[EM] Majority Criterion, hidden contradictions

[Abd ul-Rahman Lomax]

At 08:35 AM 11/7/2006, Michael Poole wrote:
>Abd ul-Rahman Lomax writes:
>
> > No voting method can use preferences that are not expressed.
> >
> > Linguistically, the Criterion contains a lost performative -- or
> > something like that. *How* do the voters answer affirmatively. It
> > could only mean that they so answer on the ballot. Which in Approval
> > *requires* that they vote for  X and not for any other candidate. And
> > if a majority of voters do this, that candidate cannot lose. So why is
> > it said that Approval fails the Majority Criterion?
>
>Nothing in the MC talks about what the ballot contains, only about how
>voters answer a specific yes/no question.

A question which is not on the ballot. If the Majority Criterion is 
held to apply to Approval Voting, and it is held that Approval Voting 
fails the criterion, it must be that the "question" asked the voters 
is *not* what is on the ballot, it is some theoretical question that 
seeks to discover any preference at all, no matter how weak. *Where 
is this question?* Is it on the ballot?

Now, it is possible for voters to answer the question posed in the 
MC, using an Approval ballot. Same as a plurality ballot. Simply vote 
for the candidate preferred and for no others.

Here is another statement of the Criterion, from Wikipedia. The one I 
quoted before is from the same article, but is not, formally, the 
definition. The "question" was mentioned in an explanation. Mr. Poole 
fell into the same trap, he also referred to "how voters answer a 
specific yes/no question."

>if a majority of voters strictly prefers a given candidate to every 
>other candidate (i.e. the given candidate is the first preference of 
>more than half the voters) and they vote sincerely, then that 
>candidate should win.

What does it mean to "strictly prefer?" And which is the Criterion, 
"a majority strictly prefers" or "the given candidate is the first 
preference"? The latter is clearer, but the former is the language I'll use.

Now, Approval is not a ranked method, exactly. I'd call a ranked 
method any method which allows the ordering of candidates by 
preference where there are more than two ranks. I.e., it becomes 
possible to express "strict preference" for more than one candidate.

Approval allows the expression of "strict preference" for only one 
candidate. If one votes for more than one, it is no longer, under 
Approval, an expression of a strict preference.

So: what does it mean that the voters "strictly prefer." Given that 
this is an election criterion, using ballots, it *must* mean that the 
voters express this preference on the ballot. If the method does not 
allow this expression, then we must also say that it does not satisfy 
the Majority Criterion. But Approval *does* allow the expression of 
strict preference. In exactly the same way as Plurality.

The appearance that Approval does not satisfy the MC is caused by the 
fact that voters may express a *group* preference, if they so choose. 
This is no longer a strict preference on one over all others.

But if a majority *expresses* a strict preference, which Approval 
*allows* them to do, they cannot fail to elect that candidate under 
Approval. Approval satisfies the Majority Criterion.

I have stated that Range does not satisfy the Criterion. That may not 
be the best analysis. If a Majority expresses a *strict* preference 
for one candidate over all others, by bullet voting that candidate at 
max rating, -- what else would "strict preference" mean? -- again, 
that candidate cannot fail to win. This is exactly the same as with approval.

It is only if some of that majority does not express such a strict 
preference, but, instead, a weak preference, i.e., less than the full 
strength, that the candidate could fail to win.

It's been argued in these posts that "But this is not Approval if 
they vote for only one, it is Plurality." No, it is not. In 
non-Approval plurality, without that strange no-overvote rule, a 
voters' ballot is disregarded if the voter votes for more than one. 
That is, Plurality *only* allows the expression of strict preference. 
That Approval allows something else does not cause it to fail the 
majority criterion.

Let me go over this with Range:

A majority votes:

A 99
B 10
C 0

With this vote, A *might* fail to win. It's unlikely, but possible. 
But this is not the expression of strict preference, there has been a 
verbal slight of hand here. Here is strict preference, where in every 
pairwise election, the majority *fully* prefers A over every other candidate:

A 99
B 0
C 0

Yes, *for these voters*, Range has reduced not only to Approval, but 
to Plurality. But that does not make the method Range or Plurality, 
for other voters may vote differently, and their votes will be counted as cast.

Michael made this argument:

>   Approval does not ask
>voters to answer according to that question.  It fails the Majority
>Criterion because if you add the constraint that each voter only
>approves of one candidate, the system stops being Approval voting.

There need be no such "constraint." Again, this extra condition has 
been supplied.

*Approval allows the expression of "strict preference," and if a 
majority so expresses a strict preference for one candidate over all 
others, that candidate must win.

If voters, on the other hand, approve of more than one, they have 
failed to express a strict preference between the candidates so 
favored. They have expressed *no* preference between these 
candidates. So they don't count as part of that majority that has 
expressed strict preference. They are irrelevant to whether or not 
the method satisfies the Majority Criterion.

Frankly, it's become utterly obvious to me. There has been a lack of 
solidity in considering the meaning of the Criterion. I made that 
same mistake myself for a long time, I readily accepted the claim 
that Approval failed the criterion. It was a lack of rigor, a mushing 
together of ideas about preference and Approval Voting, and 
recommended strategy for Approval, etc.

Indeed, the recommended strategy for Approval *for some voters* is 
not to express strict preference. Those voters are giving up their 
right to express preference between multiply-approved candidates.

>I am not arguing that Range creates the use of extreme scores (zero
>and maximum), only that it encourages it to an extent that the result
>is likely to be technically hardly better than Approval and
>practically more likely to polarize factions.

It only seems to "encourage it" in a context where people are focused 
on winning, on getting their preference. But my point has been that 
this *is* extreme preference, and if that is how people see the 
situation, it is *correct* for them to vote that way.

But Range *allows* voters to move away from that.

>The US currently has extremely polarized factions, and most of my
>criticisms apply to plurality voting as well as to Range, but I would
>rather replace the current system with one that seems robust in
>practice rather than one that merely allows higher resolution of
>polarization.

I see no reason to believe that Range would "encourage" polarization. 
Given the status quo, the introduction of Range would certainly not 
*increase* polarization, since the present system *depends* on full 
polarization. Neither would Range, by itself, eliminate polarization. 
It just makes it possible.

Systems that don't allow the expression of preference strength are 
inherently flawed.

But the real problem is attempting to cram what would intelligently 
be a deliberative process into a single election. The designers of 
democracy quite well knew that majority rule properly applied to 
single questions. Approval actually begins to restore this, by 
effectively asking the question, one question for each candidate: "Is 
this candidate acceptable?" The most broadly acceptable candidate 
wins. sStandard Plurality asks a complex question: which of these 
candidates is the most acceptable? Thus it explicitly disallows the 
separate question for each candidate.

In my view, *whatever* election method or methods are used, there is 
not full democratic process if the election is not explicitly 
accepted by a majority. The identity of a Condorcet winner is 
certainly of interest, but the Condorcet winner could fall far short 
of being accepted by a majority. Approval and Range can as well, but 
are much more likely to find the candidate who will be most broadly 
accepted and for whom, thus, the "shall we elect this candidate" 
would prevail by a majority.

If a majority don't want a candidate to take office, why do we 
presume that the election should be considered complete? It is 
blatantly undemocratic, violating the most basic principle of 
democratic decision-making, majority rule. Yet this is exactly what 
we can get with single-ballot, get-it-over-with elections.

Having a top-two runoff (which can be variously defined, and some 
ways of doing it are clearly better than others) is closer, and if 
NOTA was on the ballot as well, it would be complete.

(NOTA: None of the Above, a common Libertarian proposal.)