# [EM] Chris, majority-rule, etc.

Chris Benham chrisjbenham at optusnet.com.au
Sat Mar 17 02:48:37 PDT 2007

```
Michael Ossipoff wrote:

>
> 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 EM:
>
> 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.

> 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.

That is reasonable, and granted for the sake of argument. That implies
that you agree with Kevin Venzke that Minimal Defense(MD) must be met
no-matter-what, but while I think MD compliance can be a positive for an
otherwise bad method I think the best methods can do without it.

49: A
24: B
27: C|B

MD says "not A", but A is the only candidate in the Definite Majority
set. (C knocks out B, and A knocks out C).

> 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.

That opens up the question of how best to measure the strength of
pairwise defeats. Alternative algorithms for DMC are Beatpath(Total
Approval),
River(TA), Ranked Pairs(TA) which all measure the strength of a pairwise
defeat by the approval score of the pairwise winner.

At least in the "three candidates in the top cycle" situation, an
alternative algorithm for ASM is Approval Margins that uses one of
River,BP,RP
and measures pairwise defeat strengths by the difference between the
approval scores of the two candidates. Both DMC and ASM meet the
Definite Majority criterion.

And to round out the discussion, Approval-Weighted Pairwise (AWP)
measures defeat-strength by the number of ballots on the winning side
that approve the winner and not the loser.

>> 52: AC (offensive order-reversal)
>> 100: BA
>> 50: C/B
>
>
> A>C 152-50, C>B 102-100, B>A 150-52
> Approvals: A152, C102, B100
> Definite Majority set is {A}, so DMC, ASM, UncAOO elect A.
> TACC elects C, WV and AWP elect B.

Here {A} is not just the Definite Majority set but also the "Definite
Absolute Majority" set (which doesn't conflict with MD),
so I can't see how anyone can credibly claim that electing A here flouts
"majority rule".

> 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.

You are repeating your old trick of claiming that methods like Approval
and FPP meet criteria just because they use barbarically
restrictive ballots. You base your version of the Condorcet Criterion on
voters' sincere preferences, but for some reason this criterion
has to be purely about cast votes even with a restricted ballot. I share
the Venke (similar to Woodall's) approach that the criteria
should assume that the voters intend to submit a ranked ballot (maybe
truncated, maybe with some equal-ranking) and that voters
fill out their actual (maybe restricted) ballots in a way that is
consistent with their intended ballots, and when ballot restrictions prevent
voters from fully voting their intended ranked ballots the criteria are
based on the intended ballots.

The suggestion that methods that meet Majority for Solid Coalitions and
Schwartz and Definite Majority are somehow worse at
giving effect to "majority rule" than methods that fail Majority Loser
is ridiculous.

> Chris, not I, suggested it as a criterion.

I suggested "it" as a criterion with a different much more modest and
appropriate name.

> Chris continued:
>
> Without informed strategy Approval guarantees not much.
>
>
> 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.

Much what? By "not much" I didn't mean "nothing". It meets (or close
enough) "0-info strategy = honesty", Minimal Defense
(on the Venzke/Woodall interpretation), Plurality and "Possible Approval
Winner"(PAW). Funny about that last one, and it meets
Definite Majority (a bit embarrassing for DM). I agree that it gives big
"bang for buck" as a reform to replace FPP.

But it fails Majority Favourite and Majority Loser and is very
vulnerable to disinformation campaigns and has nasty defection/truncation
incentives.

Chris Benham

>
>

```