  Scoring protocols are a broad class of voting systems. Each is defined by a
vector $(\alpha_1,\alpha_2,...,\alpha_m)$, $\alpha_1 \geq \alpha_2 \geq >...
\geq \alpha_m$, of integers such that each voter contributes $\alpha_1$ points
to his/her first choice, $\alpha_2$ points to his/her second choice, and so on,
and any candidate receiving the most points is a winner.
  What is it about scoring-protocol election systems that makes some have the
desirable property of being NP-complete to manipulate, while others can be
manipulated in polynomial time? We find the complete, dichotomizing answer:
Diversity of dislike. Every scoring-protocol election system having two or more
point values assigned to candidates other than the favorite--i.e., having
$||\{\alpha_i \condition 2 \leq i \leq m\}||\geq 2$--is NP-complete to
manipulate. Every other scoring-protocol election system can be manipulated in
polynomial time. In effect, we show that--other than trivial systems (where all
candidates alway tie), plurality voting, and plurality voting's transparently
disguised translations--\emph{every} scoring-protocol election system is
NP-complete to manipulate.
