Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reaching a Consensus on Random Networks: The Power of Few   A community of $n$ individuals splits into two camps, Red and Blue. The
individuals are connected by a social network, which influences their colors.
Everyday, each person changes his/her color according to the majority among
his/her neighbors. Red (Blue) wins if everyone in the community becomes Red
(Blue) at some point.
  We study this process when the underlying network is the random Erdos-Renyi
graph $G(n, p)$. With a balanced initial state ($n/2$ person in each camp), it
is clear that each color wins with the same probability.
  Our study reveals that for any constants $p$ and $\varepsilon$, there is a
constant $C$ such that if one camp has $n/2 +C$ individuals, then it wins with
probability at least $1 - \varepsilon$. The surprising key fact here is that
$C$ does not depend on $n$, the population of the community. When $p=1/2$ and
$\varepsilon =.1$, one can set $C$ as small as 6. If the aim of the process is
to choose a candidate, then this means it takes only $6$ "defectors" to win an
election unanimously with overwhelming odd.

36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas