help with personal pronouns

1 March 2015

Theoretical economists have a pronoun problem. Since our models are based on a conceptualization of reality in which sex is generally irrelevant, there is no ex ante reason to assume that any particular actor is male or female. Nonetheless, it's still useful to assign a sex to agents in the model, as this is the simplest way to provide access to the simplifying power of pronouns.

Aside: this discussion skirts entirely broader issues of non-binarity of gender identification, and of personal pronouns. Because popular English has two sex-identified pronouns — he and she, and their grammar-appropriate relatives — which are more or less explicitly bound to sex, I'm constraining attention to the traditional male/female gender binary.

Computer scientists have dealt with this by custom: Alice and Bob and Carol are placeholder agents, assigned predictable genders. Matching theory has a canonical two-sided problem where men find wives — later generalized to women finding husbands, and beyond — which provides automatic access to pronouns. In general, however, we have no such luck: if two individuals are playing the prisoner's dilemma, the theoretical situation is the same no matter whether it's two men, two women, or one of each.(1) Because third-person singular pronouns are useful, and because (in English) they exist only in a gendered way, we're stuck. Osborne and Rubinstein capture the issue nicely in A Note on Personal Pronouns.(2)

It seems fair to solve this problem by random implicit gender assignment. To that end, you can use the following pseudo-app to generate unbiased random genders(3) for any of your papers — it even saves your work! You're allowed to override its suggestions, but keep in mind that that's exactly the problem we already face.

Paper sex assignment

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(1): this is true, in a no-true-Scotsman sense, for a fairly standard definition of economic theory. But it depends on how deeply you might want to model agents; see, for example, some of Burkhard Schipper's experiments, or this paper (PDF).

(2): he is, of course, English's standard “generic” third-person singular pronoun, but naturally — due to the fact that it is also a gender-specific pronoun — carries significant implications. Personally, since I do a lot of work with two agents — or two particular kinds of agents — I find it's both neutral and helpful to address one as female and the other as male. This allows for consistent addressing in shorthand, via she or he. With regard to which agent is assigned which sex, or with regard to greater numbers, the issue is still open; and, regrettably, I tend to vacillate while presenting.

(3): unbiased and random, up to the tolerance of your computers random number generator. The raw code is parseInt( Math.random() * App.pronouns.length ).

Included \(\LaTeX\) graphics are generated at LaTeX to png or by MathJax.

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