Reply to Saari on Approval Voting

Saari at Saari at
Fri Apr 18 23:55:20 PDT 1997

>Anyone who made two selections could have stayed in
>bed - because two selections is the same as not voting. As the people
>become more knowledgeable about Approval Voting they will realize that it
>is not to their benefit to make more than one selection.

A questionable conclusion if there are more than two candidates.  But even
with only two candidates it is not as simple as that.

Your conclusion may be true for standard Approval Voting, but it is not
necessarily true under other possible "rated" voting/scoring systems.

Consider a 3-level voting method, where you can vote Support, Oppose or
Neither on every candidate.  (This is already more choice than standard
Approval voting gives.)  Let's stick to the simple situation with only two

One might argue that the only "logical" vote is Support for A, Oppose for B
(or vice versa), and that any other vote wastes some possible influence.  But
this is only true for some methods of scoring the votes.  With other possible
methods for determining a winner this conclusion will not be true.

Here's another possibility for scoring by way of illustration.  Suppose the
method for determining the winner (for any number of candidates - 1,2,3 or
more) is as follows:
1) Tally the Support totals and Oppose Totals for each candidate.
2) If no candidate qualifies by achieving a 2:1 Support/Oppose ratio, then
the office will instead be filled by an appointment by the current
3) If one or more candidates qualify with a 2:1 ratio, then the candidate
with the greatest net support (Support total minus Oppose total) is the

Notice that it is now not at all clear that a vote of "Support for one,
Oppose the other" is necessarily logical or rational.  With two
fairly-matched candidates, and all voters following the above strategy, the
likely outcome is that neither candidate will achieve the 2:1 ratio.  If the
voters actually like both candidates but mistrust the likely result by
appointment, then votes of Support,support or maybe Support,neither will be
more sensible.

My "voting design" philosophy: 1) Give the voters maximum freedom to express
their true feelings (rated votes), then 2) Design the scoring system to
maximize the incentive to vote honestly.

Donald writes: We will get more gradation of the available choices if and
when the people are allowed to make preferences when they vote.
Knowledgeable persons will give their first preference to the candidate
that they feel is the best even if that candidate is low in the polls. When
everyone does this we will have a better gradation of choices - then it is
a question of reducing the field down to one.

Well, with only two candidates preference voting also boils down to simple
plurality - your only possible votes are either A>B or B>A.  Rated voting at
least gives more possible combinations (3x3 in the case of two candidates).
 Even if everybody only chooses Support,Oppose or Oppose,Support they have
the same degree of choice as in preferential voting.

With more candidates it gets more interesting.  Consider 3 candidates.  With
preference voting there are only 6 possible votes: A>B>C, A>C>B, B>A>C,
B>C>A, C>A>B, C>B>A. (Plus 3 if you include single-choices which do not rank
the bottom two.)

With rated voting (choices are only Support,Oppose,Neither) there are still
12 possible votes (++-,+0-,+--,-++,-0+,--+,+-+,-+-,0-+,0+-,+-0,-+0) even if
everybody chooses Support for one and Oppose for one.  With a better scoring
incentive system to encourage honest voting, the number of possible
expressions jumps to 3x3x3=27 possible votes.  And if further gradations are
allowed (1/2 support, etc.) the number of possible votes is truly staggering.

Compared to the 6 possible votes under preferential voting, rated voting
appears to offer  greater selection opportunities and expression of more of
the voters' true feelings.

Mike S

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