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

[Abd ul-Rahman Lomax]

At 11:53 AM 6/11/2010, Kevin Venzke wrote:
>Hi Abd,
>
>The best way to decide how to apply rank ballot criteria to Approval is to
>have a framework for all methods into which you can translate Approval.
>People may not agree with you but at least it's clear what you have done.
>
>--- En date de : Ven 11.6.10, Abd ul-Rahman 
>Lomax <abd at lomaxdesign.com> a écrit :
> > My contention there was that Approval Voting satisfies the
> > Majority Criterion if Plurality satisfies the criterion.
>
>But you say this and then quote Woodall's Majority criterion, which
>Plurality fails?

Plurality allows voters to place a candidate at 
the "top of their preference listings." Does 
Plurality fail Woodall's Majority Criterion? That 
depends on interpretations. The criterion was not 
designed and defined well enough to be sure. What is a "preference listing"?

There is social choice theory and there is 
election method theory and they are not actually 
the same, though they are certainly related.


> > 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.
>
>But within Woodall's framework, all methods have to be interpreted as
>rank. Woodall uses an interpretation of Approval so that it will fit in
>his framework. You don't have to use that interpretation. But arguing
>about whether a method satisfies a Woodall criterion without any attempt
>to stay within Woodall's framework seems futile.

Basically, the term "Majority Criterion" went on 
to be used by others in various ways, with 
various definitions and interpretations.

I think you may know that my position on "voting 
systems criteria" in general is that they are a 
failed attempt to create objective standards for 
comparing voting systems. They do have uses, but 
they become ammunition in political wars over 
voting systems, and the actual practical 
implications of the criteria are often obscure. 
In particular, some criteria *seem* to be 
obviously desirable, but turn out, on deeper 
examination, to be contradictory to what people, 
the "electorate," would be likely to decide if 
all the cards were laid on the table, all the 
preferences were thoroughly known, and then the 
group of people made the optimal decision for their collective welfare.

Great example is the Condorcet criterion. The 
Condorcet winner can be, under conditions that 
may be revealed if voters cast sincere and 
accurate Range ballot, contradictory to the 
optimal decision, *as the voters will agree when 
the true preferences and preference strengths are revealed.*

In other words, failing the Condorcet Criterion 
is not a flaw of Range Voting, it is a strength. 
However, it is also true that under some 
conditions, condorcet failure can indicate a 
problem with Range, and so some of my work has 
been aimed at detecting and fixing that problem. 
What I came across, early on in this study, was 
the fact that standard deliberative process, with 
its procedure and requirement of a majority for 
any decision, was far more sophisticated than 
anything I've seen said about it from voting 
systems theorists. Repeated ballot is a very 
powerful method! But with the vote-for-one 
limitation, it can be inefficient; in actual 
practice, candidate withdrawals and voting shifts 
handle what could be handled more directly with 
Approval. Range could make the process even more 
efficient, and then I came to the understanding 
that Bucklin was an Approval system, simulating a 
series of repeated ballot Approval elections, driven by a Range ballot.

 From there I realized that the ballot could be 
full Range and that therefore, from it, a 
Condorcet winner could be detected, and if this 
winner differs from the Bucklin/Approval/Range 
winner, a runoff could be triggered. What this 
amounts to is the rough equivalent of a 
ratification combined with a runoff. Range voting 
easily may fail to satisfy the basic democratic 
principle of majority rule, so, technically, a 
Range result should be ratified. To be efficient, 
though, the ratification may be combined with a 
consideration of at least one alternative, and 
perhaps two or three. With a good voting system, 
and with what have become, in the runoff, 
well-informed voters, having the results of the 
first poll -- which could be printed on the 
ballot! -- majority ratification of a result is quite likely.

Determining elections with a single ballot is a 
basic violation of democratic principles, when a 
true majority has not been found that has 
explicitly approved the result. Certainly it may 
be argued that efficiency requires it, but the 
claim that multiple ballots are impractical has 
been shown to be false again and again. Sure, 
there is a cost, but ... apparently it has been 
considered worthwhile, often. But don't expect 
the top two political parties, in general, to 
support it. They would rather risk an occasional 
spoiler. Hence top two runoff has *mostly* been 
confined to nonpartisan elections.

Fine. That's the place to start. Don't dump the 
best voting system in common use to replace it 
with a system with the same problems, but without 
the benefits -- other than fixing the spoiler 
effect which TTR also fixes. Instead, replace the 
primary with a system that can develop far more 
information from the electorate, that will more 
commonly find a majority, because it counts all 
the votes, and that is much more likely to find a 
condorcet winner, but which can also detect an 
approval and range winner. Bucklin, driven by a 
Range ballot with adequate resolution, used as a 
primary in a runoff system, could be, with 
certain runoff rules, not only Majority and 
Condorcet criterion compliant, but, as well, 
social utility maximizing, reserving to the 
majority the right to reject a "range winner" if 
they choose. Usually, I contend, they won't, 
unless it is so close that the difference is 
academic with little damage being done to social utility.

This is new, I believe, the concept of 
maximization of social utility with ratification 
when necessary, thus preserving majority rule 
(which is very important). Many theorists in the 
field have simply assumed that a runoff would 
ratify the Condorcet winner, a result of not 
considering how turnout affects results, and how 
turnout is a basic component of democratic 
process. People who don't care don't bother to 
vote, even if they have *some preference*. Thus 
standard vote-for-one, particularly with repeated 
ballot, was more sophisticated than we thought.