Thanks, Max, for the post, and to everyone for the comments.
I think that the objection in the post is a good one. Indeed, I think it's probably the best one. That's why I considered it in the paper: it's what I have in mind on pp. 273-4 (in the published version, 24-5 in the preprint). Those pages were inspired by the diamond-water paradox.
1. Before I reiterate my response to that objection, it might be helpful to present a simpler version of my main argument. Compare two toy economies. In the first, Worker 1 makes all the difference to output—their MRP=Y—but their labor wouldn't make any difference in the absence of the labor of Worker 2. Worker 2 makes all the difference to the difference that Worker 1 makes. And this will show up as Worker 1's MRP: making a difference to the difference that Worker 1 makes is itself to make a difference to output. So reward according to MRP has them split output evenly. In the second two economy, Worker 1 again makes all the difference, but this time depends not on a single other worker but on a group of workers, and what they only together do. Their individual MRPs, suppose, are very small. So reward according to MRP has Worker 1 take home almost all of output. My central claim is that the distributive outcome in this second economy is unfair. That claim does not depend on a failure to appreciate the diamond-water paradox; it does not require denying the obvious fact that the individual labor of Worker 1 is more valuable than the individual labor of Worker 2 through Worker n, which fact, we can suppose, is explained by the former's scarcity.
2. In the paper—on the pages mentioned above—I write: "While a worker’s marginal revenue product depends on both that worker and on groups of others, that worker is an individual; the groups are groups. In particular, the groups are unstructured or diffuse collectives—roughly, collectives that are not agentially united. (A classic example: “polluters.”) And what unstructured collectives make happen, the thought goes, in no way bears on what their members deserve." Max writes: "The workers of G don’t deserve any of W’s marginal product because each of them, on the margin, is unessential for it. That W would suffer if G and all its substitutes disappeared together shouldn’t credit the members of G any more than the fact that food is worth everything in a famine should make the prices at the grocery store go up." A common view in philosophy is that it is at least sometimes the case that members of unstructured collectives have reasons for action, and can be rendered deserving, on the basis of what the collective makes happen. This is why an individual polluter, for example, can be blamed even if their marginal contribution to the harms produced by that kind of pollution (not: their marginal contribution to the amount of pollution) is zero.
3. It is not obvious that this common view is correct. There is a famous challenge to it, which the philosopher Julia Nefsky dubbed "the inefficacy problem": How can these individuals be rendered deserving by an action that by hypothesis makes no difference? It's very weird! My argument presupposes that one of the extant solutions to the inefficacy problem can be solved, such that the "common view" mentioned above is vindicated. In the blog post, as I understand it, Max rejects this view. That is a reasonable position, but it is less a straight-on objection to my argument than a denial of one of its presuppositions.
4. Suppose that you do indeed think that the notion of individuals being rendered deserving on the basis of what a collective makes happens is implausible. Here is just one observation that might move you. It is not the case that, in the second toy economy above, the entire story of "value" in that economy is a story of individual difference-making. The collective value of the group's labor does not disappear: it shows up in the individual value of Worker 1's labor, in the straightforward sense that, in the absence of that collective labor, the value of Worker 1's labor would (by construction) be zero. This is what I had in mind when I wrote, in the Jacobin summary of my paper: "For economists tempted to dismiss this as an unproblematic and trivial consequence of the fact that wages are set by marginal and not total or average products, the point is that the marginal productivity of the one worker is itself partly determined by the total product — of the other workers." This sentence was also meant to anticipate the invocation of the diamond-water paradox. (I've been waiting for a blog post like this since I wrote the paper.) This is not a knockdown argument, but I do hope that it has some force for those who accept the view that it is only the value of individuals' labor that matters morally. Why is it okay for Worker 1 to in effect get credit for the collective value of the labor of Worker 2 through n, when Worker 2 through n don't themselves get credit?
A few commenters have wondered whether any economists have read the paper. They have, including an economist at Columbia, whose department was mentioned above. I've also presented the sequel paper to a room of mostly economists. As I mentioned, the best objection that I consider in the paper was inspired by the diamond-water paradox, although I was aware of that paradox before talking to any economists about the paper.
More generally, the paper was partly motivated by what I think is a bad (normative) response to the role of scarcity in the marginalist theory of distribution; here I think Max and I agree. You often hear people dismiss reward according to MRP out of hand by saying: MRP doesn't reflect your "contribution," it reflects the scarcity of your labor. But as Max points out these are not competing claims; all else equal scarcer labor makes a bigger contribution. On this note, to repeat, I am nowhere denying that the workers Max thinks perform more valuable labor in fact perform more valuable labor; my claim is about whether they can take all the moral credit for that value.
I think that economics is important, and that more political philosophy should engage with it. With the help of an economist friend and claude, I've been learning econometrics in part for this reason, but also so that I can read econ papers for myself. If there are any economists reading this who are interested in talking more, please email me. I'm especially interested in feedback on the sequel paper: https://ebehrle.github.io/scc.pdf. If you didn't like the first paper, I think you're going to hate this one... But I also welcome corrections to the first paper, though it's already published. (One of the commenters suggested that an LLM identified some big problems. I asked one of the Claude models to come up with objections last month and didn't find any of them compelling.)
I think the clearest way to respond is through your last argument.
You say "Suppose that you do indeed think that the notion of individuals being rendered deserving on the basis of what a collective makes happens is implausible"
But this is not what I believe. Indeed, in my view "what the collective makes happen" is the most important basis of desert for both Worker 1 and Workers 2-n.
