[EM] A four bit (sixteen slot) range style ballot

[Abd ul-Rahman Lomax]

At 03:54 AM 6/11/2010, Kevin Venzke wrote:
>Hi Abd,
>
>--- En date de : Jeu 10.6.10, Abd ul-Rahman 
>Lomax <abd at lomaxdesign.com> 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.