Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The inverse problem for power distributions in committees   Several power indices have been introduced in the literature in order to
measure the influence of individual committee members on the aggregated
decision. Here we ask the inverse question and aim to design voting rules for a
committee such that a given desired power distribution is met as closely as
possible. We present an exact algorithm for a large class of different power
indices based on integer linear programming. With respect to negative
approximation results we generalize the approach of Alon and Edelman who
studied power distributions for the Banzhaf index, where most of the power is
concentrated on few coordinates. It turned out that each Banzhaf vector of an
n-member committee that is near to such a desired power distribution, has to be
also near to the Banzhaf vector of a k-member committee. We show that such
Alon-Edelman type results are possible for other power indices like e.g. the
Public Good index or the Coleman index to prevent actions, while they are
principally impossible for e.g. the Johnston index.

23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph