At 11:31 AM 6/26/2013, Chris Benham wrote:
Jameson,
I don't like this version at all. These methods all have the problem
that the voters have a strong incentive to just submit approval
ballots, i.e. only use the top and bottom grades.
"Strong incentive" requires "strong preference."
The method provides limited later-no-harm protection. That protection
is not -- and should not be -- absolute.
We know from real Bucklin elections that many voters will add lower
preferences. No voting system is going to overcome the tendency of
voters to bullet vote.
Your suggested way of determining a winner among candidates who
first get a majority in the same round only makes that incentive a
bit stronger still.
No, it reduces the incentive to bullet vote. That is, it make a
decision to add a vote at a lower rank easier. Under the condition
that the "tiebreaker" is active, the lower vote cannot cause the
favorite to lose, because it is removed from consideration. (I have a
sense that there is a rare condition where this may not be so, but it
would not be something that voters would rationally worry about.)
There is a problem, though. Multiple majorities are likely to occur
with frontrunners. Most additional votes for the frontrunners are not
so likely to come from the supporters of the other frontrunner. They
will come from supporters of minor candidates. MAV, then, may
disregard these additional votes by backing up. Not good.
I agree with a Mike Ossipoff suggestion, that we elect the member of
that set of candidates with the most above-bottom votes.
There are four basic possibilities, outside of runoffs, given the
appearance of a multiple majority at a canvassing level.
1. Elect the most-approved candidate, considering all votes
above-bottom as approvals. Or considering all approved categories as
approvals, if it is possible to vote an unapproved category
above-bottom. Ossipoff's idea.
2. Elect the candidate with the most votes at or above the canvassed
rating level. Basic Bucklin.
3. Elect the candidate with the most votes above the canvassed level. MAV.
4. Use a graduated median, which is a compromise between 2 and 3.
5. Elect the majority-approved candidate with the highest score,
considering all the votes as scores (probably Range 4.)
If the election fails to find a majority, going through the approved
categories, the election may then, I'd suggest, flip to pure Range
evaluation. Candidate with the most votes, considering the ranked
votes as Range ratings, wins. This is a plurality result, there is no
majority approval.
This, the last option, is really similar to Mike's suggestion, except
that the canvassing uses the preference strength data that is
intrinsic to a sanely-voted Bucklin ballot. It does provide limited
later-no harm protection, because the later votes are at lower
strength. The problem with the Ossipoff suggestion is that all later
votes, if used, are taken at full strength. His is an Approval
option, I've just suggested Range.
So the method does two things. It lowers the approval cutoff until a
majority is found, if one is going to be found. It then uses Range
amalgamation to deal with the possibility of multiple majorities. It
avoids considering a "better evil" category as an approval, it only
uses the preference data from such a vote as a small contribution to
a social utility sum.
Also, given the strong truncation incentive, I think 5 grades is one
too many. In my opinion 4 grades would be adequately expressive.
Range 3, but with the preference strength between a disapproved
candidate and a minimally approved candidate being equated to the
minimally weak preference strength between a Favorite and a second
preference. (i.e., second preference is voted 2nd rank, instead of third rank.)
That's highly unrealistic. I've suggested that a Bucklin ballot is a
Range 4 ballot, realistically, with the next-to-nadir ranking being
unexpressed. So the rating values are 1.00, 0.75, and 0.50 for all
standard Bucklin votes. 0.50 is the minimal approval cutoff,
suggestive of "election expected utility." No gain, no loss. And then
we can add that rating in, but *not as an approved rating*. It is not
used for the ordinary Bucklin evaluation, seeking a majority. But
with methods 1 and 5, that rating would be used. Method 1 does a bit
of violence to the preference expression, pulling up what is sanely
half of the expected election utility to full approval.
My favourite Bucklin-like method is "Irrelevant-Ballot Independent
Fallback-Approval" (aka IBFA) that I introduced in May 2010.
<http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html>http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html
"A, B, C, D" are probably better names for the ratings slots than
the "Top, Middle1, Middle2, Bottom" in that post.
Comparing it to Bucklin, it meets Independence from Irrelevant
Ballots which means that adding or removing a few ballots that
bullet-vote for nobody (ignored on all the other ballots) can't
change the winner.
The small "price" paid for this (apart from greater complexity) is
that it fails Later-no-Help. That is mostly a benefit because it
weakens the truncation incentive.
The other advantage of IBIFA over Bucklin is that it is far more
likely to elect the Condorcet winner. If the winners are different
then the IBIFA winner will always pairwise beat the Bucklin (or
Majority Judgement) winner.
Thanks for the discussion, Chris. Now, we need a name for
Range-evaluation Bucklin.
Notice: this is pure Bucklin *unless* there are multiple majorities
or majority failure. It is similar to Oklahoma Bucklin, which did
assign fractional vote values to the lower preference votes. (The
ranks were 1, 1/2, 1/3).
I'm now seeing this as ideal from a democratic process perspective.
1. A majority is sought. "Majority" is a Yes/No decision, it is not
evaluative. The basic democratic princile is that of majority
*consent.* By voting to approve a candidate, singly or with others,
the majority is explicitly consenting to the election of that
candidate. Bucklin amalgamation allows voters to determine where in
the process to introduce additional approvals. Thus it improves their
ability to express preferences.
2. If majority choice is not clear, then Range amalgamation is used.
The Bucklin amalgamation process should encourage sincere rating with
reference to the voter's election expectation. The additional
unapproved rating above bottom allows participation in election
choice below election expectation. Range results, in theory, will
usually predict the results of a runoff. So if a plurality result is
to be accepted, a result that would be predicted from a runoff is
superior to some other result.
This method, then, could be used, the same, in a runoff system, with
top-two range selecting the nominated candidates for the runoff, and
with a pairwise test to see if any other candidate can beat the top
two. If so, that candidate would also be nominated. If there is a
Condorcet cycle, the top two members of the cycle, per range
amalgamation would be nominated, plus the Range winner, if not
already included.
As a runoff method, with write-ins allowed, sincere voting remains
fully possible and safe. A sincere categorization into the five
categories, then, becomes important for voters.
The "meaning" of the vote is an assignment of utility value to the
election of that candidate, at closest value to the fractions
expressed. Voters *may* bullet vote, but are then risking lack of
participation in the final decision. You pay your vote and you take
your choice. And this is *approval voting*, unless it defaults to
range because of no majority -- or multiple majority.
In a runoff, I'd expect a majority to be routine, multiple majorities
not uncommon, and majority failure rare.
No more original content below.
Jameson Quinn wrote (19 June 2013):
Here's the current version of the article. Note the new paragraph on
strategy at the bottom.
---------
Majority Approval Voting (MAV) is a modern,
evaluative<<http://wiki.electorama.com/wiki/Evaluative>http://wiki.electorama.com/wiki/Evaluative>
version of Bucklin voting
<<http://wiki.electorama.com/wiki/Bucklin_voting>http://wiki.electorama.com/wiki/Bucklin_voting>.
Voters rate each candidate into one of a predefined set of ratings
or grades, such as the letter grades "A", "B", "C", "D", and "F". As
with any Bucklin system, first the top-grade ("A") votes for each
candidate are counted as
approvals. If one or more candidate has a majority, then the highest
majority wins. If not, votes at next grade down ("B") are added to
each candidate's approval scores. If there are one or more candidates with a
majority, the winner is whichever of those had more votes at higher
grades (the previous stage). If there were no majorities, then the
next grade down("C") is added and the process repeats; and so on.
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