[EM] Chris, majority-rule, etc.

Michael Ossipoff 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.

I replied:

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 isn’t 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, you’re 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 wasn’t 
obvious enough for you, I’ll 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.

Chris continues:

The criterion you suggest might not be ridiculous

I reply:

Are you sure it might not? Chris is too kind.

And, by the way, I didn’t 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 
defined above.

That criterion, if it were proposed as a criterion, would be different from 
the familiar Majority Criterion.

I haven’t 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 
won’t be adding it to the criteria that I frequently cite.

When advocating a change from Plurality to Approval, it’s helpful to tell 
something that Approval offers that Plurality doesn’t offer.

Chris continues:

, but needs
a more modest and original name. Maybe something like "Majority Beatpath" 

I reply:

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

I reply:

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 it’s the obvious application of 
majority rule to single-winner outcomes.

Chris continues:

, 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

I reply:

Yes, everyone can have their pet criterion/critreria. There’s no need for 
Chris to be impressed by majority rule.

Chris continues:

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.

I reply:

To each their own. Is it necessary for me to say that I don’t 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 

Chris says:

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.

I reply:

Quite so. I’m 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 

Chris continued:

Without informed strategy Approval guarantees not much.

I reply:

You’re 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 I’ll 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. Doesn’t Plurality? No. When you 
vote for your lesser-evil, you don’t vote for your favorite because you 
aren’t allowed to, not because it isn’t good enough.

To put it differently, Approval elects the candidate who is acceptable to 
the most voters. I wouldn’t call that “doesn’t 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, 
you’re giving a Yes or a No to each candidate.

Approval meets FBC & WDSC. But that doesn’t begin to tell Approval’s 
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 aren’t 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 country’s 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 
computer counting.

As I’ve 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. You’d 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 
labor-saving machine.

Single-winner reform advocates should be unitedly working for the simplest, 
most obvious and minimal single-winner reform. There’s exactly one such. 
Then, later, while we’re arguing endlessly about which rank-count we should 
improve on Approval with, Approval will at least be already providing 
excellent single-winner democracy.

As I’ve said, it’s 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.

There’s no debate on how to count those ratings: Add them up.

I’ve 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 doesn’t 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 Condorcet’s Criterion for 
emphatic preferences.

With only two voted preference levels, there’s 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 it’s 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 there’s to be only one winner, 
we should express only one choice?

For one thing, there’s 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 won’t win. Since we’re voting on who 
should win, and there’s 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 
isn’t winnable? That’s what you’re 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 isn’t winnable. In other words, compromise is rightfully 
part of voting. That’s true in principle, and, in practice, it’s 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”. There’s 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 you’re only 
willing to compromise so far. Or maybe you’re willing to compromise as far 
as necessary, so you choose your compromise set based on how far you believe 
you have to compromise.

It’s obviously healthier for democracy when voters can vote more of their 
preferences and have them reliably counted, when they don’t have to vote 
opposite to their preferences--as I’ve said, having to makes a joke of 

And it’s 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.

Chris said:

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 

I reply:

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.

Mike Ossipoff

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