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If peer effects are zero-sum, they are neither a reason to support, nor to oppose, non-public schools, right? Because it means that who your peers are has ~no effect on performance once you control for "pre-existing traits of the students and their families."
This isn't true. Zero-sum means the overall effect of the peers is zero-sum - we have a number of children, and some offer bonuses and others maluses to the performance of their peers. This is the traditional argument for removing ability-streamed classes, incidentally, that we need to put the smarter kids in with the dumber ones in order to ensure that everyone gets a chance to get the adjacency bonus from the smart kids.
I'm not sure things function that way in reality - it runs up against obvious limitations like 'putting a mentally disabled kid in the accelerated class is going to badly screw someone over, or possibly everyone involved depending on how you run things' but the peer effects being zero-sum means your peers do have an effect on performance, but the positive externalities are strongly connected to better students who in turn yield said positive externalities themselves.
What if putting smart kids together benefits smart kids to a greater degree than putting smart kids with dumb kids benefits the dumb kids?
What if the smart kid bonus only applies to other conscientious smart kids and the dumb scumbags don't really gain from sharing a learning environment with the smart kids, they just hold the smart kids back?
I agree and think that's true - I was accelerated in high school, but then the program got shut down and I got put with the speds for a few months (on the basis that the special education teacher was trained in gifted education) until they decided to put me back into regular classes. Spending time with a guy who couldn't read did nothing for me, nor did it help him. I viewed him with contempt because I hated being sat with him, and he was barely aware of anyone's existence at all.
I'm just outlining the logic of 'something can be net zero-sum yet be bad for some and good for others'.
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Careful now, you're not supposed to be muddying the rigorous analysis of experts with silly things like logic and heuristics.
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