At 03:54 AM 6/11/2010, Kevin Venzke wrote:
Hi Abd,
--- En date de : Jeu 10.6.10, Abd ul-Rahman
Lomax <[email protected]> a écrit :
> One of the common complaints about Bucklin is that it can
> fail the Majority Criterion, but this only happens if more
> than one candidate gains a majority.
It also only happens if you don't use a rank ballot. If voters aren't
asked to compress preferences into limited slots then there's no basis
to say Bucklin fails Majority.
It is possible to use a Range ballot with
Bucklin, and the resolution can be such that
candidates can be fully ranked. To do this, there
must simply be as many ranks as candidates. If
the ballot permits full ranking, then the Bucklin
method will always detect the exclusive
preference that the Majority Criterion requires,
and it will always detect a Condorcet winner. I
had this debate several years ago, primarily with
Terry Bouricius of FairVote, on the Election
Methods Interest Group mailing list -- that
should be reactivated, look at
http://groups.yahoo.com/group/electionmethods/ --
the particular discussion is on a sublist,
http://groups.yahoo.com/group/EMIG-Wikipedia/msearch?query=Majority+Criterion&submit=Search.
My contention there was that Approval Voting
satisfies the Majority Criterion if Plurality satisfies the criterion.
The contrary argument, if I can summarize it, is
that if a majority of voters prefer A to B, but
actually vote for both A and B, then it is
possible that B wins if some other voters only
vote for B. The wording of the criterion by Woodall is
* Majority. If more than half the voters put the same set of
candidates (not necessarily in the same order) at the top of their
preference listings, then at least one of those candidates should be elected.
The way this criterion is worded, Approval
satisfies the criterion based on actual votes,
but not necessarily based on internal
preferences, for that majority might, for
example, all prefer A to B but actually vote for A and B.
It was argued by Bouricius that "put ... at the
top of their preferences listings" was a
reference to some internal list. The fatal flaw
in this argument is that no voting criterion can
be satisfied if some of the specified set of
voters in a manner contrary to what their
internal preferences indicate, or submit an
informal ballot, or for some other reason make
that preference ineffective. We must assume, I
claim, that voters vote within the limits of the
method, as specified by the criterion. And the
application of the Criterion to Approval is then
clear. There is only one way for the coalition
specified, more than half the voters, to "put"
the candidates at the top of their "preference
listing," which, with Approval, only allows one
top set, so this is the approved set. But what if
these voters *also* put someone else? They could.
That would not be the "same set." The criterion
must be referring to a set defined by the
preference list, which must be equivalent to the
ballot, not a subset arbitrarily picked from that set.
In any case, with an adequate Range ballot, used
to feed Bucklin, and for any candidate, the
voters can vote an actual preference list, i.e.,
show true preference order, and will only equal
rank if they have no significant preference.
Again, the habit of voting systems analysts is to
neglect significance, i.e., preference strength,
assuming that any preference strength, no matter
how small, is effective. My contention is that if
the preference is small enough for the voter to
have difficulty detecting it, or small enough to
be indifferent between the candidates, unwilling
to make *any* investment or risk to prefer them,
with preference only being expressed if the
method requires it (by prohibiting equal
ranking), it should properly be considered not to
exist for all practical purposes, and voting
systems criteria are useless if not practical.
Why would we be concerned about the Majority
Criterion at all? Well, if a system can readily
cause a significant strategic motivation to
appear reasonable to the voters, to suppress
their preference, then it is quite possible that
a majority truly does prefer A to B, but B is
elected because the majority, being unaware of
their position, equally rank A and B at the top.
That's the *substance* of the importance of the
criterion. Thus when Bucklin is severely limited
in its ability to rank candidates in an effective
way, it can fail the purpose of the criterion.
So what would be important is that the method not
"punish" voters for expressing that top
preference, by damaging, with any reasonable
likelihood, the outcome compared to their
preference, such that they would have obtained a
better outcome if they had not expressed it.
With Bucklin, "at the top of their preferences
listings" most reasonably means, for most
purposes, "at top rank on the ballot." In
original Bucklin, voters were not allowed to vote
for more than one candidate at the top. If they
were allowed, however, it's difficult to set up
election scenarios where a majority might, being
unaware of their status, be tempted to add an
additional vote at the top, but it's possible.
The reason why I discount this heavily is that it
does require multiple majorities at the top, and
Bucklin generally can't find a multiple majority
until the second or third round, and even then it
was rare (and Bucklin, long-term, may be more
likely to fail to find a majority at all,
particularly in some primaries.) The ability to
add multiple preferences at the top, in fact, I
only propose to avoid spoiling ballots with such
votes, and to allow voters to sincerely express
equal-top if that's a realistic picture of their
true preferences. With three approved ranks,
there is little reason to "crowd" approvals into
the top rank, unless the voter has no significant
preference, in which case it's simply a sincere
vote. And if a majority do this, the winner will indeed come from that set.
