A stochastic model of the 2007 Russian Duma election
In this paper we consider the nature of local Nash equilibrium (LNE) for a model
of the 2007 Duma election in Russia, using estimates of valence obtained from sociodemographic
We then extend this sociodemographic valence model by including institutional valences,
the approval by voters of the various institutions, including the President, the PrimeMinister,
the State Duma and the Federation Council.We show by simulation that the vote maximizing
LNE of this general stochastic model were not at the electoral origin. The dominant feature
of the election was the influence of approval or disapproval of President Putin on each voter’s
Previous empirical research has developed stochastic electoral models for Israel, Turkey, and other polities. The work suggests that convergence to an electoral center (often predicted by electoral models) is a nongeneric phenomenon. In an attempt to explain nonconvergence, a formal model based on intrinsic valence is presented. This theory showed that there are necessary and sufficient conditions for convergence. The necessary condition is that a convergence coefficient c is bounded above by the dimension w of 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-order balance condition that 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.
Long-term deep bed filtration in porous media with size exclusion particle capture mechanism is studied. For mono dispersed suspension and transport in porous media whit distributed pore sizes, the micro stochastic model allows for upscaling and the exact solution is derived for the obtained macro scale equation system. Results show that transient pore size distribution and nonlinear relation between the filtration coefficient and captured particle concentration during suspension filtration and retention are the main features of long-term deep bed filtration, which generalises the classical deep bed filtration model and its latter modifications. Furthermore, the exact solution demonstrates earlier breakthrough and lower breakthrough concentration for larger particles. Among all the pores with different sizes, the ones with intermediate sizes (between the minimum pore size and the particle size) vanish first. Total concentration of all the pores smaller than the particles turns to zero asymptotically when time tends to infinity, which corresponds to complete plugging of smaller pores.