13,116 research outputs found
Simple games versus weighted voting games: Bounding the critical threshold value
A simple game is given by a set of players and a partition
of~ into a set~ of losing coalitions~ with value
that is closed under taking subsets and a set of winning
coalitions with . Simple games with are exactly the
weighted voting games. We show that for every simple
game , confirming the conjecture of Freixas and Kurz (IJGT, 2014). For
complete simple games, Freixas and Kurz conjectured that .
We prove this conjecture up to a factor. We also prove that for graphic
simple games, that is, simple games in which every minimal winning coalition
has size~2, computing is \NP-hard, but polynomial-time solvable if the
underlying graph is bipartite. Moreover, we show that for every graphic simple
game, deciding if .Comment: 10 pages; the paper is a follow-up and merge of arXiv:1805.02192 and
arXiv:1806.0317
Bounds for the Nakamura number
The Nakamura number is an appropriate invariant of a simple game to study the
existence of social equilibria and the possibility of cycles. For symmetric
quota games its number can be obtained by an easy formula. For some subclasses
of simple games the corresponding Nakamura number has also been characterized.
However, in general, not much is known about lower and upper bounds depending
of invariants on simple, complete or weighted games. Here, we survey such
results and highlight connections with other game theoretic concepts.Comment: 23 pages, 3 tables; a few more references adde
Sequential legislative lobbying
In this paper, we analyze the equilibrium of a sequential game-theoretical model of lobbying, due to Groseclose and Snyder (1996), describing a legislature that vote over two alternatives, where two opposing lobbies, Lobby 0 and Lobby 1, compete by bidding for legislatorsâ votes. In this model, the lobbyist moving first suffers from a second mover advantage and will make an offer to a panel of legislators only if it deters any credible counter-reaction from his opponent, i.e., if he anticipates to win the battle. This paper departs from the existing literature in assuming that legislators care about the consequence of their votes rather than their votes per se. Our main focus is on the calculation of the smallest budget that he needs to win the game and on the distribution of this budget across the legislators. We study the impact of the key parameters of the game on these two variables and show the connection of this problem with the combinatorics of sets and notions from cooperative game theory.Lobbying; cooperative games; noncooperative games
Voting Power in the EU Council of Ministers and Fair Decision Making in Distributive Politics
We analyze and evaluate the different decision rules describing the Council of Ministers of the EU starting from 1958 up to date. All the existing studies use the Banzhaf index (for binary voting) or the Shapley-Shubik index (for distributive politics). We argue that the nucleolus can be considered an appropriate power measure in distributive situations and an alternative to the Shapley-Shubik index. We then calculate the nucleolus and compare the results of our calculations with the conventional measures. In the second part, we analyze the power of the European citizens as measured by the nucleolus under the egalitarian criterion proposed by Felsenthal and Machover (1998), and characterize the first best situation. Based on these results we propose a methodology for the design of the optimal (fair) decision rules. We perform the optimization exercise for the earlier stages of the EU within a restricted domain of voting rules, and conclude that Germany should receive more than the other three large countries under the optimal voting rule.
Measuring voting power: The paradox of new members vs the null player axiom
Qualified majority voting is used when decisions are made by voters of different sizes. In such situations the voters' influence on decision making is far from obvious; power measures are used for an indication of the decision making ability. Several power measures have been proposed and characterised by simple axioms to help the choice between them. Unfortunately the power measures also feature a number of so-called paradoxes of voting power. In this paper we show that the Paradox of New Members follows from the Null Player Axiom. As a corollary of this result it follows that there does not exist a power measure that satisfies the axiom, while not exhibiting the Paradox.a priori voting power, paradox of new members, null player axiom
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