[EM] Chris, majority-rule, etc.
mikeo2106 at msn.com
Fri Mar 16 12:00:21 PDT 2007
Chris Benham had said:
Regarding the above example, I can't see any justification in the actual
votes for suggesting that "majority rule" is violated by electing A.
All three candidates have a majority-strength defeat.
Correct--they do. But electing A violates majority rule as I defined it on
Majority rule is violated if we elect a candidate who has a majority
pair-wise defeat (PM) against him, and that PM is not in a cycle of P.M.s
none of which are weaker than it is.
In the example, the B>A defeat is not in such a cycle, because the C>B
defeat is weaker than the B>A defeat.
No one challenged that definition of majority rule violation.
Chris now replies:
Probably those who noticed said nothing because they were too bemused or
stunned at your attempt to highjack the
definition of such a popular 'motherhood' term/concept.
I reply now:
Spare us your angry noises.
You had made a claim regarding whether or not an example violates majority
rule, based on your own implied, in-explicit definition of majority rule,
which says (?) that majority rule isnt violated if we elect someone whose
majority pair-wise defeat is in a cycle of majority pair-wise defeats.
So either you yourself were trying hijack majority rule and motherhood, or
else you want to make statements about majority rule violation without
having a definition of it. Either way, youre being rather silly.
My definition of majority rule violation, in the context of a single-winner
outcome, is the obvious and natural one. But, since it apparently wasnt
obvious enough for you, Ill explain it:
Obviously majority rule is violated by an outcome that is contrary to what a
majority have voted that they want. For instance, if a majority vote B over
A, then we can assume that, if A or B wins, they vote that it be B.
What could nullify such a majority pair-wise defeat? Being in a cycle of
defeats that are all at least as strong as it is.
If, in such a cycle, one majority pair-wise defeat is weaker than the
others, then naturally, with several majority pair-wise defeats
contradicting each other, and if we want to enforce voted majority wishes,
then the weaker defeat is the one to disregard. Unless we have an arbitrary
rule to cancel the goal of honoring voted majority wishes when weaker ones
conflict with stronger ones.
The criterion you suggest might not be ridiculous
Are you sure it might not? Chris is too kind.
And, by the way, I didnt state the definition as the definition of a
criterion, but rather as the definition of a term. You of course can make a
criterion based on it if you want to. You can say that the Majority Rule
Criterion requires that no one be elected in violation of majority rule, as
That criterion, if it were proposed as a criterion, would be different from
the familiar Majority Criterion.
I havent given any consideration to what methods pass or fail the Majority
Rule Criterion, but:
Plurality, Approval, -1,0,1 are among the methods that pass. So, good
methods and poor methods pass. Chris, not I, suggested it as a criterion. I
wont be adding it to the criteria that I frequently cite.
When advocating a change from Plurality to Approval, its helpful to tell
something that Approval offers that Plurality doesnt offer.
, but needs
a more modest and original name. Maybe something like "Majority Beatpath"
Thanks, Chris, but majority rule already has a name. And that definition is
only for majority rule violation in the context of a single-winner outcome.
Like the "Beatpath Criterion" to me it looks too tailored
Is Chris going to start about the Beatpath Criterion again? Yes the Beatpath
Criterion is tailored. It is tailored to test for compliance with the four
majority defensive strategy criteria.
As for my definition of majority rule in the context of single-winner
outcomes being tailored, I told why its the obvious application of
majority rule to single-winner outcomes.
, but looks at least reasonable/interesting for methods that only
collect rankings. For methods that collect both rankings and explicit
approval information (allowing voters to rank among
unapproved candidates), I'm not impressed with any criterion that can insist
we elect from outside the Definite Majority
Yes, everyone can have their pet criterion/critreria. Theres no need for
Chris to be impressed by majority rule.
I don't like methods that fail "Independence from Irrelevant Ballots" (IIB),
and so I tend to economise on criteria/standards
that are vulnerable to that concept.
To each their own. Is it necessary for me to say that I dont advocate every
method that meets the Majority Rule Criterion? Nor do I reject every method
that fails it, such as MDDA. MDDA is a powerful but briefly-defined rank
method, and I recommend it as a proposal to electorates who consider SSD too
I don't want to elect the "most favourite" candidate, and I think the claim
about "many-level CR" is debatable because even if the
voters are trying to be sincere they are likely operating with different
bench-marks and generally unsynchronised minds. It would
be different if they all agree that well-known figure A is much worse than
well-known figure B and on what rating each should receive
and to rate the candidates proportionately on that scale.
Quite so. Im not an advocate of many-level CR. Approval and -1,0,1 are the
CR versions that I like. Approval is the best CR method, and one of the best
Without informed strategy Approval guarantees not much.
Youre referring to the 0-info situation.
With zero-info, with voters using the 0-info strategy of voting for the
above-mean candidates, Approval will elect the candidate who is above-mean
for the most voters. That is much.
It has been shown on EM that, with strategic voting based on winnability and
compromise, and with a few reasonable approximations, Approval maximizes the
number of voters who are pleasantly surprised by the outcome--the number of
voters for whom the outcome is better than their expectation before the
election. The 0-info maximization is a special case of that.
This is too obvious to say, but Ill say it anyway: Whether voting is
strategic or not, Approval maximizes the number of voters for whom the
winner is someone good enough to vote for. Doesnt Plurality? No. When you
vote for your lesser-evil, you dont vote for your favorite because you
arent allowed to, not because it isnt good enough.
To put it differently, Approval elects the candidate who is acceptable to
the most voters. I wouldnt call that doesnt guarantee much.