Under point 4 you explain how the value of Worker 1's labor rises with the effort of all the other workers and falls to zero without it. But just as the collective efforts of those workers shows up in Worker 1's marginal product, it also shows up in each Worker 2-n's marginal product, just with the opposite effect. In the absence of that collective labor, the value of Worker 1's labor is zero and the value of each Worker 2-n's labor would be all of output. Vice-versa with the collective labor, Worker 1's labor is worth nearly all of output and each Worker 2-n's labor is worth near zero.
The reason why each Worker from 2-n deserves only their small marginal product is exactly because of what the collective makes happen without them.
"Why is it okay for Worker 1 to in effect get credit for the collective value of the labor of Worker 2 through n, when Worker 2 through n don't themselves get credit?"
The answer to this is not that economists take an unreasonably individualistic view of production that ignores collective effort. Rather, the answer is that the collective value of the labor of Worker 2 through n is a credit to Worker 1, because their effort is complementary to Worker 1's effort, while being a demerit for Workers 2 through n, because the effort of each of these workers is a substitute for the effort of all the others.
So I don't think that the notion of individuals being rendered (un-)deserving on the basis of what a collective makes happens is implausible. I just think your arguments are accounting for that desert in the wrong direction. What the collective makes happen can make your contribution more valuable by complementing it, or less valuable by substituting for it.
This explains why the distributive outcome in the second economy under point 1 is fair. The collective impact of n workers in G makes worker n+1 ineffectual and thus undeserving. Applying this argument to all workers in G leads to the counterintuitive conclusion that the sum of the marginal values is less than the total value, but it's still the correct argument.
Consider the case of carbon emissions. (1) Total emissions are harmful but (2) for any given emitter, it is plausible that they make no difference to the harms of total emissions.
Note that this does not look like a case where the n'th emitter does not make a difference because (n-m) emitters are sufficient for the harms of total emissions. It is not really a case of inefficacy via redundancy and substitution. It looks like a "non-threshold case." (The n'th worker doesn't maker a difference; the n-1'th doesn't; and and on and on.) Whether it really is--whether there are any non-threshold cases--is a controversial question within the philosophical literature on collective impact.
But, skipping over that, what I am suggesting is: just as a common view says that each individual polluter deserves some blame on the basis of the harms of total emissions, despite none making a difference to those harms, each worker in a collective might deserve some credit on the basis of the benefits of their collective labor, despite each making only a tiny difference to those benefits (differences that sum to less than the total).
This is just a different understanding of the normative significance of collective impact. Whether that understanding is correct, or whether your directionally opposite alternative is correct, is a normative question, not an empirical one. I think that adopting your alternative would require us to abandon moral judgments that we make in other cases of collective impact, like pollution. Sometimes a group makes a difference much bigger than the sum of the differences that its members make, and we seem to think that the first difference redounds to the (dis)credit of the members. We do not think that marginal inefficacy renders one undeserving. That's the heart of it.
This is getting into the weeds, but it's maybe worth saying that I don't think in the actual economy we are normally dealing with cases of true overdetermination, where the n'th input literally makes no difference. This is what's going on in footnote 60. There's more on this in section 4.1.2 of the sequel paper: https://ebehrle.github.io/scc.pdf.
PS: For anyone who comes across this later, it might be helpful to see that effectively the same point can be made even when we do have substitutability, as in Max's interpretation of my toy economy.
Two unconnected assassins shoot a victim. The victim dies. Each shot was sufficient to kill. So neither makes any difference. This is a case of overdetermination; each is an "overdeterminer." The standard view in philosophy, and in the outside world, is that overdeterminers are causes: each assassin is a cause of the victim's death, and in at least that sense morally responsible for it, despite making no difference.
Marginalism, and the diamond-water paradox, explain something that is easy to explain: how can it be true that each shot made no difference, if shooting was in some sense obviously important for the victim's death? It's no harder to answer the analogous question about water or workers.
The question that I address in the paper, by contrast, is the normative question of whether the difference one makes on the margin determines what one deserves. Invoking the diamond-water paradox in response to this question (without any normative supplement; cf. the word "legitimate" in the last sentence of the original post) is merely to reiterate that, and why, some people make a small difference at the margin, and so is a non sequitur.
Your 2nd toy economy has an internal contradiction. You can NOT treat a group as irreplaceable (as a group, a set of people) and also give its members very small MRPs. Small individual MRPs mean that removing one person barely changes output. That is only true if someone else, or some other method, can take their place. Once that is true, the group is not a closed package like Worker 2 in your first economy. That group does not command a large joint surplus, because the function they perform can be restaffed.
And hat is the general problem here. In a real economy, Worker 1’s product does not depend on one fixed, irreplaceable group or method. Take a shoe-factory worker. If every current trucker vanished at once, his output would NOT fall to 0. Other people can learn to drive trucks. Firms can use trains, planes, donkeys, cars etc. Wages for trucking would spike, then new (and probably old ones, too, when they hear about salaries) workers and other methods would enter until those wages fell back. This potential entry and substitutes are what set the marginal product of the current set of truckers (and trucking as a profession), and therefore their deserved share of the value of every shoe sold.
If I’m the only person in the world who has figured out how to develop a vaccine against cancer, but I need another person to be present throughout the process to read measurements from a regular lab instrument—the kind found in every lab—does he deserve to split the profits with me? No. I think he deserves to be paid what anyone else doing the same job in another laboratory would be paid.