But the Majority Criterion has come to mean
something else, it is not normally stated as
referring to a set. It's usually stated with
reference to a single candidate. And James
Green-Armytage, aware to some extent of the
problem, and believing that Approval failed the
criterion, tried to define sincere vote in a way
that allowed the majority to prefer A to B but
still vote, in Approval, A=B. In substance he was
correct in his intuition. There is a problem, due
to strategic motivation that is possible to
incentivize A=B in spite of a significant
preference. But, of course, the criterion doesn't
mention "strategy," or any of many reasons why
voters might vote differently. He was inventing a
criterion definition to cause the result that was
intuitive to him, I suggest. And this is far from
objective, and, frankly, it didn't work. His
definition ended up defining sincere vote as
being not-not-sincere. Not sincere is reversing
preference. So any vote that is not-not sincere
is sincere, by his definition, which is excluding
the middle, i.e., a vote which is neither sincere
(expressing true preferences) nor not-sincere
(not expressing true preferences), because it is
expressing set preferences, not individual ones.
Thus the "sincere vote" can fail to express the necessary exclusive preference.
Bucklin completely resolves this, for all
practical purposes. I cannot imagine a
*realistic* scenario where a majority would
*substantially* prefer A to B and not vote only
for A in top rank. The higher the resolution of
the range ballot that feeds Bucklin, the more true this becomes.
With Range 1, ("Bucklin" becomes Approval), it
isn't true. I can easily imagine a scenario, a
simple misidentification of the frontrunners.
Approval is still an improvement over Plurality,
though, and is probably better than IRV. But it
has the obvious flaw of not allowing that
exclusive top preference to be expressed.
With Range 2, we have two-rank Bucklin, which
some prefer to having higher numbers of approved
ranks. (Isn't this "Majority Choice Approval?)
But there is still some degree of "push" to cram
multiple approvals into the top rank. Range 2
Bucklin might work well. With the device I've
described, multiple marks, in fact, this becomes
Range 3 (with three approved ranks.) (This might
make a nifty first modern application of Bucklin.)
With Approved Range 3, the motivation to equally
rank top becomes very low, probably so low that
it could be completely neglected. Even with Range
2, I think few voters would add multiple top
approvals if they have an easy preference to
express. That's obviously what the ballot is
soliciting. Vote for your favorite at the top,
and then other additional approvals, and
equal-top ranking is only there to avoid spoiling
ballots and to make it easier for voters who have
trouble distinguishing the top. But a voter
might, for example, prefer two candidates to the
frontrunners, not terribly unusual, as we can see
from the Burlington IRV results.
With higher resolution range, and including
disapproved ratings, some very interesting
possibilities open up. In particular, if voters
have sufficient resolution to rank all the
candidates, they will only equally rank if they
have preference strength patterns that deprecate
certain rankings. To *truly* allow maximum
flexibility, for N candidates, including a
write-in space, there should be 2*(N-1) ratings
possible, so that voters can rank all but one
candidate top, or all but one candidate bottom,
and still have the rating flexibility to rank all
the rest of the candidates within their approved/disapproved class.
My sense, though, is that the gain from this high
a resolution is minor, and that having N ratings
would be quite sufficient. And, indeed, because
we have some evidence that 3-rank Bucklin worked
with many candidates, in actual practice, it may
not be necessary to have that many ratings.
Voters, generally, have difficulty ranking more
than a few candidates with any significant
preference strength. I do think I'd have voted
for Loyal Ploof, though, just because of the
name. But not at an approved rank, just an an
elevated disapproved rank. Sorry, Loyal. Here,
take this bone, I'm not ready to elect you mayor just yet.
I like the idea of using a full Range 10 ballot,
and what I've shown is that this can be done
simply by allowing a reasonable interpretation of
the "overvotes" that are still possible with
Bucklin-ER, which is multiple ranking marks for a
single candidate. Obviously, they cannot just be
counted, because these would then add multiple
votes for the same candidate, a true one-person,
one-vote violation (which also shows why the
other "multiple votes," i.e., votes for more than
one candidate, aren't. They are, rather,
alternative votes. No two are *effective* for
election, only one at the most. Or none.
So the ballot, on the face, would be a Range 5
ballot, with three approved ranks and three
disapproved ranks, and with the flexibility to
vote middle ranks by making two marks, thus there
are really 5 clearly approved ranks, 5 clearly
disapproved ranks, plus a "middle rank" that
would be interpreted as absolute minimum
approval. So there are six approved ranks. The
middle rank, in utility theory, represents
indifference, and the Range ratings can then be
seen as positive/negative Range, i.e, rating on a scale from -5 to +5.
My sense is that preference strength below 1/10
vote is becoming difficult to discern, and, as
well, that in a properly designed Bucklin/Runoff
system, there would be hardly any advantage at
all, under any realistic scenario, to do anything
other than vote with sincerity or to rank
sincerely if pushed by strategic considerations,
i.e., to preserve any significant preferences
while making some strategic decisions, relatively
easy ones, as to where to put the approval cutoff.
