6,674 research outputs found
Does a Single Zealot Affect an Infinite Group of Voters ?
A method for studying exact properties of a class of {\it inhomogeneous}
stochastic many-body systems is developed and presented in the framework of a
voter model perturbed by the presence of a ``zealot'', an individual allowed to
favour an opinion. We compute exactly the magnetization of this model and find
that in one (1d) and two dimensions (2d) it evolves, algebraically () in 1d and much slower () in 2d, towards the unanimity
state chosen by the zealot. In higher dimensions the stationary magnetization
is no longer uniform: the zealot cannot influence all the individuals.
Implications to other physical problems are also pointed out.Comment: 4 pages, 2-column revtex4 forma
Public Sector Personnel Economics: Wages, Promotions, and the Competence-Control Trade-off
We model personnel policies in public agencies, examining how wages and promotion standards can partially offset a fundamental contracting problem: the inability of public sector workers to contract on performance, and the inability of political masters to contract on forbearance from meddling. Despite the dual contracting problem, properly constructed personnel policies can encourage intrinsically motivated public sector employees to invest in expertise, seek promotion, remain in the public sector, and develop policy projects. However, doing so requires internal personnel policies that sort slackers from zealots. Personnel policies that accomplish this task are quite different in agencies where acquired expertise has little value in the private sector, and agencies where acquired expertise commands a premium in the private sector. Finally, even with well-designed personnel policies, there remains an inescapable trade-off between political control and expertise acquisition
Voting and Catalytic Processes with Inhomogeneities
We consider the dynamics of the voter model and of the monomer-monomer
catalytic process in the presence of many ``competing'' inhomogeneities and
show, through exact calculations and numerical simulations, that their presence
results in a nontrivial fluctuating steady state whose properties are studied
and turn out to specifically depend on the dimensionality of the system, the
strength of the inhomogeneities and their separating distances. In fact, in
arbitrary dimensions, we obtain an exact (yet formal) expression of the order
parameters (magnetization and concentration of adsorbed particles) in the
presence of an arbitrary number of inhomogeneities (``zealots'' in the
voter language) and formal similarities with {\it suitable electrostatic
systems} are pointed out. In the nontrivial cases , we explicitly
compute the static and long-time properties of the order parameters and
therefore capture the generic features of the systems. When , the problems
are studied through numerical simulations. In one spatial dimension, we also
compute the expressions of the stationary order parameters in the completely
disordered case, where is arbitrary large. Particular attention is paid to
the spatial dependence of the stationary order parameters and formal
connections with electrostatics.Comment: 17 pages, 6 figures, revtex4 2-column format. Original title ("Are
Voting and Catalytic Processes Electrostatic Problems ?") changed upon
editorial request. Minor typos corrected. Published in Physical Review
Zealots in the mean-field noisy voter model
The influence of zealots on the noisy voter model is studied theoretically
and numerically at the mean-field level. The noisy voter model is a
modification of the voter model that includes a second mechanism for
transitions between states: apart from the original herding processes, voters
may change their states because of an intrinsic, noisy in origin source. By
increasing the importance of the noise with respect to the herding, the system
exhibits a finite-size phase transition from a quasi-consensus state, where
most of the voters share the same opinion, to a one with coexistence. Upon
introducing some zealots, or voters with fixed opinion, the latter scenario may
change significantly. We unveil the new situations by carrying out a systematic
numerical and analytical study of a fully connected network for voters, but
allowing different voters to be directly influenced by different zealots. We
show that this general system is equivalent to a system of voters without
zealots, but with heterogeneous values of their parameters characterizing
herding and noisy dynamics. We find excellent agreement between our analytical
and numerical results. Noise and herding/zealotry acting together in the voter
model yields not a trivial mixture of the scenarios with the two mechanisms
acting alone: it represents a situation where the global-local (noise-herding)
competitions is coupled to a symmetry breaking (zealots). In general, the
zealotry enhances the effective noise of the system, which may destroy the
original quasi--consensus state, and can introduce a bias towards the opinion
of the majority of zealots, hence breaking the symmetry of the system and
giving rise to new phases ...Comment: 13 pages, 15 figure
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