Standardly a worker's MRP is defined as the difference between output with them and without them, where they aren't replaced by a new hire. This is already there in Pigou's classic treatment. The neoclassical theory of wage determination would not work if we assumed that firms would not be willing to pay a worker more than $0 if there were a perfect replacement avaialble from outside the firm. It is closer to a ceteris paribus notion. (This is what I am saying in footnote 11.) A scarcer form of labor will tend to have a higher MRP because it will be allocated to more efficient uses than the n'th worker of that type would be allocated to were there more of them, i.e. were n greater. But given an allocation--once a worker is doing an actual job--the question of replaceability does not bear directly on their MRP, though it can bear on their bargaining power and thus their wage.
You write, "If every current trucker vanished at once, his output would NOT fall to 0. Other people can learn to drive trucks." I think this is an important point. It's one of the main themes of the sequel paper: https://ebehrle.github.io/scc.pdf
1) “Given an allocation” is doing a lot of work her. The allocation is not given by God. How many people can do the job determines how much of that labor is used and what the last unit adds. How many people can drive, what other ways goods can be moved, and so on. The current set of truckers is paid the cost of getting that function performed, given entry and substitutes. They are not paid what output would be if movement of goods were impossible forever.
Why would you want “given an allocation” to be the stage for determining moral desert?
2) An occupation that is easy to enter does not start with a high MRP that bargaining then knocks down. Its MRP is low because that type of labor is not scarce.
3) A perfect replacement outside the firm does not mean pay is $0 (unless that worker’s supply price is 0). Easy replacement keeps the occupation’s wage and MRP near the opportunity cost.
( 4) Textbook definition doesn't even work for your 2nd toy example, where each member of (G) has a tiny MRP, and (G) as a set is asked to play Worker 2. Tiny individual MRPs already mean dropping one person barely matters. In this example that is only possible if other members, outsiders, or another method can fill the gap. This is the fact about group (not individual workers), which can not replace Player 2 from your first toy model,.so that is why they don't get 50%.)
5) You are using 2 counterfactuals. For pay: remove one person, do not replace them, get a small number. For desert: the scarce worker’s big number exists only because the group jointly does the complementary task. Those are different things. Once outsiders and other methods are allowed, “what they only together do” is already priced as a restaffable service. There is no second unpaid group-share inside the factory worker’s rent.
Indispensable and scarce are different. Trucking can be necessary for shoes and still cheap.
I'm having trouble understanding some of your points, and where this leaves us.
On 4. Your "only possible" claim is not true. There are many other possible explanations. (See, for example, the case of pollution in some of my other comments.) But I'm not sure that this matters.
On 5. You suggest that I am saying that there are considerations (including counterfactual ones) that bear on what workers deserve that are different than the considerations that determine their pay. That is correct. That is the point of my paper.
"Indispensable and scarce are different. Trucking can be necessary for shoes and still cheap." I agree. This is the theme of the sequel paper: https://ebehrle.github.io/scc.pdf
Yes i saw that, but it did not convince me you actually understood the concept. You describe it correctly, but then define something called “Shapley value_p” which is… exactly the same thing. The rhetorical questions about the investment bank analyst do not make much sense either. Their marginal contribution to production if they are the one and only person in the economy is whatever they can produce themselves. Obviously that would be something different than what they could produce in a modern complex economy (Shapley value can easily handle such cases) but that doesnt mean that, as you assert, “these questions do not make sense”. They make perfect sense if you specify the problem correctly. You basically misspecify the problem and then claim that is an issue with the concept rather than with your understanding of it.
You do the same thing with your Constructors (Trurl and Klapaucius?) example. In the definition you say that “no individual makes a difference to (the houses) construction”. It still gets built, presumably with 49/50 mud and thatch or vice versa. But then you say that the workers built the house “together”. Which one is it?
Let me make a suggestion. Specify precisely what is required to built the house. Give a mathematical formula. If 99 workers contribute, does it get built? 98? What if as a group they bring more mud than thatch? What are the thresholda? Be rigorus here. Commit.
Because here is the thing. Once you do that, then calculating the Shapley Value for each worker is trivial. And guess what? Some extreme situations aside (i can elaborate if youre interested) the Shapley Value will give the egalitarian solution, contradiction your own claim. Indeed, thats one of the well known and appealing properties of SV value - identical individuals get identical rewards.
But isnt the “last worker” still different? No. Because anyone could be the last worker. You correctly note the confusion and wrongness of identifying the “last worker” with the “marginal worker” in earlier commentary on page 9 in your discussion of Amartya Sen but then slip into that fallacy yourself.
And this happens exactly because you're unwilling to be precise. The mudding of waters you engage in your Constructors example and discussion of SV is what lets you pretend that the concepts of MRP and SV imply something they dont.
I agree that the Shapley value_p is at least sometimes equivalent to the standard Shapley value, but as far as I can tell it's not the very same thing. There are cases in which it seems like you can affect someone else's productivity, and indeed the sum of marginal products in an economy, without affecting total output. (Imagine that you somehow make someone else necessary to an economy's functioning without changing total output.) If that is right, then a difference made to another's productivity is not definitionally the same as a difference made to output--and the same for the Shapley value, since it's parasitic on the former. Anyway this doesn't matter for the argument.
You write, "Their marginal contribution to production if they are the one and only person in the economy is whatever they can produce themselves. Obviously that would be something different than what they could produce in a modern complex economy." This is the idea I am responding to in footnote 61: "One might wonder whether we can avoid the present problem by asking not what the analyst’s labor would contribute in the different counterfactual sequences but what the analyst herself would contribute (where “analyst” is now a name instead of a definite description). But the contribution that someone would make if they performed a different kind of labor in a counterfactual economy is not an answer to the question of how much they contribute by doing what they actually do in the actual economy."
