[EM] Someone thinks that Approval should meet the Mutual Majority Criterion

Jameson Quinn jameson.quinn at gmail.com
Thu Jun 6 11:56:21 PDT 2013

2013/6/6 Abd ul-Rahman Lomax <abd at lomaxdesign.com>

> 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.

This fails FBC. I am sympathetic to Abd's arguments about how the
electorate will change based on preference strength, and how well-informed
voters will tend to find a way to avoid FBC failure, but that doesn't mean
that it passes the criterion, merely that the failure is minor.

> 2. Top two approval where a candidate with a majority can win, otherwise
> two candidates advance.

Still fails, although it's slightly better.

> 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.

This is true... but only if there's a hard threshold for making it to the
second round. That is, "all candidates with over 1/3 approval advance", or
some such; and if there are fewer than 2 such candidates, the highest
approval wins in the first round.

> (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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