At 05:28 PM 10/4/2005, Rob Lanphier wrote:
I've seen a lot of different definitions of the "majority criterion",
but for purposes of this email, I'll describe a minimal version:
"If a strict majority of the voters rank a particular alternative as
their unique first choice, then the voting method must select that
alternative as a unique winner" (Anderson, 1994)
This seems like a very minimal litmus test for mainstream acceptability
of a voting system. Plurality, IRV, and all Condorcet variants meet it.
Approval arguably meets it, in that the only way to "rank" a single
candidate as a unique first choice is to bullet vote. Range does not.
Range does not because it allows the voter additional freedom. The
key word here is "rank." By defining the criterion violation through
"ranking" rather than through "preference" -- which might be
unexpressed because of the limitations of the voting system, yes,
Range does not pass that criterion, and you can be sure this will be
used against it. However, the same argument will be made against
Approval, the difference is that the opponents will substitute
"prefer" for "rank." And the argument will have the same impact, and
it will need to be similarly addressed.
I have recently been considering and writing about two modified
versions of Approval, which posts have not gone to the Approval
Voting list I was banned by the moderator for no specified violation
of any established rule, not even "don't post unless I permit you."
Those versions are what I've called A+, which is simply Approval
voting "plus" an expression of favorite, which, in basic A+ does not
affect the election outcome, but which *would* affect such far from
irrelevant matters as the ability of voters to express a preference,
the assignment of public campaign finance money, and perhaps ballot
position in succeeding elections.
A+ *is* basic Approval as an election method, but A+, obviously,
would fail the majority criterion. Now, if basic Approval is
considered to satisfy the majority criterion, and A+ fails it, then
surely the difference is only apparent and not real. Approval appears
to satisfy the criterion only because ranking information is concealed.
If, however, one wants to satisfy the criterion, then one could take
the same ballot as A+ and *use* the information. Essentially the
ballot becomes a truncated Condorcet ballot, with only three ranks,
which I've called Favorite, Preferred [over unmarked], and Not
Preferred [unmarked].
The election is counted pairwise, and the Favorite vote is considered
the same as a Preferred vote, *except* in the pairwise contest
between a Favorite and a Preferred candidate, in which case the
Favorite is used.
This method satisfies the Condorcet criterion and the majority
criterion. Yet it is Approval with respect to all other candidates
except the Favorite. Because the very simple ballot forces ranking to
express Approval (any ranked candidate is presumed approved), methods
like DMC can be used to determine the winner if there is a Condorcet
cycle. I originally proposed that the winner be the most-approved
candidate in the Smith set, but there may be problems with this,
about which I am unsure.
What I think interesting is that A+ could easily become A+PW (the
acronym, which irritates some, means Approval Plus, counted
PairWise). The ballot stays the same. Or additional ranks could be
added; once you have done two, three should get easier. Or, if the
ballot complication problem can be overcome, Range could be an
evolutionary step.
Indeed, theoretically, one might be able to get A+ implemented where
the Approval votes are not counted.... I.e., the election method
remains plurality, and the counting of the Approval votes might be at
private expense (anyone who wants to do it). I think this would lead
to real Approval voting in a flash!
But this also suggests something for Range, we could call it R+. This
would be range with the expression of a favorite. That addition, I
think, is going to be necessary if Range is to be implemented in
general elections, where ballot position and campaign financing are
real issues. Whether or not this additional information is actually
used is a separate question.
By the way, also, normalization is really necessary in the
justification of Range as a one-person, one-vote method. What it
boils down to is that Range allows a person one vote at the most in
any pairwise election, same as Approval. Range allows voters to
weaken their vote, but not to strengthen it beyond that. These
weakened votes create an impression of majority criterion failure,
but if "ranked above all others" means that one full vote has been
cast for the candidate, there are no weakened votes cast by that
majority, and the candidate will win unless there are *more* such
votes cast for another candidate. "Majority" criterion, if Approval
is considered to pass, could not mean "majority" only, but must mean
"more than any other" as well. Otherwise Approval fails.
Incidentally, Range voting wouldn't have prevented slavery. Black
suffrage was a pretty important prerequisite which didn't exist back
then. Also, I don't think that a bunch of people who were willing to
secede from the union and fight a war on their own soil would express a
mild preference for slavery in a Range vote.
I honestly can't believe I'm rewarding your ad hominem attack with a
response. I'll endeavor not to make the same mistake twice.
Rob
Footnote:
Anderson, 1994: Research draft by L. Bruce Anderson titled "How To Take
Votes: New Ideas on Better Ways to Determine the Winners", March, 1994.
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