In other words, it's true that there's in principle an answer to the question of what the investment banker as a person would contribute in a one-person economy. (Not that we can figure it out.) But this can't help us answer our question about the value of their investment banking labor. (The "name" versus "definite description" distinction in the footnote is the distinction between "person who is in the actual world an investment banker" and "that person qua investment banker.")
Importantly, when applying the Shapley value in the context of a bargaining game--its home context--what the investment banker as a person would do is relevant. That's a difference between that context and the context of reward according to contribution for an actual bit of performed labor.
So I continue to believe that the Shapley value can't be applied even in principle to the latter context, and for that reason it wouldn't matter whether we specified a threshold for the house in Constructors: we could in that case apply the SV there but still not to the actual economy for which it's meant to be an analogy.
(This also doesn't matter, but my use of "the last worker" in Constructors is just a way to refer to the more productive worker without giving them a dumb name. It's not the sense of last worker at work in the footnote you reference.)
I wonder if the editors of The Journal of Philosophy asked any economists to review the article before publishing. My guess is that the real reason for its popularity is not its cogent logic, but that the author has claimed to undermine the moral legitimacy of markets.
How many economists are willing to serve as peer reviewers for philosophy journals? I think their services would be highly valued by philosophers, but I don’t think there are too many potential referees out there (and if they are, how would a philosophy editor know how to find them?).
Fair enough. Probably not many economists would be willing to serve as peer reviewers for philosophy journals.
As for finding them, perhaps email...
I am skeptical that philosophers would highly value feedback from economists. In my experience, there is quite alot of inter-disciplinary hostility and turf wars.
I guess the bigger question is whether Evan Behrle asked for feedback from economists before publication. My guess is the answer is No.
I’m sorry that’s been your experience. Turf wars suck.
For what it’s worth, many of us love economics and want to build bridges between the two disciplines! I think it’s great that Tabarrok is writing about Behrle, for example, and I’m looking forward to seeing how Behrle responds.
As someone working at the intersection and an econ by phd and phil by publication, I agree. Turf wars everywhere. But the econs I hang out with would always be open to reviewing phil papers.
As to whether EB asked for advice: that is a good point. Every econ would have seen the problems immediately. In fact an LLM would have done it as well. I just fed the paper to Claude: its not pretty.
It is now so easy to feed a draft of a paper into an LLM and identify weaknesses in a paper. At the very least a paper should mention them and explain why it does not undermine the main point of the paper.
I thought about this too. But I don’t think that is too difficult in the end. After all, Columbia does have a large and prestigious econ dept. One only needs an epistemic virtue: humility. Just go and ask. I also think that the best 25 selection committee made the same mistake. Just ask!
Lloyd Shapley covered this 75 years ago. Look up Shapley Value.
Also: "The injustice is that none of the trucker’s wages, nor their sum, reflect the massive economic impact of all truckers stopping work at once." - but it does
The entire argument seems quite reductive in general. If you get money for your work, there is a long list of factors that go into your pay:
-The rarity of your skills
-The (un-)pleasantness of the work
-The location of the employment
-A possible bonus dependent on how happy the customer and/or employer is with your actual output
- yes, the (marginal) value of the work itself
... And a million other factors, all of which are not prima facie unreasonable. If you want to argue that different pay is unfair in general, you need to show that ALL of these are inappropriate. A tough, in my opinion near-impossible, task!
My objection is that there is not only one Worker 1, and one Worker 2. There may be thousands in functionally identical jobs, with equal skills. If Worker 2 #XKZ13579 for any external reason can't do Job 2, there are thousands of replacements who can. In physics it would be an Ideal Gas situation, not a Pauli Exclusion situation.
The desert-island counterfactual is doing something sneakier than Behrle admits: taken seriously, it doesn't redistribute desert more fairly, it dissolves the concept entirely. If W's $200k depends on group G, G's product depends on group H, and so on back to whoever invented the plow — then nobody 'deserves' anything and we're left with pure consequentialism wearing a desert costume. Which might be fine! But then the argument isn't 'pay people what they deserve,' it's 'stop pretending desert was ever doing the work.'
I think a better refutation of the argument is that according to Behrle’s argument, it only observes this in one direction. You already addressed this when talking about the multiplication in economic worth models.
What exactly is the value of G's contribution without W? Also 0$.
The "revelation" that G's input is necessary for Ws contribution is not new at all, and the premise of Behrle’s argument is simply false.
This is what motivates Section 4. I write, there, "The challenge is merely prima facie because it only focuses on one direction of dependence. The simple reply to which it is vulnerable is one for which it itself supplies the resources: if a given worker loses credit for their own marginal revenue product to the extent that it depends on others, then that worker they should gain credit for others’ marginal revenue products to the extent that those marginal revenue products depend on them. It is in light of this reply that egalitarians need more than Scanlon’s observation that “[an individual’s marginal productivity] depends on the overall productive system,” or that—as Barbara Fried put it in another context—“society is the but-for cause of all market incomes.”"
Thanks, Max, for the post, and to everyone for the comments.
I think that the objection in the post is a good one. Indeed, I think it's probably the best one. That's why I considered it in the paper: it's what I have in mind on pp. 273-4 (in the published version, 24-5 in the preprint). Those pages were inspired by the diamond-water paradox.
