Application of a Theorem in Stochastic Models of Elections

Previous empirical research has developed stochastic electoral models for Israel, Turkey, and other polities. The work suggests thatconvergence to an electoral center(often predicted by electoral models) is a nongeneric phenomenon. In an attempt to explain nonconvergence, a formal model based onintrinsic valenceis presented. This theory showed that there are necessary and sufficient conditions for convergence. The necessary condition is that a convergence coefficientcis bounded above by the dimensionwof the policy space, while a sufficient condition is that the coefficient is bounded above by 1. This coefficient is defined in terms of the difference in exogenous valences, the “spatial coefficient”, and the electoral variance. The theoretical model is then applied to empirical analyses of elections in the United States and Britain. These empirical models include sociodemographic valence and electoral perceptions of character trait. It is shown that the model implies convergence to positions close to the electoral origin. To explain party divergence, the model is then extended to incorporate activist valences. This extension gives a first-orderbalance conditionthat allows the party to calculate the optimal marginal condition to maximize vote share. We argue that the equilibrium positions of presidential candidates in US elections and by party leaders in British elections are principally due to the influence of activists, rather than the centripetal effect of the electorate.

Natural selection in a Cretaceous oyster

A population of shells of the Cretaceous oyster Agerostrea mesenterica was obtained from a single locality. The age at death for each shell could be determined, and the population was deemed to be essentially undisturbed and capable of providing a mortality record of the local population averaged over a span of time. We measured four morphometric characters which, on the basis of a functional morphologic model, could be expected to have adaptive value. The frequency distribution of each character was analyzed separately for the three year old and for the six year and older specimens in order to determine which individuals died young and which survived to old age. Ontogenetic effects were separated from those of differential mortality by independent means. The results indicated that there was (1) directed selection for maximum curvature, (2) centripetal selection for a plica number of about 8, and (3) a net centripetal effect on both arc length and plica height, composed of selection against largest values coupled with a possible selection against smaller values that cannot be separated from ontogenetic effects. Only the selection for maximum curvature and optimal plica number can be reconciled with the predictions of the model.