Thursday, April 12, 2012

Hendriks, de Hoop, and de Swart in Journal of Logic, Language, and Information (2012)

In their brief introduction to a special issue on game theory and bidirectional game theory, Petra Hendriks, Helen de Hoop, and Henriëtte de Swart discuss the parallels between the two frameworks and their limits.

Handy References

The text contains the following references on bidirectional optimality theory:
In addition, they cite the following paper as pointing out "the connection between bidirectional Optimality Theory and Game Theory" (p. 2):

A Theoretical Point

Besides the general introduction of the field and the players, the three authors point to a possible theoretical shortcoming of both bidirectional optimality theory and game theory.

The problem they point out is that "these frameworks generally predict a one-to-one pairing of forms and meanings," which is not empirically true (p. 2). They illustrate this with the Dutch question Wie heeft Frank vermoord?, which is ambiguous between Who did Frank kill? and Who killed Frank?

More specifically, they note that while it is true that "marked forms go with marked meanings," the reverse is not: "unmarked forms can often be used to express unmarked as well as marked meanings" (p. 3). This claim is supported by a reference to a paper in Lingua, but I don't know exactly what the example they have in mind is.

A Note On That Point

Just on the face of it, there doesn't seem to be anything wrong, from the standpoint of microeconomics, with the many-to-many relation, but it does require a slightly more sophisticated model of the "cost" of an utterance. Consider for instance:
  • He is dead (+m) = "He is dead" (+m)
  • He is gone (–m) = "He is dead" (+m)
  • He is dead (+m) = *"He is gone" (–m)
  • He is gone (–m) = "He is gone" (–m)
I haven't done the math here, but this might be explained by pragmatic effects under the right assumptions: If all messages are equally cheap, then we should indeed expect a one-to-one correspondence to emerge; however, since one of the meanings is taboo, it will tend to increase the cost of whatever message gravitates towards it. This might sustain the incentive to use analogical references instead of direct (unambiguous) references.

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