A Second Test of a Single Seat Election Method

[Saari at aol.com]

>     When I wrote the post titled: Does the Method confirm the Majority
>Winner? I forgot about a second test of a single seat method. That test
>being:
>
>     Will the method always elect with a majority?

Any method which successively eliminates candidates until there are only two
left will usually produce a "majority" of one over the other.  But in my mind
this is no assurance that the best candidate was chosen.

For that matter, I do not agree that the majority choice is necessarily what
most pleases a group.

Consider a simple case with only two candidates.  Candidate A is well-liked
by everybody.  Candidate B is liked even more by 2/3 of the group, but is
hated by the other 1/3.  Which candidate is best?

1) For some people, the bare fact that two-thirds prefer B over A means that
B *must* be the correct choice - end of discussion.

2) However, an alternate view is that a candidate who is liked by 100% of a
group is better than a candidate who is liked by only 67% of the group.  For
instance, generally I would rather *always* get a choice that I "like" rather
than only 2/3 of the time.  I would happily give up having my "top choice"
2/3 of the time (in favor of someone else who I also liked) if it meant
avoiding choosing my "awful" choice the other 1/3 of the time.

The truth is that neither view is always correct, yet each view is correct at
least some of the time.  Sometimes the most excellent choice is best (even if
it upsets some people).  Other times the "liked by the most people" choice is
correct.

The best election method is one that can allow for either outcome - depending
on the exact feelings of the voters.  Approval Voting is an example of such.
 If the 2/3 vote Yes on both candidates (feeling that either one is
acceptable) then the 100%-liked choice will win.  But if the 2/3 feel that
only the "best" candidate will do, then they will choose candidate B over the
objections of the rest of the group.

In my view, the so-called "non-determinacy" of Approval Voting simply means
that it allows for either outcome - meaning that it better reflects the
particular wishes of that group of people than a more determinate
preferential method (which generally forces a win for the candidate disliked
by 1/3 of the group).

(I agree with objections that AV doesn't allow one to distinguish a "top"
choice from a second-best but still acceptable choice.  The remedy is more
"resolution", i.e. a gradation of available choices.)

Mike S