[EM] Using Borda to Set an Agenda

[Forest Simmons]

It seems to me that the ideal method for setting an agenda is sequential
PAV.

The method uses plain old Approval ballots. In this context "approval"
means some degree of urgency regarding the item, not that you are in the
"pro" camp for that item.

At the each stage, the weight of a ballot B is 1/(1+k) where k is the
number of items "approved" by ballot B that already have a place on the
agenda.

Since we start with no item on the agenda, the number k is zero for all
ballots at the initial stage, which makes the ordinary approval winner the
first item on the agenda.

This is probably the simplest "broad support" method that is truly
proportional at each stage (for the number of agenda items up to that
stage) independent of the total number of agenda items.

It isn't quite as easy to count as Borda, but can still be done with a
hand held calculator in reasonable time if neither the number of agenda
items nor the number of ballots is too large.

Any computer with enough storage to hold an N by M matrix of zeroes and
ones, where N is the number of committee members and M is the number of
agenda items, could process the information instantly.  The most time
consuming part would be typing in the zeroes and ones.

The matrix entry in row n and column m is a one if and only if the voter
of ballot n indicated significant interest in agenda item m by a check
mark in the appropriate place next to the name of the item.

Any programmer could write a twenty line code (in any language) to process
the matrix to yield the agenda order according to the sequential PAV rule
mentioned above.

Forest


On Thu, 23 Oct 2003, James Green-Armytage wrote:

>
> Dear Jeffrey O'Neill,
>
> 	Your proposal is an interesting one, and worthy of further thought. It is
> often easier to think that there are only a few election methods which are
> simply the best, and the rest are junk, but it is true that some voting
> situations are very different from other, and require different methods.
> Getting a broader understanding of these situations is indeed a valuable
> direction in which to take election methods discussions, especially for
> people who have hashed over the ins and outs of traditional single winner
> elections and PR very thoroughly.
>
>
> >Hello,
> >
> >Poor Mr. Borda was recently dissed on this list. :)  I'd like to suggest
> >a use
> >of the Borda count.
> >
> >What is the proper voting system to set an agenda for a meeting.  Suppose
> >50
> >proposals are submitted for consideration at a meeting which is to last
> >eight
> >hours.  How do you choose which proposal should be considered first,
> >second,
> >and so on until the meeting is over?
>
> 	Apparently there is no specific time allotted for a single proposal?
> >
> >In just such a situation, I first proposed using STV.  STV was used to
> >select
> >the top five.  This was then repeated to choose the next five and so on.
> >The
> >hand count was tedious and it isn't clear to me if PR is appropriate for
> >this
> >situation.
>
> 	Ah, is the use of computers not allowed?
>
> >Why spend time on a proposal supported only by a small group if a
> >majority is required for approval?
>
> 	If you take this argument to its logical extreme, then the answer to your
> question is much more clear. That is, if one is only interested in
> pleasing the majority, than one should use a version of Condorcet that
> gives a complete ordering of outcomes, such as Kemeny, beatpath, or ranked
> pairs. It might be a pain to do these without computers, though.
> >
> >For the next meeting I sugested using a Borda count.  Intuitively, a Borda
> >count seems more appropriate, but I find it difficult to express the
> >proper
> >principles.  Practically, it is a straightforward method for ranking all
> >of the
> >proposals.
>
> 	Your proposal seems to make use of the fact that multi-seat Borda
> occupies a sort of weird grey area between proportional representation and
> majoritarianism. That's interesting. What I'm curious about is whether
> another method could do the same thing as well, without being as gauche as
> Borda.
> 	STV is at an immediate disadvantage because it is used to do PR when the
> number of slots is fixed. This aside, it might be interesting to play
> around with the STV rules to make it slightly less proportional. For
> example, to mess with the retention fractions of elected candidates such
> that they are too low, so that a candidate's surplus would be higher than
> it should be.
> 	Condorcet doesn't have this weakness, but it is hard to make Condorcet
> proportional or semi-proportional without getting clumsy, at least on the
> order of Borda's clumsiness. (CPO-STV is proportional, but again, this is
> STV as much as it is Condorcet, and the STV difficulties apply again.)
> There have been various proposals to make a sort of proportional or
> semi-proportional multi-seat Condorcet method such that when one winner is
> elected the voting strength of those who helped elect this winner is
> reduced by some degree. It is hard to be fair in terms of whose voting
> strength you diminish, and it intuitively seems that the strategic
> incentives created would be truly weird.
> >
> >Any thoughts?
> >Jeff
> >
> >PS. I'd also like to point out that there is some proportionality to
> >using a
> >Borda Count with multi-member districts.  Let me give an example for a
> >3-seat
> >district.  Using SNTV, IRV, or STV, a candidate is guaranteed to be
> >elected if
> >he or she receives at least 25% of the vote.  This is sometimes called the
> >"threshold of exclusion."  With Borda, the threshold of exclusion will be
> >higher (it is straightforward to compute it exactly) but there will still
> >be
> >some proportionality.
>
> 	You are right. It is a strange thing. I suppose that it is
> semi-proportional, but not quite in the same way as cumulative voting and
> limited voting, which I think are fully proportional under ideal
> conditions, that is perfect knowledge and strategy on the part of the
> voters, parties, etc.
>
> 	Anyway, I don't have any good answers, but I hope that someone else can
> do better.
>
> my best,
> James Green-Armytage
>
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