The obvious research question: Is there an assignment system where the best strategy is to list your true preferences, and is Pareto efficient (no win/win trading of assignment is possible)?
What's wrong with simply randomizing the list of students, then walking the randomized list and giving each student his/her highest-ranked school that hasn't yet been filled by the assignment of students higher on the list?
Does some variant of Arrow's impossibility theorem [1] apply to this situation?
It might also shed light on the causes and dynamics of poverty to figure out the exact causal mechanism by which "students from poorer neighborhoods make more strategic mistakes."
Is poor strategic decision-making ability a cause of poverty (the poor are poor because they don't make smart strategic decisions about money and life choices)? Or is it an effect of poverty (having a single parent or parents working multiple jobs means less intellectual stimulation and help with homework, not being able to afford nutritious food or have time to cook it causes poor nutrition which affects brain development, etc., which leads to lower general intelligence and strategic thinking ability)?
[1] https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...