One set of applications
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OK, I admit, this should maybe have been in the reading, and no one can now read all of this. But here at least is one paragraph, and a link.
Rachel Croson and Ury Gneezy, Gender Differences in Preferences
After reviewing experimental literature of the type we have read a good deal of, but oriented toward eliciting gender differences, the authors conclude:
“We believe, as suggested by Gilligan (1982), that men’s decisions are less context-specific than women’s. Participants of both genders are likely maximizing an underlying utility function, but the function that men use is less sensitive to the conditions of the experiment, information about the other party, and (even) the other party’s actions, than the function that women use. This causes what appear to be inconsistent results in our experimental studies; sometimes men appear more altruistic than women and other times, women appear more altruistic than men. But primarily what we see is women’s behavior is more context-dependent than that of men.”
This is another way of beginning to answer Steve’s question of, what do we do with “difference” as a driver of policy?

