  Given a predicate $P: \{-1, 1\}^k \to \{-1, 1\}$, let $CSP(P)$ be the set of
constraint satisfaction problems whose constraints are of the form $P$. We say
that $P$ is approximable if given a nearly satisfiable instance of $CSP(P)$,
there exists a probabilistic polynomial time algorithm that does better than a
random assignment. Otherwise, we say that $P$ is approximation resistant.
  In this paper, we analyze presidential type predicates, which are balanced
linear threshold functions where all of the variables except the first variable
(the president) have the same weight. We show that almost all presidential-type
predicates $P$ are approximable. More precisely, we prove the following result:
for any $\delta_0 > 0$, there exists a $k_0$ such that if $k \geq k_0$, $\delta
\in (\delta_0,1 - 2/k]$, and ${\delta}k + k - 1$ is an odd integer then the
presidential type predicate $P(x) = sign({\delta}k{x_1} + \sum_{i=2}^{k}{x_i})$
is approximable. To prove this, we construct a rounding scheme that makes use
of biases and pairwise biases. We also give evidence that using pairwise biases
is necessary for such rounding schemes.
