[EM] The billiard ball theory of voting

[Narins, Josh]

FYI

In computer science there is no difference in the results between a bubble
sort, a quick sort, et cetera, the only difference is the O(n) expectation
of how long the sort would take.

At least, to the best of my knowledge.



-----Original Message-----
From: Forest Simmons [mailto:fsimmons at pcc.edu]
Sent: Saturday, June 01, 2002 5:04 PM
To: election-methods-list at eskimo.com
Subject: Re: [EM] The billiard ball theory of voting


A variation on Martin Harper's Approval procedure takes it out of the
realm of Approval:

Between step 2 and step 3 in the description of his method insert step 2.5
which is to bubble sort the list so that every name defeats the name below
it head to head.

This changes nothing if the resolution of the ballots is only two.

Another possibility is to do the initial ordering with ranked pairs or
some other method that fully ranks the candidates.

Even Borda could be used to order the list initially, then bubble sort,
and finally transfer the votes to the highest approved candidate on each
list.  Demorep style ballots would be appropriate.

Note that this method would satisfy the first choice majority rule
requirement, since the bubble sort would put the majority candidate name
at the top, and more than fifty percent of the billiard balls would go to
that candidate.

This is meant to stimulate thought, NOT a serious proposal.

Another possible way to accommodate the billiard ball mentality (in
Approval) is to emphasize that each voter gets one billiard ball for each
candidate, and they must choose whether to give the candidates their
billiard balls or to withhold them :-)

For Condorcet Methods in general the candidates are ranked according to
the method in question, and then each voter's billiard ball vote is
transferred to their preferred of the top two onethe list.  Naturally, the
method gives the win to the top name on the list.

On Fri, 31 May 2002, Forest Simmons wrote:

> 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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>
>

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