  This paper studies problems of inferring order given noisy information. In
these problems there is an unknown order (permutation) $\pi$ on $n$ elements
denoted by $1,...,n$. We assume that information is generated in a way
correlated with $\pi$. The goal is to find a maximum likelihood $\pi^*$ given
the information observed. We will consider two different types of observations:
noisy comparisons and noisy orders. The data in Noisy orders are permutations
given from an exponential distribution correlated with \pi (this is also called
the Mallow's model). The data in Noisy Comparisons is a signal given for each
pair of elements which is correlated with their true ordering.
  In this paper we present polynomial time algorithms for solving both problems
with high probability. As part of our proof we show that for both models the
maximum likelihood solution $\pi^{\ast}$ is close to the original permutation
$\pi$.
  Our results are of interest in applications to ranking, such as ranking in
sports, or ranking of search items based on comparisons by experts.
