15 research outputs found
Measuring voting power in convex policy spaces
Classical power index analysis considers the individual's ability to
influence the aggregated group decision by changing its own vote, where all
decisions and votes are assumed to be binary. In many practical applications we
have more options than either "yes" or "no". Here we generalize three important
power indices to continuous convex policy spaces. This allows the analysis of a
collection of economic problems like e.g. tax rates or spending that otherwise
would not be covered in binary models.Comment: 31 pages, 9 table
Generalized roll-call model for the Shapley-Shubik index
In 1996 Dan Felsenthal and Mosh\'e Machover considered the following model.
An assembly consisting of voters exercises roll-call. All possible
orders in which the voters may be called are assumed to be equiprobable. The
votes of each voter are independent with expectation for an individual
vote {\lq\lq}yea{\rq\rq}. For a given decision rule the \emph{pivotal}
voter in a roll-call is the one whose vote finally decides the aggregated
outcome. It turned out that the probability to be pivotal is equivalent to the
Shapley-Shubik index. Here we give an easy combinatorial proof of this
coincidence, further weaken the assumptions of the underlying model, and study
generalizations to the case of more than two alternatives.Comment: 19 pages; we added a reference to an earlier proof of our main resul
Which criteria qualify power indices for applications? : A comment to "The story of the poor Public Good index"
We discuss possible criteria that may qualify or disqualify power indices for
applications. Instead of providing final answers we merely ask questions that
are relevant from our point of view and summarize some material from the
literature.Comment: 6 pages; typos correcte
Axiomatizations for the Shapley-Shubik power index for games with several levels of approval in the input and output
The Shapley-Shubik index is a specialization of the Shapley value and is
widely applied to evaluate the power distribution in committees drawing binary
decisions. It was generalized to decisions with more than two levels of
approval both in the input and the output. The corresponding games are called
simple games. Here we present a new axiomatization for the
Shapley-Shubik index for simple games as well as for a continuous
variant, which may be considered as the limit case.Comment: 25 page