With voters allowed to rate all the candidates, Approval elects the
candidate who is, overall, the best-rated--without the strategic-vs.-sincere
problem of many-level CR. And the meaning of Yes and No is more reliably
interpreted for everyone than ratings from 0 to 100. For whatever reason,
youre giving a Yes or a No to each candidate.
Approval meets FBC & WDSC. But that doesnt begin to tell Approvals
advantages and appeal. Improving on 1-vote Plurality by letting people rate
each candidate as they wish, Approval is the minimal method that does so.
But that one minimal improvement makes all the difference. I too suggest
rank methods to improve on Approval, but the trouble is that each of us
wants to improve on Approval with a different rank method. A member of the
public would say Why this rank method instead of some other one? And many
rank methods, such as IRV and Borda arent as good as Approval, as judged by
many (but not by their advocates).
As one Approvalist pointed out, Approval tremendously, qualitatively,
improves on 1-vote Plurality, without any increase in complexity or change
in ballot or balloting equipment. The best rank methods may improve on
Approval (I believe that they do for this countrys electorate) relatively
slightly--at the cost of wordier definitions and the need to convince people
why one rank-count should be enacted instead of another. And at the cost of
more expensive balloting equipment and more computation-intensive counting,
with the security, legitimacy and validity questions that arise with
As Ive said, I liken Approval to a solid, reliable hand-tool. A rank method
is a labor-saving machine. Some labor-saving machines are well-made, and
some are junk. Youd be much better off with the hand tool than with the
shoddy junk machine (such as IRV). And the machines are expensive and
require laborious set-up. Even if you want a machine, I recommend using the
hand-tool while shopping for, debating the choice of, and setting up your
Single-winner reform advocates should be unitedly working for the simplest,
most obvious and minimal single-winner reform. Theres exactly one such.
Then, later, while were arguing endlessly about which rank-count we should
improve on Approval with, Approval will at least be already providing
excellent single-winner democracy.
As Ive said, its a minimal but natural change from 1-vote Plurality to let
people rate all the candidates as they wish, instead of forcing them to give
bottom rating to all of them but one, when, ridiculously, their favorite is
often one of those whom they are strategically forced to bottom-rate.
Theres no debate on how to count those ratings: Add them up.
Ive recently told here some things that Approval offers and guarantees.
If an emphatic preference is a pair-wise preference that you consider
important enough be to one of those that you vote, when rating everyone high
or low doesnt allow you to vote all of your pair-wise preferences, and if
we substitute emphatically prefer for prefer in the definitions of CW
and voting a preference, and falsifying a preference (for use in the
definition of sincere voting), then Approval meets Condorcets Criterion for
With only two voted preference levels, theres always a beats-all candidate,
and s/he always wins in Approval. And the Borda winner is the same candid
date as the beats-all candidate.
1-vote Plurality defenders and Approval opponents (usually the same people)
rebel against Approval because its unfamiliar to them, or seems unnatural,
due to their 1-vote Plurality conditioning. But which method is really
natural? How natural is it to force people to completely abandon, to
bottom-rate their favorite? How natural is it to undemocratically tell
people how they have to rate all but one of the candidates? Well, but how do
you answer the person who says that, because theres to be only one winner,
we should express only one choice?
For one thing, theres one winner and many candidates. Who says that the
number of candidates we may rate should match the number of winners instead
of the number of candidates? The principle of the desirability of freedom
suggests that voters should be able to rate as many candidates as they want
to. The burden of proof is on the person who wants to limit, deny or take
away freedom of choice.
We should vote for only one candidate because we only have one favorite? But
everyone knows that millions of people feel strategically forced to abandon
their favorite. And what does favorite-ness have to do with anything, when
we all know that Favorite very likely wont win. Since were voting on who
should win, and theres no particular reason why your favorite can be
expected to win, then why should favorite-ness be a requirement or the
assumption for whom we should vote for when voting on who should win?
Because your favorite might well not win, it should be obvious that
compromise is part of voting. Should you be disenfranchised if your favorite
isnt winnable? Thats what youre saying if you say you should only vote
for one, because you just have one favorite to vote for.
Everyone has a right to equally vote to influence the outcome, even if
his/her favorite isnt winnable. In other words, compromise is rightfully
part of voting. Thats true in principle, and, in practice, its obvious
that compromise is very much part of voting in 1-vote Plurality,
That principle of compromise being inherent in voting means that it makes no
sense to say that we should only be able to high-rate one candidate, and
should have to bottom-rate all the others. Compromise, and the arguments in
the previous paragraphs, mean that you should be able to help, to high-rate,
candidates other than your favorite.
So much for there being something more natural about voting for only one
In Approval, then, you vote your compromise set. Theres no reason why
anyone other than you should choose the cardinality of that set. Each voter
divides the candidates into two sets, the preferred and the unpreferred
sets. In choosing your preferred set, your compromise set, maybe youre only
willing to compromise so far. Or maybe youre willing to compromise as far
as necessary, so you choose your compromise set based on how far you believe
you have to compromise.
Its obviously healthier for democracy when voters can vote more of their
preferences and have them reliably counted, when they dont have to vote
opposite to their preferences--as Ive said, having to makes a joke of
And its healthy for democracy when a wide, varied, and interesting variety
of candidates appealing to the same voters can run in an election, without
strategic reason not to, thereby allowing a selection unheard of now.
Hopefully a set of democratic reforms that include a good rank method will
attract a lot of new voters with more courage and sense than your "LO2E
Yes, but hopefully those LO2E progressives will get some courage. Even with
Approval--after the first few elections show them that candidates whom they
can actually like and respect are a lot more winnable than their friendly tv
commentator has been telling them.
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