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Here is a proposed solution. Let X be the traditional signal, Y be the new signal, and Z be the trait(s) being advertised by both. Let people continue doing X, but subsidize Y on top of X for people with very high Z. Soon Y is a signal of higher Z than X is, and understood by the recipients of the signals to be a better indicator. People who can’t afford to do both should then prefer Y to X, since Y is is a stronger signal, and since it is more socially efficient it is likely to be less costly for the signal senders.

I don't see how this validates the new test. If you filter it like that, then you have range restriction problems: you've shown the scores of the MIT graduates are such and such, but you haven't shown that the scores of the non-MIT graduates are less than that, and so you haven't shown that it filters at all, much less as well as the 'MIT vs non-MIT'. (Imagine the test is 'how tall you are in centimeters'.) You still also have the adverse selection problem for the new test.