1. Before I reiterate my response to that objection, it might be helpful to present a simpler version of my main argument. Compare two toy economies. In the first, Worker 1 makes all the difference to output—their MRP=Y—but their labor wouldn't make any difference in the absence of the labor of Worker 2. Worker 2 makes all the difference to the difference that Worker 1 makes. And this will show up as Worker 1's MRP: making a difference to the difference that Worker 1 makes is itself to make a difference to output. So reward according to MRP has them split output evenly. In the second two economy, Worker 1 again makes all the difference, but this time depends not on a single other worker but on a group of workers, and what they only together do. Their individual MRPs, suppose, are very small. So reward according to MRP has Worker 1 take home almost all of output. My central claim is that the distributive outcome in this second economy is unfair. That claim does not depend on a failure to appreciate the diamond-water paradox; it does not require denying the obvious fact that the individual labor of Worker 1 is more valuable than the individual labor of Worker 2 through Worker n, which fact, we can suppose, is explained by the former's scarcity.
2. In the paper—on the pages mentioned above—I write: "While a worker’s marginal revenue product depends on both that worker and on groups of others, that worker is an individual; the groups are groups. In particular, the groups are unstructured or diffuse collectives—roughly, collectives that are not agentially united. (A classic example: “polluters.”) And what unstructured collectives make happen, the thought goes, in no way bears on what their members deserve." Max writes: "The workers of G don’t deserve any of W’s marginal product because each of them, on the margin, is unessential for it. That W would suffer if G and all its substitutes disappeared together shouldn’t credit the members of G any more than the fact that food is worth everything in a famine should make the prices at the grocery store go up." A common view in philosophy is that it is at least sometimes the case that members of unstructured collectives have reasons for action, and can be rendered deserving, on the basis of what the collective makes happen. This is why an individual polluter, for example, can be blamed even if their marginal contribution to the harms produced by that kind of pollution (not: their marginal contribution to the amount of pollution) is zero.
3. It is not obvious that this common view is correct. There is a famous challenge to it, which the philosopher Julia Nefsky dubbed "the inefficacy problem": How can these individuals be rendered deserving by an action that by hypothesis makes no difference? It's very weird! My argument presupposes that one of the extant solutions to the inefficacy problem can be solved, such that the "common view" mentioned above is vindicated. In the blog post, as I understand it, Max rejects this view. That is a reasonable position, but it is less a straight-on objection to my argument than a denial of one of its presuppositions.
4. Suppose that you do indeed think that the notion of individuals being rendered deserving on the basis of what a collective makes happens is implausible. Here is just one observation that might move you. It is not the case that, in the second toy economy above, the entire story of "value" in that economy is a story of individual difference-making. The collective value of the group's labor does not disappear: it shows up in the individual value of Worker 1's labor, in the straightforward sense that, in the absence of that collective labor, the value of Worker 1's labor would (by construction) be zero. This is what I had in mind when I wrote, in the Jacobin summary of my paper: "For economists tempted to dismiss this as an unproblematic and trivial consequence of the fact that wages are set by marginal and not total or average products, the point is that the marginal productivity of the one worker is itself partly determined by the total product — of the other workers." This sentence was also meant to anticipate the invocation of the diamond-water paradox. (I've been waiting for a blog post like this since I wrote the paper.) This is not a knockdown argument, but I do hope that it has some force for those who accept the view that it is only the value of individuals' labor that matters morally. Why is it okay for Worker 1 to in effect get credit for the collective value of the labor of Worker 2 through n, when Worker 2 through n don't themselves get credit?
A few commenters have wondered whether any economists have read the paper. They have, including an economist at Columbia, whose department was mentioned above. I've also presented the sequel paper to a room of mostly economists. As I mentioned, the best objection that I consider in the paper was inspired by the diamond-water paradox, although I was aware of that paradox before talking to any economists about the paper.
More generally, the paper was partly motivated by what I think is a bad (normative) response to the role of scarcity in the marginalist theory of distribution; here I think Max and I agree. You often hear people dismiss reward according to MRP out of hand by saying: MRP doesn't reflect your "contribution," it reflects the scarcity of your labor. But as Max points out these are not competing claims; all else equal scarcer labor makes a bigger contribution. On this note, to repeat, I am nowhere denying that the workers Max thinks perform more valuable labor in fact perform more valuable labor; my claim is about whether they can take all the moral credit for that value.
I think that economics is important, and that more political philosophy should engage with it. With the help of an economist friend and claude, I've been learning econometrics in part for this reason, but also so that I can read econ papers for myself. If there are any economists reading this who are interested in talking more, please email me. I'm especially interested in feedback on the sequel paper: https://ebehrle.github.io/scc.pdf. If you didn't like the first paper, I think you're going to hate this one... But I also welcome corrections to the first paper, though it's already published. (One of the commenters suggested that an LLM identified some big problems. I asked one of the Claude models to come up with objections last month and didn't find any of them compelling.)
Thank you for reading and replying Evan!
I think the clearest way to respond is through your last argument.
You say "Suppose that you do indeed think that the notion of individuals being rendered deserving on the basis of what a collective makes happens is implausible"
But this is not what I believe. Indeed, in my view "what the collective makes happen" is the most important basis of desert for both Worker 1 and Workers 2-n.
Under point 4 you explain how the value of Worker 1's labor rises with the effort of all the other workers and falls to zero without it. But just as the collective efforts of those workers shows up in Worker 1's marginal product, it also shows up in each Worker 2-n's marginal product, just with the opposite effect. In the absence of that collective labor, the value of Worker 1's labor is zero and the value of each Worker 2-n's labor would be all of output. Vice-versa with the collective labor, Worker 1's labor is worth nearly all of output and each Worker 2-n's labor is worth near zero.
