[EM] majority rule criteria

[James Green-Armytage]

Mike,

Yes, it's true that "majority rule" is an ambiguous term, and so there is
no one 'correct' definition. However, I find some definitions more useful
than others. Let me suggest 4 general categories of majority rule methods,
based on 4 basic criteria.

Criterion 1: If a majority of the electorate coordinates their efforts,
they can assure that a given candidate is elected, or that another given
candidate is not elected.
Criterion 2: Mutual majority criterion
Criterion 3: Condorcet efficiency
Criterion 4: Minimal dominant set (Smith, GeTChA) efficiency

Criterion 1 only: Pseudomajority methods.
Criteria 1 and 2 only: Weak majority rule methods.
Criteria 1, 2, and 3: Intermediate majority rule methods.
Criteria 1, 2, 3, and 4: Strong majority rule methods.

Pseudomajority methods: Plurality, approval, range voting, Borda
Weak majority rule methods: single-winner STV
Intermediate majority rule methods: Minimax (aka SD, PC, etc.), Nanson,
Black, etc.
Strong majority rule methods: ranked pairs, beatpath, river, cardinal
pairwise (assuming that a strong-majority base method is used)

You are correct in saying that in pseudomajority methods (like plurality
and range voting), a given majority of the electorate *can* coordinate
their intentions and decide the winner, but this merely postpones the
question of how they do this. The stronger majority methods not only
enable firmly coordinated majorities to assert themselves, but they allow
majorities to *reveal* themselves, with out any need for prior
coordination. I think that voting methods that facilitate this process of
revelation are superior to those that do not.

The remaining three categories allow mutual majorities to reveal
themselves (in the absence of a self-defeating strategy by supporters of
this majority). Strong majority rule methods not only reveal mutual
majorities, but they reveal minimal dominant sets and Condorcet winners
(in the absence of a severe burying strategy). This is especially valuable
because it means revealing possible compromises on divisive issues, thus
avoiding a lot of political polarization and strife. 

As you have said, many progressive policies may be supported by a
majority, but they have not been brought to a fair vote. A major goal of a
good voting system is to *reveal* these majority-supported policies, to
avoid their getting lost in the noise of the two party system. Can they be
revealed if we use a pseudomajority method like range voting? Yes, it's
quite possible, but it's more difficult. In many cases it means that the
intention-revealing part of the process, which is ideally the purpose of
the voting system, will have to be deferred to some other mechanism or
institution.

Sincerely,
James Green-Armytage
http://fc.antioch.edu/~james_green-armytage/voting.htm
http://fc.antioch.edu/~jarmyta@antioch-college.edu/voting.htm

>
>James--
>
>You wrote:
>
>Range voting is neither a majority rule method...
>
>I reply:
>
>That depends on what you mean by a majority-rule method. You define it
>below 
>as a Smith-Criterion method, but you mustn't expect others to share that 
>definition. Range-Voting, which I call CR, meets WDSC, which says:
>
>If a majority of all the voters prefer X to Y, they should have a way of 
>voting that ensures that Y won't win, without any member of that majority 
>voting a less-liked candidate over a more-liked one.
>
>[end of WDSC definition]
>
>In most any method a majority has the power to make some pariticular 
>candidate lose. In CR (including Approval) they can do that without 
>reversing a sincere preference.
>
>When a majority can easily nsure the defeat of a candidate, they can
>enforce 
>majority rule. CR is a majority-rule method by that reasonable standard.
>
>You continued:
>
>Therefore, its
>applications are very limited.
>
>How do you justify the claim that the applications of methods that don't 
>meet the Smith Criterion are very limited?
>
>You continued:
>
>Let's say that our voting scenario is a large group of people choosing an
>executive (e.g. a mayor or president), and there is enough at stake that
>people cannot be relied upon to vote sincerely.
>
>I don't think that range voting should be used for this scenario. Why not?
>Because it is not a majority rule system. It is possible for a candidate
>to win in range voting even if they are the last choice of 99% of the
>voters. Unlikely, but mathematically true.
>
>I reply:
>
>But nothing prevents you from voting strategically to prevent that. If
>you 
>choose to rate sincerely, it's because you choose to accept the
>consequent 
>loss of strategic power.
>
>The ridiculously unlikely scenario that you worry about shouldn't
>distract 
>you from the tremendous benefit of having CR instead of IRV or Plurality.
>
>
>You continued:
>
>In contentious executive elections, I think that we should stick to
>majority rule methods. What is my operational definition of majority rule?
>The winner should be a member of the minimal dominant set (aka GeTChA or
>Smith). A weaker definition would be the mutual majority criterion. Range
>voting passes neither of these criteria
>
>I reply:
>
>You haven't told us why you consider the Smith Criterion necessary.
>
>MMC is good, but much benefit can be gained without it. You want
>everything. 
>I've already said that the best rank methods, the wv Condorcet versions, 
>offer additional criterion compliances that are desirable. You need to 
>understand the difference between everything and enough.
>
>You continued:
>
>, and so I say it has no claim on
>being a majority rule method.
>
>I reply:
>
>...as you define that term.
>
>As for considerations other than majority rule:
>
>As I said, sometimes CR will maximize SU when Condorcet or Cardinal
>Pairwise 
>wouldn't. Sometimes the reverse is true.
>
>You continued:
>
>In some non-contentious election
>scenarios, perhaps it can be. But in a contentious election, it is not. If
>a Condorcet winner is not elected, it does not necessarily mean that
>another candidate had a higher utility. More likely, it means that
>supporters of the other candidate pulled off a successful strategy. The
>interpersonal utility comparison aspect of range voting is just too easy
>to hijack for strategic purposes, so that it essentially becomes
>meaningless in a contentious election.
>
>I reply:
>
>Not at all. As I said, you can vote strategically in CR if you choose to,
> 
>to protect the CW &/or majority rule.
>
>You continued:
>
>If one is concerned about the tyranny of the majority, range voting is not
>the answer, because a well-coordinated majority can still guarantee
>victory for their candidate of choice. [without reversing a sincere 
>preference]
>
>I reply:
>
>And yet you say that CR isn't a majority method :-)
>
>Mike Ossipoff
>
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