Another issue that was left a bit hanging in discussions on the CES list:
Does top-two Approval fail the Favorite Betrayal Criterion? There are
really two forms of top-two Approval to be considered, plus a third detail.
1. Top two approval where two candidates advance to the general election.
2. Top two approval where a candidate with a majority can win,
otherwise two candidates advance.
3. If write-in votes are allowed in the runoff, the primary is
actually a nomination device, not the actual election. The actual
election being Approval, the combination must satisfy FBC if Approval
does, and it does.
(If write-in votes are allowed, in this concept, the runoff must also
be Approval.)
Arizona had a method up for legislative passage that would have
allowed municipalities to use a two-stage voting system with an
Approval primary, top-two advancing to the general election with
ballot placement, and, apparently, write-ins allowed in the general
election (as well as in the primary). The primary has no majority
test, it is top-two plurality, but voters may vote for as many
candidates as they choose. The runoff is standard vote-for-one.
So, first of all, does this method fail FBC? If so, is the scenario
plausible for real voters? These are nonpartisan elections.
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