The reason why each Worker from 2-n deserves only their small marginal product is exactly because of what the collective makes happen without them.
"Why is it okay for Worker 1 to in effect get credit for the collective value of the labor of Worker 2 through n, when Worker 2 through n don't themselves get credit?"
The answer to this is not that economists take an unreasonably individualistic view of production that ignores collective effort. Rather, the answer is that the collective value of the labor of Worker 2 through n is a credit to Worker 1, because their effort is complementary to Worker 1's effort, while being a demerit for Workers 2 through n, because the effort of each of these workers is a substitute for the effort of all the others.
So I don't think that the notion of individuals being rendered (un-)deserving on the basis of what a collective makes happens is implausible. I just think your arguments are accounting for that desert in the wrong direction. What the collective makes happen can make your contribution more valuable by complementing it, or less valuable by substituting for it.
This explains why the distributive outcome in the second economy under point 1 is fair. The collective impact of n workers in G makes worker n+1 ineffectual and thus undeserving. Applying this argument to all workers in G leads to the counterintuitive conclusion that the sum of the marginal values is less than the total value, but it's still the correct argument.
Thanks, Max.
Consider the case of carbon emissions. (1) Total emissions are harmful but (2) for any given emitter, it is plausible that they make no difference to the harms of total emissions.
Note that this does not look like a case where the n'th emitter does not make a difference because (n-m) emitters are sufficient for the harms of total emissions. It is not really a case of inefficacy via redundancy and substitution. It looks like a "non-threshold case." (The n'th worker doesn't maker a difference; the n-1'th doesn't; and and on and on.) Whether it really is--whether there are any non-threshold cases--is a controversial question within the philosophical literature on collective impact.
But, skipping over that, what I am suggesting is: just as a common view says that each individual polluter deserves some blame on the basis of the harms of total emissions, despite none making a difference to those harms, each worker in a collective might deserve some credit on the basis of the benefits of their collective labor, despite each making only a tiny difference to those benefits (differences that sum to less than the total).
This is just a different understanding of the normative significance of collective impact. Whether that understanding is correct, or whether your directionally opposite alternative is correct, is a normative question, not an empirical one. I think that adopting your alternative would require us to abandon moral judgments that we make in other cases of collective impact, like pollution. Sometimes a group makes a difference much bigger than the sum of the differences that its members make, and we seem to think that the first difference redounds to the (dis)credit of the members. We do not think that marginal inefficacy renders one undeserving. That's the heart of it.
This is getting into the weeds, but it's maybe worth saying that I don't think in the actual economy we are normally dealing with cases of true overdetermination, where the n'th input literally makes no difference. This is what's going on in footnote 60. There's more on this in section 4.1.2 of the sequel paper: https://ebehrle.github.io/scc.pdf.
PS: For anyone who comes across this later, it might be helpful to see that effectively the same point can be made even when we do have substitutability, as in Max's interpretation of my toy economy.
Two unconnected assassins shoot a victim. The victim dies. Each shot was sufficient to kill. So neither makes any difference. This is a case of overdetermination; each is an "overdeterminer." The standard view in philosophy, and in the outside world, is that overdeterminers are causes: each assassin is a cause of the victim's death, and in at least that sense morally responsible for it, despite making no difference.
Marginalism, and the diamond-water paradox, explain something that is easy to explain: how can it be true that each shot made no difference, if shooting was in some sense obviously important for the victim's death? It's no harder to answer the analogous question about water or workers.
The question that I address in the paper, by contrast, is the normative question of whether the difference one makes on the margin determines what one deserves. Invoking the diamond-water paradox in response to this question (without any normative supplement; cf. the word "legitimate" in the last sentence of the original post) is merely to reiterate that, and why, some people make a small difference at the margin, and so is a non sequitur.
Your 2nd toy economy has an internal contradiction. You can NOT treat a group as irreplaceable (as a group, a set of people) and also give its members very small MRPs. Small individual MRPs mean that removing one person barely changes output. That is only true if someone else, or some other method, can take their place. Once that is true, the group is not a closed package like Worker 2 in your first economy. That group does not command a large joint surplus, because the function they perform can be restaffed.
And hat is the general problem here. In a real economy, Worker 1’s product does not depend on one fixed, irreplaceable group or method. Take a shoe-factory worker. If every current trucker vanished at once, his output would NOT fall to 0. Other people can learn to drive trucks. Firms can use trains, planes, donkeys, cars etc. Wages for trucking would spike, then new (and probably old ones, too, when they hear about salaries) workers and other methods would enter until those wages fell back. This potential entry and substitutes are what set the marginal product of the current set of truckers (and trucking as a profession), and therefore their deserved share of the value of every shoe sold.
If I’m the only person in the world who has figured out how to develop a vaccine against cancer, but I need another person to be present throughout the process to read measurements from a regular lab instrument—the kind found in every lab—does he deserve to split the profits with me? No. I think he deserves to be paid what anyone else doing the same job in another laboratory would be paid.
Standardly a worker's MRP is defined as the difference between output with them and without them, where they aren't replaced by a new hire. This is already there in Pigou's classic treatment. The neoclassical theory of wage determination would not work if we assumed that firms would not be willing to pay a worker more than $0 if there were a perfect replacement avaialble from outside the firm. It is closer to a ceteris paribus notion. (This is what I am saying in footnote 11.) A scarcer form of labor will tend to have a higher MRP because it will be allocated to more efficient uses than the n'th worker of that type would be allocated to were there more of them, i.e. were n greater. But given an allocation--once a worker is doing an actual job--the question of replaceability does not bear directly on their MRP, though it can bear on their bargaining power and thus their wage.
