Prospects after the Voting Reform of the Lisbon Treaty

The European Union used to make decisions by unanimity or near unanimity. After a series of extensions, with 27 member states the present decision making mechanisms have become very slow and assigned power to the members in an arbitrary way. The new decision rules accepted as part of the Lisbon Treaty did not only make decision making far easier, but streamlined the process by removing the most controversial element: the voting weights. The new system relies entirely on population data. We look at the immediate impact of the reform as well as the long term effects of the dfferent demographic trends in the 27 member states. We find that the Lisbon rules benefit the largest member states, while medium sized countries, especially Central Eastern European countries suffer the biggest losses.European Union, Council of Ministers, qualified majority voting, Banzhaf index, Shapley-Shubik index, a priori voting power, demographics

The Core of a Partition Function Game

We consider partition function games and introduce new definitions of the core that include the effects of externalities. We assume that all players behave rationally and that all stable outcomes arising are consistent with the appropriate generalised concept of the core. The result is a recursive definition of the core where residual subgames are considered as games with fewer players and with a partition function that captures the externalities of the deviating coalition. Some properties of the new concepts are discussed.

The minimal dominant set is a non-empty core-extension

A set of outcomes for a transferable utility game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible (or admissible) and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. The minimal (for inclusion) dominant set is non-empty and for a game with a non-empty coalition structure core, the minimal dominant set returns this core. We provide an algorithm to find the minimal dominant set.dynamic solution, absorbing set, core, non-emptiness

The men who weren't even there: Legislative voting with absentees

Voting power in voting situations is measured by the probability of changing decisions by altering the cast 'yes' or 'no' votes. Recently this analysis has been extended by strategic abstention. Abstention, just as 'yes' or 'no' votes can change decisions. This theory is often applied to weighted voting situations, where voters can cast multiple votes. Measuring the power of a party in a national assembly seems to fit this model, but in fact its power comprises of votes of individual representatives each having a single vote. These representatives may vote yes or no, or may abstain, but in some cases they are not even there to vote. We look at absentees not due to a conscious decision, but due to illness, for instance. Formally voters will be absent, say, ill, with a certain probability and only present otherwise. As in general not all voters will be present, a thin majority may quickly melt away making a coalition that is winning in theory a losing one in practice. A simple model allows us to differentiate between winning and more winning and losing and less losing coalitions reected by a voting game that is not any more simple. We use data from Scotland, Hungary and a number of other countries both to illustrate the relation of theoretical and effective power and show our results working in the practice.a priori voting power; power index; being absent from voting; minority; Shapley-Shubik index; Shapley value

The minimal dominant set is a non-empty core-extension

A set of outcomes for a transferable utility game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible (or admissible) and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. The minimal (for inclusion) dominant set is non-empty and for a game with a non-empty coalition structure core, the minimal dominant set returns this core. We provide an algorithm to find the minimal dominant set

Stable Allocations of Risk

Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games. We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games.Coherent Measures of Risk, Risk Allocation Games, Totally Balanced Games, Exact Games