1,894 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
Derivative of functions over lattices as a basis for the notion of interaction between attributes
The paper proposes a general notion of interaction between attributes, which
can be applied to many fields in decision making and data analysis. It
generalizes the notion of interaction defined for criteria modelled by
capacities, by considering functions defined on lattices. For a given problem,
the lattice contains for each attribute the partially ordered set of remarkable
points or levels. The interaction is based on the notion of derivative of a
function defined on a lattice, and appears as a generalization of the Shapley
value or other probabilistic values
Cooperation through social influence
We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley-Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.Peer ReviewedPostprint (author’s final draft
On anonymous and weighted voting systems
Many bodies around the world make their decisions through voting systems in which voters have several options and the collective result also has several options. Many of these voting systems are anonymous, i.e., all voters have an identical role in voting. Anonymous simple voting games, a binary vote for voters and a binary collective decision, can be represented by an easy weighted game, i.e., by means of a quota and an identical weight for the voters. Widely used voting systems of this type are the majority and the unanimity decision rules. In this article, we analyze the case in which voters have two or more voting options and the collective result of the vote has also two or more options. We prove that anonymity implies being representable through a weighted game if and only if the voting options for voters are binary. As a consequence of this result, several significant enumerations are obtained.This research was partially supported by funds from the Spanish Ministry of Science and Innovation grant PID2019-I04987GB-I00. We are grateful to the associate editor and two anonymous referees whose interesting comments allowed us to improve the paper.Peer ReviewedPostprint (author's final draft
Mixture Selection, Mechanism Design, and Signaling
We pose and study a fundamental algorithmic problem which we term mixture
selection, arising as a building block in a number of game-theoretic
applications: Given a function from the -dimensional hypercube to the
bounded interval , and an matrix with bounded entries,
maximize over in the -dimensional simplex. This problem arises
naturally when one seeks to design a lottery over items for sale in an auction,
or craft the posterior beliefs for agents in a Bayesian game through the
provision of information (a.k.a. signaling).
We present an approximation algorithm for this problem when
simultaneously satisfies two smoothness properties: Lipschitz continuity with
respect to the norm, and noise stability. The latter notion, which
we define and cater to our setting, controls the degree to which
low-probability errors in the inputs of can impact its output. When is
both -Lipschitz continuous and -stable, we obtain an (additive)
PTAS for mixture selection. We also show that neither assumption suffices by
itself for an additive PTAS, and both assumptions together do not suffice for
an additive FPTAS.
We apply our algorithm to different game-theoretic applications from
mechanism design and optimal signaling. We make progress on a number of open
problems suggested in prior work by easily reducing them to mixture selection:
we resolve an important special case of the small-menu lottery design problem
posed by Dughmi, Han, and Nisan; we resolve the problem of revenue-maximizing
signaling in Bayesian second-price auctions posed by Emek et al. and Miltersen
and Sheffet; we design a quasipolynomial-time approximation scheme for the
optimal signaling problem in normal form games suggested by Dughmi; and we
design an approximation algorithm for the optimal signaling problem in the
voting model of Alonso and C\^{a}mara
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