[EM] Rob Richie's critiscism of approval voting

Anthony O'Neal thasupasacfitinman at gmail.com
Wed Jun 14 11:30:54 PDT 2006

election-methods at electorama.com

Jonathan Lundell <jlundell at pobox.com> wrote:

    At 2:18 PM -0600 6/13/06, Jan Kok wrote:
    >One bit of help I could use: Is anyone familiar with the article Rob
    >mentions in this paragraph?
    >> Jack Nagel, a UPenn professor, has an important new article out
    >>this year called "Burr's Dilemma" that goes into how this flaw
    >>played out in the 1796 and 1800 presidential election, where the
    >>presidential electors (who at that time had two equally weighted
    >>votes), made strategic mistakes with major consequences in both
    >>elections. Nagel used to say approval voting was better, but now
    >>says IRV is better.

    The key slide from Nagel's presentation:

    Statement of the Burr Dilemma

    When three or more candidates compete for an office that only one can
    win, and voters (V) may support two (or more) of them by casting
    equal (approval) votes, candidates (C1 and C2) seeking support from
    the same group (G) of voters will maximize their respective votes if
    all members of G vote for both C1 and C2. Both candidates thus have
    an incentive to appeal for shared support. However, if such appeals
    succeed completely and neither candidate receives votes from members
    of V-G, the outcome will be at best a tie in which neither C1 nor C2
    is assured of victory. Each candidate therefore has an incentive to
    encourage some members of G to vote only for himself or herself. If
    both C1 and C2 successfully follow such a strategy, either or both
    may receive fewer votes than some other candidate C3 supported by
    members of V-G. The risk that both C1 and C2 will lose is
    exacerbated if a retaliatory spiral increases the number of single
    votes cast by members of G. At the limit, such retribution reduces
    approval voting to conventional single-vote balloting among the
    members of G or, if the problem is endemic, among all voters. The
    nearer that limit is approached, the lower the probability that
    advantages claimed for approval voting will be realized..

    I believe that range voting could mostly solve such problems.  Parties
could instruct people to vote all their voting power for their favorite of
the candidates and all of their voting power minus 1 for the next
favorite... if all voters pursued this strategy, the most preferred of the
group would get elected while taking little from the groups' total
strength.  It would be unlikely that a competitor could gain much from such
a small loss in total strength unless the amount of range is somewhere like
1-10, but if you give people more range to deal with the effects are

    Such a strategy is actually somewhat equivalent to Borda count.  Borda
count has the effect of giving the win to the person with the highest
average rank, it would make sense to use the same method for deciding
between two people, although if a group used it to decide between more than
three people burying and the other negative effects of Borda would come into

    Range actually solves a lot of approvals' problems.  For one, people
often complain about the "lowest common denominator" problem, which happens
because approval forces people to give out thier full range.  Such a lowest
common denominator is likely to get far less votes under range than
approval, because if you had the option you'd likely give out smaller
approval to such a candidate.

    Range is really starting to make more and more sense to me as the days
go by.  I originally disliked it because I assumed people would always vote
approval-esque, but this isn't exactly true, and it never really can make
the results worse than approval. I'm trying to come  up with a range
equivalent of proportional approval voting, but I really haven't put much
thought into it yet, even though it seems easy.  The reweighted range voting
method that already exists shares many of the same problems as sequential
approval voting - I.E. it is strategically optimal to withold votes from
people you know are going to win.
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