Related papers: The power of the largest player
Based on Holler (1982) and Armijos-Toro et al. (2021) we propose two power indices to measure the influence of the players in the class of weighted majority games in partition function form. We compare these new power indices with their…
The concept of power among players can be expressed as a combination of their utilities. A player who obeys another takes into account the utility of the dominant one. Technically it is a matter of superimposing some weighted sum or product…
Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called…
Members of a shareholder meeting or legislative committee have greater or smaller voting power than meets the eye if the nucleolus of the induced majority game differs from the voting weight distribution. We establish a new sufficient…
Binary yes-no decisions in a legislative committee or a shareholder meeting are commonly modeled as a weighted game. However, there are noteworthy exceptions. E.g., the voting rules of the European Council according to the Treaty of Lisbon…
In this paper we study rankings induced by power indices of players in simple game models of bicameral legislatures. For a bicameral legislature where bills are passed with a simple majority vote in each house we give a condition involving…
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…
Weighted voting games apply to a wide variety of multi-agent settings. They enable the formalization of power indices which quantify the coalitional power of players. We take a novel approach to the study of the power of big vs.~small…
Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights,…
Weighted voting games are a family of cooperative games, typically used to model voting situations where a number of agents (players) vote against or for a proposal. In such games, a proposal is accepted if an appropriately weighted sum of…
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…
Power indices are essential in assessing the contribution and influence of individual agents in multi-agent systems, providing crucial insights into collaborative dynamics and decision-making processes. While invaluable, traditional…
A committee's decisions on more than two alternatives much depend on the adopted voting method, and so does the distribution of power among the committee members. We investigate how different aggregation methods such as plurality runoff,…
We investigate the manipulation of power indices in TU-cooperative games by stimulating (subject to a budget constraint) changes in the propensity of other players to participate to the game. We display several algorithms that show that the…
Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting…
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The…
Within the domain of game theory, power indexes are defined as functions that quantify the influence of individual participants in collective decision-making processes. Felsenthal [D. Felsenthal. A Well-Behaved Index of a Priori P-Power for…
In social network analysis, there is a common perception that influence is relevant to determine the global behavior of the society and thus it can be used to enforce cooperation by targeting an adequate initial set of individuals or to…
We exhibit the hidden beauty of weighted voting and voting power by applying a generalization of the Penrose-Banzhaf index to social choice rules. Three players who have multiple votes in a committee decide between three options by…
In a strategy-proof mechanism, the influence of an agent may be measured as the set of outcomes an agent can bring about by varying her (reported) type. More specifically, we refer to an agent's influence on her own relevant outcomes as her…