[...]


[...] Recalling the social choice setting of Chapter 2.5, consider a $2$candidate, $n$voter election using a monotone voting rule $f : \{1,1\}^n \to \{1,1\}$. We assume the impartial culture assumption (that the votes are independent and uniformly random), but with a twist: one of the candidates, say $b \in \{1,1\}$, is able to secretly bribe $k$ [...] A very important quantity in the analysis of a boolean function is the sum of its influences. Definition 26 The total influence of $f : \{1,1\}^n \to {\mathbb R}$ is defined to be \[ \mathbf{I}[f] = \sum_{i=1}^n \mathbf{Inf}_i[f]. \] [...] 

Copyright © 2017 Ryan O'Donnell  All Rights Reserved 
Recent comments