Directional and static equilibrium in social decision processes

Social sciences

Matthews, Steven A. ; Plott, Charles R.

University:California Institute of Technology

Department:Humanities and Social Sciences

关键词: Social sciences;   

Others  :  https://thesis.library.caltech.edu/7238/1/Matthews_sa_1978.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

This thesis proposes a model of social decision processesthat is applicable to situations in which social change must beincremental. In the limit, only the direction and not the speedof a shift in the status quo can be decided at each point in time.Individual preferences over directions are induced myopically viathe inner product of direction (unit) vectors with the gradients ofutility functions. Then the direction of shift at each instantis taken to be an equilibrium of a game that has directional outcomes.

Both two-person non-cooperative games in which two candidatesadopt directional strategies to maximize their shares of castvotes, and n-person simple games of which absolute majority rule isa special case, are studied. Directional equilibria for the formerand directional cores for the latter are characterized. Resultsinclude the following: (1) directions "pointing" towards pointequilibria are directional equilibria; (2) a mobile candidate willdiverge from a rigid, extremist opponent; (3) a status quo x simultaneouslyapproaches each winning coalition's preferred-to-x set ifand only if it shifts in an undominated direction; (4) given Euclideanpreferences, a status quo that shifts in undominated directions willconverge to the point core or to the set of points with emptydirectional cores; (5) an empty directional core at a point implieslocal cycling occurs in a neighborhood of the point; (6) stringentpairwise symmetry conditions must be satisfied by utility gradientsat a point that has a nonempty directional core in a majority rulegame; and (7) undominated directions exist at boundary points ofa global cycling set and "point back into" the cycling set. Results(6) and (7) indicate that for majority games in spaces of dimensiongreater than three, directional cores are usually empty and globalcycling sets are usually the entire space.

The disseration appendix is a self-contained paper inits own right. In a behaviorally-intuitive fashion, it establishespairwise symmetry conditions for a point contained in the interioror boundary of a convex feasible set to be quasi-undominated inan anonymous simple game.