Reply to The downside of the DC school lottery

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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]The real problem is that the school lottery is a repeated game with highly correlated outcomes and it is being modelled as a single outcome.    As pointed out by a previous poster, it also exaggerates the idea of the ordering of choices being meaningful when there are really tiers of preference.  For example, if the preference between two choices is either zero or swamped by the noise of uncertainty, then this heavy emphasis on efficiency with respect to trading after assignment is silly. Ordinal ranking just isn't communicating all the information that parents have compiled.[/quote]

One legit complaint about the current lottery is that it has no way of accounting for intensity of preference. If I slightly prefer A to B but you strongly prefer A to B, then utility would be maximized by giving you A and me B, even if that's not a trade I would voluntarily agree with. The problem is there's no way of formalizing that and trying to do so opens all sorts of avenues for gaming.

The current system doesn't deal with ties well either. Imagine there are schools A and B, equivalent in all ways but some  distance apart. I live equidistant between them so I am indifferent, but you live within walking distance of A and strongly prefer it. I list my choices as A then B, strictly because of alphabetical order, and I have a higher lottery number so I get A and you get B. We could trade and both be better off (I would have the psychic income of helping you out).

But these are edge cases. [/quote]

These are interesting points. One way to address intensity would be to give each kid 100 points which they could distribute however they want among up to 12 schools. The school I assign the most points would be my #1, etc. That way there would be both a ranking and intensity would be shown by the varying number of points. I recognize this is probably not practical and too confusing, but an interesting thought. Also not a statistician so can't say how an algorithm would process the point numbers.[/quote]

Then you open the door to strategizing. Should I load my points into a hard-to-get-into school, or should I spread them around? Once you allow strategizing you open the door to suboptimal outcomes.[/quote]

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