part 6, 1st Choice Criterion

[Mike Ositoff]

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