You write, "If every current trucker vanished at once, his output would NOT fall to 0. Other people can learn to drive trucks." I think this is an important point. It's one of the main themes of the sequel paper: https://ebehrle.github.io/scc.pdf
1) “Given an allocation” is doing a lot of work her. The allocation is not given by God. How many people can do the job determines how much of that labor is used and what the last unit adds. How many people can drive, what other ways goods can be moved, and so on. The current set of truckers is paid the cost of getting that function performed, given entry and substitutes. They are not paid what output would be if movement of goods were impossible forever.
Why would you want “given an allocation” to be the stage for determining moral desert?
2) An occupation that is easy to enter does not start with a high MRP that bargaining then knocks down. Its MRP is low because that type of labor is not scarce.
3) A perfect replacement outside the firm does not mean pay is $0 (unless that worker’s supply price is 0). Easy replacement keeps the occupation’s wage and MRP near the opportunity cost.
( 4) Textbook definition doesn't even work for your 2nd toy example, where each member of (G) has a tiny MRP, and (G) as a set is asked to play Worker 2. Tiny individual MRPs already mean dropping one person barely matters. In this example that is only possible if other members, outsiders, or another method can fill the gap. This is the fact about group (not individual workers), which can not replace Player 2 from your first toy model,.so that is why they don't get 50%.)
5) You are using 2 counterfactuals. For pay: remove one person, do not replace them, get a small number. For desert: the scarce worker’s big number exists only because the group jointly does the complementary task. Those are different things. Once outsiders and other methods are allowed, “what they only together do” is already priced as a restaffable service. There is no second unpaid group-share inside the factory worker’s rent.
Indispensable and scarce are different. Trucking can be necessary for shoes and still cheap.
I'm having trouble understanding some of your points, and where this leaves us.
On 4. Your "only possible" claim is not true. There are many other possible explanations. (See, for example, the case of pollution in some of my other comments.) But I'm not sure that this matters.
On 5. You suggest that I am saying that there are considerations (including counterfactual ones) that bear on what workers deserve that are different than the considerations that determine their pay. That is correct. That is the point of my paper.
"Indispensable and scarce are different. Trucking can be necessary for shoes and still cheap." I agree. This is the theme of the sequel paper: https://ebehrle.github.io/scc.pdf
I'd be happy to chat more. Shoot me an email at evanbehrle@fas.harvard.edu if you'd like.
Guy? Lloyd Shapley covered this 75 years ago. You mistook your own ignorance for ignorance of economists.
My response to the invocation of the Shapley value is on pp. 280-1 of the published version, 32-33 of the preprint.
Yes i saw that, but it did not convince me you actually understood the concept. You describe it correctly, but then define something called “Shapley value_p” which is… exactly the same thing. The rhetorical questions about the investment bank analyst do not make much sense either. Their marginal contribution to production if they are the one and only person in the economy is whatever they can produce themselves. Obviously that would be something different than what they could produce in a modern complex economy (Shapley value can easily handle such cases) but that doesnt mean that, as you assert, “these questions do not make sense”. They make perfect sense if you specify the problem correctly. You basically misspecify the problem and then claim that is an issue with the concept rather than with your understanding of it.
You do the same thing with your Constructors (Trurl and Klapaucius?) example. In the definition you say that “no individual makes a difference to (the houses) construction”. It still gets built, presumably with 49/50 mud and thatch or vice versa. But then you say that the workers built the house “together”. Which one is it?
Let me make a suggestion. Specify precisely what is required to built the house. Give a mathematical formula. If 99 workers contribute, does it get built? 98? What if as a group they bring more mud than thatch? What are the thresholda? Be rigorus here. Commit.
Because here is the thing. Once you do that, then calculating the Shapley Value for each worker is trivial. And guess what? Some extreme situations aside (i can elaborate if youre interested) the Shapley Value will give the egalitarian solution, contradiction your own claim. Indeed, thats one of the well known and appealing properties of SV value - identical individuals get identical rewards.
But isnt the “last worker” still different? No. Because anyone could be the last worker. You correctly note the confusion and wrongness of identifying the “last worker” with the “marginal worker” in earlier commentary on page 9 in your discussion of Amartya Sen but then slip into that fallacy yourself.
And this happens exactly because you're unwilling to be precise. The mudding of waters you engage in your Constructors example and discussion of SV is what lets you pretend that the concepts of MRP and SV imply something they dont.
I agree that the Shapley value_p is at least sometimes equivalent to the standard Shapley value, but as far as I can tell it's not the very same thing. There are cases in which it seems like you can affect someone else's productivity, and indeed the sum of marginal products in an economy, without affecting total output. (Imagine that you somehow make someone else necessary to an economy's functioning without changing total output.) If that is right, then a difference made to another's productivity is not definitionally the same as a difference made to output--and the same for the Shapley value, since it's parasitic on the former. Anyway this doesn't matter for the argument.
You write, "Their marginal contribution to production if they are the one and only person in the economy is whatever they can produce themselves. Obviously that would be something different than what they could produce in a modern complex economy." This is the idea I am responding to in footnote 61: "One might wonder whether we can avoid the present problem by asking not what the analyst’s labor would contribute in the different counterfactual sequences but what the analyst herself would contribute (where “analyst” is now a name instead of a definite description). But the contribution that someone would make if they performed a different kind of labor in a counterfactual economy is not an answer to the question of how much they contribute by doing what they actually do in the actual economy."
