifying and sharing the means, Bob! There are some significant differences to the medians for some species, so it looks like it would be important to see whether the extremes of the distributions are being well represented.
Hi again,
Sorry, I forgot to touch on this point:
Do you think the extremes of your moral weight distributions are reasonable? If so, even if the mean is skewed towards them, it would become more accurate. Anyways, I would say sharing the mean would be important, such that people could see how much influence extremes have (i.e. how heavy-tailed is the moral weight distribution).
Sorry for the slow reply, Vasco. Here are the means you requested. My vote is that if people are looking for placeholder moral weights, they should use our 50th-pct numbers, but I donāt have very strong feelings on that. And I know you know this, but I do want to stress for any other readers that these numbers are not āmoral weightsā as that term is often used in EA. Many EAs want one number per species that captures the overall strength of their moral reason to help members of that species relative to all others, accounting for moral uncertainty and a million other things. We arenāt offering that. The right interpretation of these numbers is given in the main post as well as in our Intro to the MWP.
Are there concrete reasons for neglecting large welfare ranges which have not been considered in the estimation of the welfare range distributions? If not, why should one use the medians instead of the means? The mean welfare range of shrimp is 4.67 (= 0.21/ā0.045) times the median welfare range of shrimp, whereas the mean welfare range of chickens is 1.00 (= 0.368/ā0.368) times the median welfare range of chickens. So using medians instead of means makes the cost-effectiveness of helping chickens as a fraction of that of helping shrimp 4.67 times as high.
Hi Vasco,
Thanks for the good question! I think itās important to note that there are (at least) 3 types of model choices and uncertainty at work:
a) we have a good deal of uncertainty about each theory of welfare represented in the model,
b) we donāt have a ton of confidence that the function we included to represent each theory of welfare is accurate (especially the undiluted experiences function, which partially drives the high mean results),
a) we could have uncertainty that our approach to estimating welfare ranges in general is correct, but weāve not included this overall model uncertainty. For instance, our model has no āpriorā welfare ranges for each species, so the distribution output by the calculation entirely determines our judgement of the welfare range of the species involved. We also might be uncertain that simply taking a weighted mixture of each theory of welfare is a good way to arrive at an overall judgement of welfare ranges. Etc.
Our preliminary method used in this project incorporates model uncertainty in the form of (a) by mixing together the separate distributions generated by each theory of welfare, but we donāt incorporate model uncertainty in the ways specified by (b) or (c). I think these additional layers of uncertainty are epistemically important, and incorporating them would likely serve to ādampenā the effect that the mean result of the model affects our all-things-considered judgement about the welfare capacity of any species. Using the median is a quick (though not super rigorous or principled) of encoding that conservatism/āadditional uncertainty into how you apply the moral weight projectās results in real life. But there are other ways to aggregate the estimates, which could (and likely would) be better than using the median.
Thanks for the good reply too, Laura.
I tend to agree.
I wondered whether it would be better for you to aggregate the results from the different models with the geometric mean of odds. For example, if models 1 and 2 implied a probability of 50 % and 90 % of the welfare range being smaller than 0.2, corresponding to odds of 1 (= 0.5/ā(1 ā 0.5)) and 9 (= 0.9/ā(1 ā 0.9)), the aggregated model would imply odds of 3 (= (1*9)^0.5) of the welfare range being smaller than 0.2, corresponding to a probability of 75 % (= 1/ā(1 + 1ā3)). There is some evidence for using the geometric mean of odds, so I believe an approach like this combined with using the means of the aggregated distributions would be better than your approach of using the medians of the final distributions at the end.
Thanks for clarifying and sharing the means, Bob! There are some significant differences to the medians for some species, so it looks like it would be important to see whether the extremes of the distributions are being well represented.