50,327 research outputs found
Representation-Compatible Power Indices
This paper studies power indices based on average representations of a
weighted game. If restricted to account for the lack of power of dummy voters,
average representations become coherent measures of voting power, with power
distributions being proportional to the distribution of weights in the average
representation. This makes these indices representation-compatible, a property
not fulfilled by classical power indices. Average representations can be
tailored to reveal the equivalence classes of voters defined by the Isbell
desirability relation, which leads to a pair of new power indices that ascribes
equal power to all members of an equivalence class.Comment: 28 pages, 1 figure, and 11 table
On minimum sum representations for weighted voting games
A proposal in a weighted voting game is accepted if the sum of the
(non-negative) weights of the "yea" voters is at least as large as a given
quota. Several authors have considered representations of weighted voting games
with minimum sum, where the weights and the quota are restricted to be
integers. Freixas and Molinero have classified all weighted voting games
without a unique minimum sum representation for up to 8 voters. Here we
exhaustively classify all weighted voting games consisting of 9 voters which do
not admit a unique minimum sum integer weight representation.Comment: 7 pages, 6 tables; enumerations correcte
Ready for the design of voting rules?
The design of fair voting rules has been addressed quite often in the
literature. Still, the so-called inverse problem is not entirely resolved. We
summarize some achievements in this direction and formulate explicit open
questions and conjectures.Comment: 10 page
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
- …