8,317 research outputs found
Average Weights and Power in Weighted Voting Games
We investigate a class of weighted voting games for which weights are
randomly distributed over the standard probability simplex. We provide
close-formed formulae for the expectation and density of the distribution of
weight of the -th largest player under the uniform distribution. We analyze
the average voting power of the -th largest player and its dependence on the
quota, obtaining analytical and numerical results for small values of and a
general theorem about the functional form of the relation between the average
Penrose--Banzhaf power index and the quota for the uniform measure on the
simplex. We also analyze the power of a collectivity to act (Coleman efficiency
index) of random weighted voting games, obtaining analytical upper bounds
therefor.Comment: 12 pages, 7 figure
Interim efficient mechanisms for a public decision making in a discrete framework.
In this paper. I characterize the set of Bayesian incentive compatible anonymous mechanisms in a discrete public good problem when preferences are private information. With this result in hand, I characterize the set of interim incentive efficient mechanisms as voting schemes in which votes are weighted according to the tax paid by each agent.Public goods; Voting mechanisms; Interim efficiency;
A Statistical Model of Abstention under Compulsory Voting
Invalid voting and electoral absenteeism are two important sources of abstention in compulsory voting systems. Previous studies in this area have not considered the correlation between both variables and ignored the compositional nature of the data, potentially leading to unfeasible results and discarding helpful information from an inferential standpoint. In order to overcome these problems, this paper develops a statistical model that accounts for the compositional and hierarchical structure of the data and addresses robustness concerns raised by the use of small samples that are typical in the literature. The model is applied to analyze invalid voting and electoral absenteeism in Brazilian legislative elections between 1945 and 2006 via MCMC simulations. The results show considerable differences in the determinants of both forms of non-voting; while invalid voting was strongly positively related both to political protest and to the existence of important informational barriers to voting, the influence of these variables on absenteeism is less evident. Comparisons based on posterior simulations indicate that the model developed in this paper fits the dataset better than several alternative modeling approaches and leads to different substantive conclusions regarding the effect of different predictors on the both sources of abstention
The Inverse Shapley Value Problem
For a weighted voting scheme used by voters to choose between two
candidates, the \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of
provide a measure of how much control each voter can exert over the overall
outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley
and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice
theory as a measure of the "influence" of voters. The \emph{Inverse Shapley
Value Problem} is the problem of designing a weighted voting scheme which
(approximately) achieves a desired input vector of values for the
Shapley-Shubik indices. Despite much interest in this problem no provably
correct and efficient algorithm was known prior to our work.
We give the first efficient algorithm with provable performance guarantees
for the Inverse Shapley Value Problem. For any constant \eps > 0 our
algorithm runs in fixed poly time (the degree of the polynomial is
independent of \eps) and has the following performance guarantee: given as
input a vector of desired Shapley values, if any "reasonable" weighted voting
scheme (roughly, one in which the threshold is not too skewed) approximately
matches the desired vector of values to within some small error, then our
algorithm explicitly outputs a weighted voting scheme that achieves this vector
of Shapley values to within error \eps. If there is a "reasonable" voting
scheme in which all voting weights are integers at most \poly(n) that
approximately achieves the desired Shapley values, then our algorithm runs in
time \poly(n) and outputs a weighted voting scheme that achieves the target
vector of Shapley values to within error $\eps=n^{-1/8}.
A Simple Scheme to Improve the Efficiency of Referenda
This paper proposes a simple scheme designed to elicit and reward intensity of preferences in referenda: voters faced with a number of binary proposals are given one regular vote for each proposal plus an additional number of bonus votes to cast as desired. Decisions are taken according to the majority of votes cast. In our base case, where there is no systematic difference between proposals’ supporters and opponents, there is always a positive number of bonus votes such that ex ante utility is increased by the scheme, relative to simple majority voting. When the distributions of valuations of supporters and opponents differ, the improvement in efficiency is guaranteed if the distributions can be ranked according to first order stochastic dominance. If they are, however, the existence of welfare gains is independent of the exact number of bonus votes.
Harmonic Analysis of Boolean Networks: Determinative Power and Perturbations
Consider a large Boolean network with a feed forward structure. Given a
probability distribution on the inputs, can one find, possibly small,
collections of input nodes that determine the states of most other nodes in the
network? To answer this question, a notion that quantifies the determinative
power of an input over the states of the nodes in the network is needed. We
argue that the mutual information (MI) between a given subset of the inputs X =
{X_1, ..., X_n} of some node i and its associated function f_i(X) quantifies
the determinative power of this set of inputs over node i. We compare the
determinative power of a set of inputs to the sensitivity to perturbations to
these inputs, and find that, maybe surprisingly, an input that has large
sensitivity to perturbations does not necessarily have large determinative
power. However, for unate functions, which play an important role in genetic
regulatory networks, we find a direct relation between MI and sensitivity to
perturbations. As an application of our results, we analyze the large-scale
regulatory network of Escherichia coli. We identify the most determinative
nodes and show that a small subset of those reduces the overall uncertainty of
the network state significantly. Furthermore, the network is found to be
tolerant to perturbations of its inputs
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