There's also a class of methods called the "pairwise-count" or "pairwise" methods. They start out: Voters rank as many candidates as they wish. A beats B if more voters rank A over B than vice-versa. If 1 candidate beats each of the others, he wins. Sometimes there isn't such a candidate. When there is, he's a CW. When there isn't, however, that doesn't necessarily mean there isn't a CW. Maybe there is one, but he's losing his win due to truncation or order-reversal. Truncation means voting a short ranking rather than ranking everyone. Order-reversal means strategic reversal of a preference ordering. In general, pairwise methods fail weak & strong versions of the 1st Choice Criterion. Truncation is all it takes to makek them fail the strong version. Order reversal makes them fail the weak version. Mike
