Approximate Inference of Outcomes in Probabilistic Elections

We study the complexity of estimating the probability of an outcome
  in an election over probabilistic votes. The focus is on voting
  rules expressed as positional scoring rules, and two models of
  probabilistic voters: the uniform distribution over the completions
  of a partial voting profile (consisting of a partial ordering of the
  candidates by each voter), and the Repeated Insertion Model (RIM)
  over the candidates, including the special case of the Mallows
  distribution. Past research has established that, while exact
  inference of the probability of winning is computationally hard
  (\#P-hard), an additive polynomial-time approximation (additive
  FPRAS) is attained by sampling and averaging.  There is often,
  though, a need for multiplicative approximation guarantees that are
  crucial for important measures such as conditional
  probabilities. Unfortunately, a multiplicative approximation of the
  probability of winning cannot be efficient (under conventional
  complexity assumptions) since it is already NP-complete to
  determine whether this probability is nonzero. Contrastingly, we
  devise multiplicative polynomial-time approximations (multiplicative
  FPRAS) for the probability of the complement event, namely, losing
  the election.