[EM] The billiard ball theory of voting

[Forest Simmons]

Craig Layton recently reminded us of the prevalent superstition that
considers a vote to be an indivisible entity like a billiard ball.

IRV supporters cater to this superstition by describing their method in
terms of the "single transferable vote" and by claiming that Approval
violates the "one person, one vote" axiom.

Many good answers have been given to this charge ... mostly by debunking
the billiard ball theory of voting one way or another.

But some of you will remember Martin Harper showing us that there is
another approach ... a formulation of Approval that patently satisfies the
requirements of the billiard ball theory.

Martin came up with his ingenious idea to show how ridiculous the billiard
ball requirement was, so he wasn't seriously suggesting that we use it to
sell Approval.

But if Craig Layton is right (as he usually is on things like this), then
we are not going to succeed in debunking this billiard ball superstition
in the minds of most of the public any time in the near future.

With that in mind, I suggest that we consider using Martin Harper's
vote transfer formulation of Approval in public proposals for Approval
voting:

(1) Voters make a mark next to the name of each candidate that they
consider acceptable.

(2) The names get sorted into a list according to the number of ballots on
which they were marked as acceptable (greatest to least).

(3) Each voter's single immutable vote is applied to the highest name on
the list which is marked acceptable on that voter's ballot.

[End of description of Approval]

As Martin pointed out, this method always picks the name at the top of the
list, so it is just a round about way of picking the same candidate with
the same ballots, i.e. it really is Approval.

Note how reasonable it is: your vote goes to the candidate (among those
acceptable to you) which is closest to winning.

If we use this formulation of Approval in place of the second step of our
"Majority Choice" method, then we will satisfy the billiard ball
requirement as well as the majority requirement and the distinct favorite
requirement, while solving the spoiler problem ... all without the
complexity and other problems of IRV.

Forest

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