And it's important to keep in mind that many
voters are likely to bullet vote, both in a
primary and in a runoff (naturally, if there are
only two candidates in the runoff, we'd expect
complete or almost complete bullet voting, but
with a well-designed system, I believe, the
possibility of three runoff candidates, plus a possible write-in, would exist)
It is possible to limit the write-in candidates
to two with little harm, to the Approval winner
and any Cordorcet winner, if they differ, or to
the top two Range winners, say -- I haven't
studied this in detail -- so the most one would
have in a runoff would be two plus write-in, yet
a Condorcet winner would always make it into the
runoff. (The other possible winner is the Range
winner). I'd also like to consider the
possibility of a "runoff nomination" shown by
high rating of a write-in in a primary, with a
certain minimum number of supporters. Runoff
elections could become quite exciting!
And, folks, the write-in option should be present
in *all* elections. The voters hands should not
be tied in the name of gaining a "majority." If
they are, it is a false majority, the system is
presenting a deceptive appearance. It is a
separate argument whether or not what happens in
a runoff is allowed to be an election by
plurality. In normal parliamentary procedure, it
is *never* allowed, and if the majority are
willing to continue duking it out, they can. They
are in charge at all times in a democracy, should
they choose to exercise their authority. They can
move to adjourn. They can put off the election to
another day. They can appoint an interim
office-holder, for a critical function. They can do all kinds of things.
We recognize that in public elections, an
indefinite series isn't practical, but we could,
if we wanted, throw the single-winner election
process into an Assembly or electoral college
that can, indeed, engage in ordinary deliberative
process. Making all our fuss about advanced
voting methods into so much old, dead, hot air.
Except that Bucklin would still be a great way to
make that process far more efficient. My guess is
that two rounds of Bucklin, if needed, using a
Range ballot input, could substitute for a far
longer series of vote-for-one majority required elections.
I now intend, if I'm presented with the
opportunity, and I might create one, to use a
Bucklin ballot for a single-winner election in a
real organization. I'm personally quite happy
with the 5-rank (expandable to 10 by
"overvoting", plus there is an explicit zero)
ballot design. It seems simple to vote, with no
need to worry about "strategy" beyond the
obvious. (Approve a frontrunner, unless you'd rather put that off to a runoff.)
In a deterministic election, if a runoff is
considered impractical, I'd just keep counting
down the ranks to the first, simulating a series
of repeated approval ballots, and if there still
isn't a majority there, I'd jump ship. The
organization is a collection of cantankerous,
uncooperative individuals, unwilling to accept
any compromise. Staying would, in the end, be a waste of time.
Speaking of cantankerous, uncooperative
individuals, please consider joining EMIG by
subscription to that list I mention above. This
was conceived as an FA/DP organization, so you
can name a proxy, and there is a proxy table. The
idea was to solicit membership by every expert in
the field, and, indeed, every interested student
of the field, but I do not expect that a busy
professor, for example, would want to follow all
the traffic, so I made the suggestion that people
name a "representative' to the list -- that's
what the proxy is -- who functions as a kind of
liason. Because it's an FA/DP organization, and
because of the way it would function, there is
little risk if you make a mistake and name some
jerk, it can be easily undone. The proxy doesn't
actually vote for you, but is merely considered
to be the most representative member of the list,
and, if the person you think is *most likely to
represent a sensible position,* is wllling to
accept the responsibility, you can simply name
that person. But an easy option for a professor
would be to name a decent student. The function
of the proxy is to maintain connection between
EMIG and the expert or other member. The proxy
should have direct access to the client, and
vice-versa, preferably face-to-face access, but,
if not that, phone access, or, at least regular
email access, with the emails probably being read
and considered. The proxy is a filter, in both directions.
EMIG is designed not merely to discuss, but to
discover and document consensus, and the idea was
to publish a journal, OverVotes, that would be a
peer-reviewed journal using EMIG process. There
could be more than one journal, and FA/DP
organizations are designed to maintain central
*connection* through voluntary means. The proxy
structdure does not allow central *domination,*
because proxies would always have direct contact
information, the central communication structures
of the organization, control of which is how
organizations classically brecome co-opted by a
faction, could easily be bypassed. Every
significant faction has the ability to
immediately and without any difficulty, organized
themselves separately, without cost and fuss, and
the very fact that this is easy probably makes it
normally unnecessary except that there will form
transient "caucuses," as needed.
EMIG, in the short period it was active, did
attract a number of experts, but, hint: any
organization that depends heavily on my activity
is going to run into seriously flat spots. It's
the nature of my life. I can function through
bursts of activity, but I have many projects, too
many, probably. I think I'll do something to stir
the EMIG pot, but not today, beyond this.
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