Approval/Plurality combinations

[Mike Ositoff]

> 
> Approval's simplicity is tempting despite its drawbacks.  Even if you


Again, my shell elm mailer is leaving out the 1st lines of
letters that I copy. The proposal below is for Approval
& Plurality voting in an election.

> hold a separate FPP vote to detect a majority winner, the two votes
> together are simpler than full ranking and can be conducted on any
> equipment, including punch-card ballots and paper "X" voting.  Of course
> if you are going to hold both votes, it would make sense to come up with
> a counting method that makes better use of the available information.

But when defining a new count rule, you lose the simplicity
and have the problem of selling a completely new method, and
you open the can-of-worms of a count rule debate.

The suggestion of combining Plurality & Approval on a ballot
is a good one. Disadvantage: The ballot has to be different
from now, and  the 2 votes require twice the ballot space.

Advantage: The Plurality count can be used to find out if
there's a majority candidate & elect him/her.

But, rather than the new count rules described later in the
letter, I prefer the very minimal use of the Plurality vote:

If someone gets a majority in the Plurality vote, he/she is
elected. If not, then the winner of the Approval count wins.

For the sake of simplicity, that's the only way I'd suggest
using the Plurality/Approval ballot. Using any kind of new
count procedure places us in the same predicament as when
advocating a rank-count rule.

Disadvantage: If no one gets a majority in the Plurality count,
and it's obvious that the Plurality winner is different from
the Approval winner who won the election, the supporters of
that Plurality winner would fight to repeal the reform and
replace it with plain Plurality.

Summary: Approval/Plurality, counted simply as I suggested
improves results by electing majority winners, but requires
different ballots from now, doubles the length of the ballot,
and could generate great dis-satisfaction from supporters 
of the Plurality winner if he doesn't win the election.
Overall, then, though Approval/Plurality would improve results,
over plain Approval, plain Approval seems simpler & more
problem-free. Of course if public sentiment about electing
the 1st place majority winner is strong, then Plurality/Approval
would likely be the better proposal.

But it should be understood that a majority winner can lose
under plain Plurality, if his supporters instead vote for 
a more winnable lesser evil, and that failure happens twice
as easily in Plurality than in Approval. It seems that in
Plurality/Approval, people would feel free to vote sincerely
in the Plurality section, since they can protect their more
winnable 2nd choices in the Approval section.

That concludes my reply. I don't delete the remainimg lines
because I don't want the keyboard lockup problem to happen
before I send this.

Mike



> 
> IMO the combination of an Approval and an FPP vote would yield most of
> the useful information obtainable from ranked balloting.  While you only
> have three ranking levels (first choice/middle choices/rejected), you
> also gain a piece of information not available with ranking: the cutoff
> between acceptable and unacceptable candidates (note DEMOREP's repeated
> calls for a YES/NO vote to be used along with ranking).
> 
> ***
> 
> I see two basic approaches to using this information: collated and
> uncollated.  The collated approach would retain the information
> contained in the relationship between a voter's first choice and his
> Approval choices; in other words, increment an entry in a
> two-dimensional array indexed by [first choice, approval choice] for
> every approval vote.  This would be difficult to do with paper ballots,
> and would require software modification to punch-card voting equipment. 
> Election methods possible under this approach would include Condorcet
> and a fairly accurate form of IRO.
> 
> The uncollated approach would simply tabulate the first-choice and
> approval votes separately.  This should work on any existing equipment
> and would be straightforward with paper ballots as well.  Election
> methods possible under this approach include a simplified IRO and a
> Plurality-Approval hybrid that should address some of the objections to
> both.  The uncollated methods are described below.
> 
> QUESTION:  Have the following methods already been done?  If so, by whom
> and what are they really called?
> 
> ***
> 
> Simplified IRO:
> 
> The simplified IRO simply uses the plurality vote to choose the top two
> finalists, and the approval vote to decide between them.  This is
> equivalent to transferring losers' votes, since the finalists' plurality
> totals are duplicated in the approval vote.  Caveats: if a loser gives
> approval to both finalists, the two votes simply cancel out.  Likewise,
> if one finalist gives an approval vote to the other, his vote is
> canceled out.
> 
> ***
> 
> Plurality-Approval Hybrid
> 
> The idea is to vary smoothly between FPP and Approval, using Approval
> only as needed to obtain a majority winner.  This method works a little
> like Borda, in that the second-choice totals are weighted and then added
> to the first-choice totals.  A candidate's second-choice total is
> defined as his approval total minus his first-choice total.  The
> weighting used is the minimum required for one of the candidates to
> reach a bare majority (50%), and is limited to a value between 0 and 1. 
> The formula to calculate the candidate's total is
> C = F + W(A - F)  where:
> 
> C = computed total  (always 50%, unless there is a first-choice majority
> or no approval majority is possible)
> F = first-choice total
> A = Approval total  (note the "A - F" term is equivalent to
> "second-choice total")
> W  = Weighting factor  (see below)
> 
> If a candidate has a first-choice majority, the minimum weight factor is
> 0 (the Approval vote is unused).  If not, the easiest way to find the
> winner is to work backwards from the totals for each candidate, to find
> the weight factor required for that candidate to reach 50%.  The formula
> to do this is:
> 
> W = (T/2 - F) / (A - F)
> 
> The candidate with the lowest weight factor is the winner, at 50%.  This
> weight can then be used to compute the other totals using the first
> formula.  If the lowest weight factor is greater than 1, then 1 is used
> and the final vote is equivalent to Approval with no majority (using a
> factor greater than one would give approval votes more weight than the
> first-choice vote).
> 
> I played around with this method a little, using some simple examples
> and obvious strategies.  The results seem to be similar to Approval (or
> Condorcet or IRO for that matter, when corresponding strategies are
> used).  It does seem to exclude some very weak Condorcet winners in
> favor of one who is both the plurality and runoff winner, though.  More
> later, if anybody's interested.
> 
>