An axiomatization of the Banzhaf value
International Journal of Game Theory
A Fourier-theoretic perspective on the Condorcet paradox and Arrow's theorem
Advances in Applied Mathematics
Thresholds and Expectation Thresholds
Combinatorics, Probability and Computing
Decision trees and influences of variables over product probability spaces
Combinatorics, Probability and Computing
On the influences of variables on boolean functions in product spaces
Combinatorics, Probability and Computing
Journal of Combinatorial Theory Series A
A simple reduction from a biased measure on the discrete cube to the uniform measure
European Journal of Combinatorics
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity
ACM Transactions on Computation Theory (TOCT)
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The notion of the influence of a variable on a Boolean function on a product space has attracted much attention in combinatorics, computer science and other fields. Two of the basic papers dealing with this notion are by Kahn, Kalai and Linial (KKL) and Bourgain, Kahn, Kalai, Katznelson and Linial (BKKKL).In this paper we survey the results in those papers and offer some simpler proofs, corrections, and extensions of the theorems presented there. We present several related open problems.