First, I note that this comment thread was previously about Shapley values, and you don’t seem to have done any Shapley calculations. If this is meant to be the same rule, but explained from a different angle, then I don’t see how to establish equivalence. If this is meant to be a new system, then I don’t see how it generalizes to more complex examples, such as where the factory output scales with the number of workers (rather than being all-or-nothing). (I also don’t see why you’d choose this particular comment to start promoting your alternative system.)
Second, you’re analyzing a situation where a required input can be provided by any of multiple parties; that is, if there are 2 owners, you only need 1 owner to agree in order to make the factory run. But the story problem above was about a situation where you need all of multiple parties; i.e. replace the 1 owner with 1 capitalist + 1 technologist and you need both of them to make the factory run.
If I came to you and said, here’s a game with 3 people (1 worker + 1 capitalist + 1 technologist), you need all 3 people working together to produce anything, how do they split the profits? I suspect you’d say an even 3-way split. But that implies that the owner from the 2-person can divide himself into 2 dummy agents (1 capitalist + 1 technologist) and then demand 2⁄3 of the profit (up from 1⁄2) because he’s now (nominally) doing 2 out of 3 jobs.
How do you prevent this exploit?
Third, I don’t buy your claim in your advanced examples that “any lesser split has a better alternative that one party can force”. For instance, in the 1 owner + 2 workers example, if the owner offers worker A a 70-30 split, that’s better for both the owner and worker A than your proposed split, and I don’t see what worker B can do about it.
You seem to be arguing that worker A should reject this split on some sort of timeless logic (?) where A reasons that there was an equal chance the offer would have been made to B and so if A+B are the sort of people who accept this offer then they each get 15 in expectation across all counterfactuals. Even if you buy the timeless logic, this only works if A and B use correlated strategies such that A is effectively choosing for both of them; otherwise, after A rejects this split, the owner proposes it to B and A gets nothing in all counterfactuals. So that seems to me like a coordinated solution, not a solution that a single party can unilaterally force.
In fact, it looks to me like you’ve said something pretty close to “my system rewards monopolies, so A and B are incentivized to form a cartel and act like a single agent, and therefore I assume they do so.”
First, I note that this comment thread was previously about Shapley values, and you don’t seem to have done any Shapley calculations. If this is meant to be the same rule, but explained from a different angle, then I don’t see how to establish equivalence. If this is meant to be a new system, then I don’t see how it generalizes to more complex examples, such as where the factory output scales with the number of workers (rather than being all-or-nothing). (I also don’t see why you’d choose this particular comment to start promoting your alternative system.)
Second, you’re analyzing a situation where a required input can be provided by any of multiple parties; that is, if there are 2 owners, you only need 1 owner to agree in order to make the factory run. But the story problem above was about a situation where you need all of multiple parties; i.e. replace the 1 owner with 1 capitalist + 1 technologist and you need both of them to make the factory run.
If I came to you and said, here’s a game with 3 people (1 worker + 1 capitalist + 1 technologist), you need all 3 people working together to produce anything, how do they split the profits? I suspect you’d say an even 3-way split. But that implies that the owner from the 2-person can divide himself into 2 dummy agents (1 capitalist + 1 technologist) and then demand 2⁄3 of the profit (up from 1⁄2) because he’s now (nominally) doing 2 out of 3 jobs.
How do you prevent this exploit?
Third, I don’t buy your claim in your advanced examples that “any lesser split has a better alternative that one party can force”. For instance, in the 1 owner + 2 workers example, if the owner offers worker A a 70-30 split, that’s better for both the owner and worker A than your proposed split, and I don’t see what worker B can do about it.
You seem to be arguing that worker A should reject this split on some sort of timeless logic (?) where A reasons that there was an equal chance the offer would have been made to B and so if A+B are the sort of people who accept this offer then they each get 15 in expectation across all counterfactuals. Even if you buy the timeless logic, this only works if A and B use correlated strategies such that A is effectively choosing for both of them; otherwise, after A rejects this split, the owner proposes it to B and A gets nothing in all counterfactuals. So that seems to me like a coordinated solution, not a solution that a single party can unilaterally force.
In fact, it looks to me like you’ve said something pretty close to “my system rewards monopolies, so A and B are incentivized to form a cartel and act like a single agent, and therefore I assume they do so.”