Elchanan Mossel

The geometry of manipulation — A quantitative proof of the Gibbard-Satterthwaite theorem

We prove a quantitative version of the Gibbard-Satterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of q ≥ 4 alternatives and n voters will be manipulable with probability at least 10−4∈2n−3q−30, where ∈ is the minimal statistical distance between f and the family of dictator functions.Our results extend those of [11], which were obtained for the case of 3 alternatives, and imply that the approach of masking manipulations behind computational hardness (as considered in [4,6,9,15,7]) cannot hide manipulations completely.Our proof is geometric. More specifically it extends the method of canonical paths to show that the measure of the profiles that lie on the interface of 3 or more outcomes is large. To the best of our knowledge our result is the first isoperimetric result to establish interface of more than two bodies.

Majority dynamics and aggregation of information in social networks

Consider

Strategic Learning and the Topology of Social Networks

n

Standard Simplices and Pluralities are Not the Most Noise Stable

n individuals who, by popular vote, choose among

VC bounds on the cardinality of nearly orthogonal function classes

q ge 2

The Speed of Social Learning

q≥2 alternatives, one of which is “better” than the others. Assume that each individual votes independently at random, and that the probability of voting for the better alternative is larger than the probability of voting for any other. It follows from the law of large numbers that a plurality vote among the