In other words, it's true that there's in principle an answer to the question of what the investment banker as a person would contribute in a one-person economy. (Not that we can figure it out.) But this can't help us answer our question about the value of their investment banking labor. (The "name" versus "definite description" distinction in the footnote is the distinction between "person who is in the actual world an investment banker" and "that person qua investment banker.")
Importantly, when applying the Shapley value in the context of a bargaining game--its home context--what the investment banker as a person would do is relevant. That's a difference between that context and the context of reward according to contribution for an actual bit of performed labor.
So I continue to believe that the Shapley value can't be applied even in principle to the latter context, and for that reason it wouldn't matter whether we specified a threshold for the house in Constructors: we could in that case apply the SV there but still not to the actual economy for which it's meant to be an analogy.
(This also doesn't matter, but my use of "the last worker" in Constructors is just a way to refer to the more productive worker without giving them a dumb name. It's not the sense of last worker at work in the footnote you reference.)
I wonder if the editors of The Journal of Philosophy asked any economists to review the article before publishing. My guess is that the real reason for its popularity is not its cogent logic, but that the author has claimed to undermine the moral legitimacy of markets.
How many economists are willing to serve as peer reviewers for philosophy journals? I think their services would be highly valued by philosophers, but I don’t think there are too many potential referees out there (and if they are, how would a philosophy editor know how to find them?).
Fair enough. Probably not many economists would be willing to serve as peer reviewers for philosophy journals.
As for finding them, perhaps email...
I am skeptical that philosophers would highly value feedback from economists. In my experience, there is quite alot of inter-disciplinary hostility and turf wars.
I guess the bigger question is whether Evan Behrle asked for feedback from economists before publication. My guess is the answer is No.
I’m sorry that’s been your experience. Turf wars suck.
For what it’s worth, many of us love economics and want to build bridges between the two disciplines! I think it’s great that Tabarrok is writing about Behrle, for example, and I’m looking forward to seeing how Behrle responds.
Anyone reading the comments here would certainly be hard-pressed to imagine that economists could ever be hostile.
LOL
You are right about that!
As someone working at the intersection and an econ by phd and phil by publication, I agree. Turf wars everywhere. But the econs I hang out with would always be open to reviewing phil papers.
As to whether EB asked for advice: that is a good point. Every econ would have seen the problems immediately. In fact an LLM would have done it as well. I just fed the paper to Claude: its not pretty.
Yes, good point.
It is now so easy to feed a draft of a paper into an LLM and identify weaknesses in a paper. At the very least a paper should mention them and explain why it does not undermine the main point of the paper.
I thought about this too. But I don’t think that is too difficult in the end. After all, Columbia does have a large and prestigious econ dept. One only needs an epistemic virtue: humility. Just go and ask. I also think that the best 25 selection committee made the same mistake. Just ask!
There’s no order to the list other than alphabetical. Your title is misleading.
Lloyd Shapley covered this 75 years ago. Look up Shapley Value.
Also: "The injustice is that none of the trucker’s wages, nor their sum, reflect the massive economic impact of all truckers stopping work at once." - but it does
Thanks. Copying my reply above: My response to the invocation of the Shapley value is on pp. 280-1 of the published version, 32-33 of the preprint.
The entire argument seems quite reductive in general. If you get money for your work, there is a long list of factors that go into your pay:
-The rarity of your skills
-The (un-)pleasantness of the work
-The location of the employment
-A possible bonus dependent on how happy the customer and/or employer is with your actual output
- yes, the (marginal) value of the work itself
... And a million other factors, all of which are not prima facie unreasonable. If you want to argue that different pay is unfair in general, you need to show that ALL of these are inappropriate. A tough, in my opinion near-impossible, task!
My objection is that there is not only one Worker 1, and one Worker 2. There may be thousands in functionally identical jobs, with equal skills. If Worker 2 #XKZ13579 for any external reason can't do Job 2, there are thousands of replacements who can. In physics it would be an Ideal Gas situation, not a Pauli Exclusion situation.
The desert-island counterfactual is doing something sneakier than Behrle admits: taken seriously, it doesn't redistribute desert more fairly, it dissolves the concept entirely. If W's $200k depends on group G, G's product depends on group H, and so on back to whoever invented the plow — then nobody 'deserves' anything and we're left with pure consequentialism wearing a desert costume. Which might be fine! But then the argument isn't 'pay people what they deserve,' it's 'stop pretending desert was ever doing the work.'
That is sort of the argument of Alm 2010, but not mine---see n. 43.
I think a better refutation of the argument is that according to Behrle’s argument, it only observes this in one direction. You already addressed this when talking about the multiplication in economic worth models.
What exactly is the value of G's contribution without W? Also 0$.
The "revelation" that G's input is necessary for Ws contribution is not new at all, and the premise of Behrle’s argument is simply false.
This is what motivates Section 4. I write, there, "The challenge is merely prima facie because it only focuses on one direction of dependence. The simple reply to which it is vulnerable is one for which it itself supplies the resources: if a given worker loses credit for their own marginal revenue product to the extent that it depends on others, then that worker they should gain credit for others’ marginal revenue products to the extent that those marginal revenue products depend on them. It is in light of this reply that egalitarians need more than Scanlon’s observation that “[an individual’s marginal productivity] depends on the overall productive system,” or that—as Barbara Fried put it in another context—“society is the but-for cause of all market incomes.”"
The best I can say for it is quaint. Is Behrle a philosopher, no, he's a pampleteer.