Charlie DeTar wrote:
Howdy,
I'm on the board of a small non-profit, and have been tasked with
revising the portion of the bylaws that defines how to elect the board
of directors. Having had some exposure to better election methods
through a colleague, I'm interested in exploring how we might use a
ranked voting system effectively. Most of the methods I've seen,
however, are intended for electing a single winner -- and for the board
of directors, we have multiple seats. Additionally, the number of seats
is variable.
I'm looking for methods that would more or less "optimally" (by variable
definitions of optimal) elect a variable number of people. "Single
Transferable Vote" seems to be the most talked-about multi-winner ranked
system; but the vote transfer process requires a pre-defined number of
seats to fill. It seems like the option to have a variable number of
seats opens up possibilities for improving representation by adding a
winner, or eliminating polarizing candidates by removing one.
Thoughts?
As far as I can see, there are two ways you might accomplish sufficient
representation. The first is to have a vote about how large the board
should be, and the second is to somehow do it in an algorithmic manner.
Let's take the first way first. It's not possible for the voters to know
the composition of the board in advance. Thus either the method has to
be iterated, like your old majority rule system, or the voters have to
be provided the results for all possible board sizes. Since methods like
STV are complex, I would suggest the latter.
A system of this form might go as follows: First the voters rank all the
candidates. Then the system calculates the board composition for all
sizes from 5 to 9. Finally, there is a supermajority vote for which size
board to pick. The point of a supermajority is that if the board is
supposed to be representative, a simple majority will not be enough
since a majority might force a board made up only of their own
representatives to the detriment of the minority representation.
If one uses a proportional ranking method like the one Schulze talked
about, this might be further simplified. After the first ballot, the
list is calculated and shown. Then one starts with the top 5 entries
included (shown in another color) and holds a "include the next member?"
vote. If a supermajority says no, the process is over; if it says yes,
one includes the next member and repeats until either all 9 entries have
been included or a later "no" stops the process. If the margin is narrow
(say 51-49) so there's no supermajority in either direction, I'm not
sure what to do, though.
-
The second way is more difficult because inferring proportionality or
the kind of optimality you mention is not a simple task. I don't know of
any formal methods to do this, but you could automate the proceed/stop
iteration above.
One possible way of doing that would be to consider the currently
included board's topmost ranked candidate on each ballot. If one of the
candidates on the current size board appears in the first voter's top
rank, then that ballot is associated with the value 1; if second rank,
2; and so on. You could then set a threshold for the mean value of this
across all ballots and stop the process when the mean is less than the
threshold. The threshold may have to be adjusted for the number of
candidates running, though.
Raph has given another idea using the effective number of political
parties. See his post for that. The idea would not use the iteration
procedure I have mentioned; instead, it would determine the number of
seats after examining the ballots. As such, one could use ordinary STV
with little problem.
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