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Notes -
A network of N people working on a problem requires at least order
logNoverhead to synchronize their efforts and receive instructions/feedback.So unless someone accepts working 75% time for 50% pay, they are gonna naturally scale to working more.
No, it's not O(log(N)) overhead. It's at least O(N) overhead. O(log(N)) is the depth of the hierarchy, but the entire thing is O(N). That is, the number of people doing the coordination tasks is a linear function of those doing the work.
First, I claimed
O(logN)as an absolute lower bound, which I think suffices for the purposes of this discussion to disprove the claim that IB could just hire more people.Second, I think in the absolute (totally imaginary, of course) best case, each instruction would come from the top and be distributed to O(1) people on each level of the hierarchy: CEO tells the VP, VP tells the director, ... and the results are reviewed back on the way up, thus traverse 2*M levels where M is the depth of the hierarchy which is
logN. No actual firm runs like this, but it's a lazy way to derive a lower bound / impossibility result.More options
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Fortunate log(N) grows really slowly compared to N. Doubling N only requires adding a constant amount of extra overhead regardless of how big your company is, which can easily be handled by big employers.
The true extra costs of doubling N is the doubling of the total salaries you'll have to pay out, not the O(log(N)) extra overhead and if AI increases productivity to the point where the former is viable then the increased costs of the latter will be easily covered by a few extra months of productivity gains, your argument is at best one that this transition might have to be delayed for a few months to account for overhead costs, not one that it's not feasible.
You're already getting O(N) increase in costs due to the extra headcount by paying people the same but working them for half as long, the O(log(N)) increase in overhead is a minor triviality compared to that.
Hold up -- I thought we're paying people proportionally -- folks at 4 days would be paid 80% of the current salary.
Otherwise what you're talking about is just an across-the-board 25% pay raise for everyone. And that, in turn, just further shifts things from labor to capital, which is (IIUC) the opposite of what you want.
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