Explicit mathematical models for behavioral science theories

[摘要] Physical science theories are often expressed as precise mathematical relationships from which researchers can derive empirically testable consequences. Mathematical modeling takes on additional tasks in the conduct of behavioral science research because behavioral science theories are typically expressed verbally, permitting a variety of mathematical representations for their conceptual relationships. This paper contains three different applications that (1) specify explicit mathematical models for various behavioral science theories, (2) verify the logical consistency of the formalized set of assumptions, and (3) examine the deductive content of the theories' models.The first application, "Stability in the Prisoners' Dilemma," corrects some theorems by Robert Axelrod and others asserting the existence of "evolutionarily stable strategies" and extends this work. This is accomplished by: (1) formalizing the concept of strategy for iterated games and showing that the original proofs only establish "pair-distinct" stability, (2) showing that all strategies for playing the Iterated Prisoners' Dilemma (IPD) are dynamically unstable, (3) deriving a measure of the degree of instability of IPD Strategies, and (4) demonstrating that mutual cooperation can reduce instability, even though it does not eliminate it.The second application, "Models for Long Cycles in War and Production," produces (1) a differential equation model consistent with Joshua Goldstein's long cycle theory that produces simple harmonic motion with fixed cycle times in contrast to his observation that the duration of individual cycles varies from 30 to 70 years, and (2) a second model that corroborates three primary features of long cycles observed by Goldstein including variable cycle times.The third application, "Measuring the Rate of War Outbreak," (1) develops a variable intensity Poisson process model, (2) uses this model to explicitly derive statistically precise predictive estimates of the rate of war outbreak, and (3) derives descriptive estimates of the rate of war outbreak that provide strong, unanticipated corroboration of Goldstein's long cycle dating scheme and of the "resource interpretation" of his long cycle theory developed in the second application.

[效力级别] Psychology, Social

[关键词] Mathematics;Psychology, Social;Political Science, International Law and Relations