Alternate vote optimizes first choices; while there are edge
cases (including possibilities for ties) something basically has
to be someone's first choice in order to win.
Condorcet optimizes one particular preference model. In
particular, as Charles's model illustrates very well, it assumes
that an option that is everyone's second choice is better than
any option that is the first choices of a minority of the
voters. As such, one might think of it as one version of the
model that a good choice is the one that leaves everyone more or
less equally unhappy.
It is important to note that any of the systems, including the
ones discussed below, get a lot more complicated, with more ways
to get into strange cases, as the number of options rises above
three. And any of them can be gamed by colluding voters,
although some are more easily gamed than others.
But there are many other options. For example, in a situation
like the one we have, there is a strong argument that one should
first examine "I completely hate this" votes, eliminating any
options that are intensely disliked by a non-trivial number of
people, and only then applying a model based on affirmative
preferences to what is left. Some feel that works better in
environments in which there is a lot of indifference (as long as
an answer is found) but a desire to eliminate really bad choices
before one is approved based on weak preferences. This sort of
system is often considered bad for elections but good for some
other types of preference choices.
