[EM] Critique of FairVote's "approval voting" report

[Jameson Quinn]

The critique now has a number of comments in the margin, from a number of
people, including responses from Rob Richie (probably the original author of
the report). At the bottom, I've added my critique of the pervasive error
Fairvote (Richie?) makes. Here is a copy of my critique:

Strategy in Approval: the real story

In order to understand what the effect of “strategic” approval voting is, we
must first have some definition of “honest” approval voting to compare it
against. Various definitions are possible:

   1.

   Approve any candidate who’s better than the average serious candidate.
   -

      This is close to perfect strategy, so while it’s a fair definition of
      “honest”, we can’t really use this as a basis for comparing how
much of an
      advantage strategy gives. To do so could be criticized as biased
in favor of
      approval.
      2.

   Bullet vote. That is, approve only a single candidate.
   -

      This is apparently Fairvote’s (mistaken) idea of a strategy, so I
      guess we can’t use this as a basis for comparison either.
      3.

   Anti-bullet vote. That is, approve all but a single candidate.
   -

      This is a stupid strategy, and one which most people, who tend to be
      partisan and tribal, would not naturally tend to use. I only mention it
      because it’s the definition of “honest” used by Tideman. We will
not use it
      here.
      4.

   Set your approval threshold arbitrarily, somewhere in between your
   favorite and least-favorite candidate, and approve everyone above the
   threshold.
   -

      Obviously, people will be more likely to approve of a candidate the
      more they like that candidate. With enough voters, the law of
averages will
      even out the randomness of the arbitrary decisions, and so the
system will
      become roughly equivalent to range voting. (Technically speaking, it
      will be range voting, with the true range vote passed through some
      monotonically increasing, probably roughly integral-sign-shaped,
probability
      function; and with some slight random noise proportional to the
square root
      of the number of voters, around 0.1% for a million voters).

   Since definitions 1 and 2 could be called biased in favor of approval
   voting, and definition 3 is just stupid, we’ll use definition 4 for the rest
   of this analysis.

   Note that under definition 4, the honest approval winner is just the
   honest range winner. That has been shown to be the system which comes
   closest to electing the true utility winner for the voters - the winner who
   makes the average voter happiest. So this is an excellent result for honest
   approval.

   So, what about strategy? Is it true, as Fairvote claims, that “strategic
   voters will always earn a significant advantage over less informed voters”?
   Well, that depends what you mean by “strategy”.

   Let’s start by trying Fairvote’s definition:

   “...[V]oters who vote tactically by casting a single vote for their
   favorite candidate will gain an advantage over those voters who indicate
   support for more than one candidate....”

   This is totally false. Such voters will only gain an advantage if their
   favorite candidate wins. On the other hand, they will be hurting themselves
   if they happen to have favored the candidate who ends in second place, over
   the candidate who ends in first place. In a 5-candidate election, they gain
   in an average of about 20% of the cases, and lose in an average of about
   40%; that is, they lose on average of about twice as often as they gain.
   Since this is not even advantageous, Fairvote is flatly incorrect to
   repeatedly claim that bullet voting is even “strategic”, let alone
   “always... a significant advantage”.

   What about other strategies? Correct Approval strategy is, approximately,
   to set your approval threshold at the average quality of the candidates whom
   you think might win. Unless the election is abnormally close, only two
   candidates have a real chance of winning, and of those two one is clearly
   leading, so that means you should approve one of the two frontruners and
   everyone you like better.

   This strategy, unlike Fairvote’s false “strategy”, does indeed give the
   voter a significant advantage. Since, as we’ve seen, our definition of
   honest Approval voting is probabilistically equivalent to Range voting, the
   advantage for strategic voting is the same as it would be in Range. This is
   in fact “always ... a significant advantage”. However, several things should
   be noted:
   -

      The actual advantageous strategy is precisely the opposite of the
      so-called “strategy” which Fairvote claims will be the pervasive problem
      with Approval.
      -

      If everyone uses their best strategy, the winner will be the Condorcet
      winner, if one exists. Far from being a problematic or
pathological result,
      this is seen by many as the most democratic result for the society as a
      whole.
      -

      This is actually the same as the “honest” result with our first
      proposed definition of honesty.

   In conclusion, Fairvote’s critique of strategy under approval voting
   suffers from an acute lack of understanding of game theory, and is 180
   degrees wrong in several important ways. If Fairvote had confined themselves
   to talking about the actions of what they call “strategic actors” --- that
   is, candidates and their proxies --- they might have had a point. But for
   voters, their supposed “strategy” is just the opposite.





2011/10/10 Jameson Quinn <jameson.quinn at gmail.com>

> I would like to make a detailed critique of the FairVote report they've put
> up at approvalvoting.blogspot.com and rangevoting.com. I believe that
> every single one of the conclusions of that report is dangerously wrong.
> I've created a google doc<https://docs.google.com/document/d/1YgXEqjmhEv05-FHc1PtPs0O9zzwWzKgoy4sBuaEsEcg/edit?hl=en_US>to help make this critique collaboratively. Please add comments to the doc
> to help critique.
>
> Thanks,
> Jameson
>
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