4,593 research outputs found
Asymptotic bias of some election methods
Consider an election where N seats are distributed among parties with
proportions p_1,...,p_m of the votes. We study, for the common divisor and
quota methods, the asymptotic distribution, and in particular the mean, of the
seat excess of a party, i.e. the difference between the number of seats given
to the party and the (real) number Np_i that yields exact proportionality. Our
approach is to keep p_1,...,p_m fixed and let N tend to infinity, with N random
in a suitable way.
In particular, we give formulas showing the bias favouring large or small
parties for the different election methods.Comment: 54 page
Optimal inference in a class of regression models
We consider the problem of constructing confidence intervals (CIs) for a
linear functional of a regression function, such as its value at a point, the
regression discontinuity parameter, or a regression coefficient in a linear or
partly linear regression. Our main assumption is that the regression function
is known to lie in a convex function class, which covers most smoothness and/or
shape assumptions used in econometrics. We derive finite-sample optimal CIs and
sharp efficiency bounds under normal errors with known variance. We show that
these results translate to uniform (over the function class) asymptotic results
when the error distribution is not known. When the function class is
centrosymmetric, these efficiency bounds imply that minimax CIs are close to
efficient at smooth regression functions. This implies, in particular, that it
is impossible to form CIs that are tighter using data-dependent tuning
parameters, and maintain coverage over the whole function class. We specialize
our results to inference on the regression discontinuity parameter, and
illustrate them in simulations and an empirical application.Comment: 39 pages plus supplementary material
Hydrodynamic models of preference formation in multi-agent societies
In this paper, we discuss the passage to hydrodynamic equations for kinetic
models of opinion formation. The considered kinetic models feature an opinion
density depending on an additional microscopic variable, identified with the
personal preference. This variable describes an opinion-driven polarisation
process, leading finally to a choice among some possible options, as it happens
e.g. in referendums or elections. Like in the kinetic theory of rarefied gases,
the derivation of hydrodynamic equations is essentially based on the
computation of the local equilibrium distribution of the opinions from the
underlying kinetic model. Several numerical examples validate the resulting
model, shedding light on the crucial role played by the distinction between
opinion and preference formation on the choice processes in multi-agent
societies.Comment: 30 pages, 15 figure
Election turnout statistics in many countries: similarities, differences, and a diffusive field model for decision-making
We study in details the turnout rate statistics for 77 elections in 11
different countries. We show that the empirical results established in a
previous paper for French elections appear to hold much more generally. We find
in particular that the spatial correlation of turnout rates decay
logarithmically with distance in all cases. This result is quantitatively
reproduced by a decision model that assumes that each voter makes his mind as a
result of three influence terms: one totally idiosyncratic component, one
city-specific term with short-ranged fluctuations in space, and one long-ranged
correlated field which propagates diffusively in space. A detailed analysis
reveals several interesting features: for example, different countries have
different degrees of local heterogeneities and seem to be characterized by a
different propensity for individuals to conform to the cultural norm. We
furthermore find clear signs of herding (i.e. strongly correlated decisions at
the individual level) in some countries, but not in others.Comment: 15 pages, 9 figures, 7 table
- …