Mutual Majority Criterion

classic Classic list List threaded Threaded
2 messages Options
Reply | Threaded
Open this post in threaded view
|

Mutual Majority Criterion

Craig Carey-2
As I understand it, the Mutual Majority Criterion says that if
there's a group of voters, consisting of a full majority of all the
voters, who all rank all of the candidates in some set, S, over
all the other candidates, then the winner should be chosen from S.

Since they all prefer everythng in S to everything else, then each
of those voters has something in S as his favorite. So the members
of that group all prefer eachother's favorites, perhaps along with
some other alternatives too, to everything else. That's why I
call it the Mutual Majority Criterion. That's a very special &
particular kind of a majority, which is why I don't call that the
Generalized Majority Criterion.

Howabout the example that I've been using:

40%: Dole, Clinton, Nader
25%: Clinton
35%: Nader, Clinton, Dole

The Clinton-Nader majority don't all rank _anyone_ over Dole.
The Dole-Clinton majority don't all rank anyone over Nader.

So there's no particular candidate or set of candidates that
Mutual Majority says to choose from here. We can do whatever
we like without violating Mutual Majority. We, for instance,
can use MPV, which immediately eliminates the Condorcet winner.
In general, MPV meets Mutual Majority.

But say the Clinton voters all rank Dole 2nd.

Then we do have a set of candidates from which Mutual Majority
says we must choose: We must choose either Dole or Clinton.
Well, that's reasonable, but Mutual Majority doesn't say anything
about which one we should choose. It quite ignores the majority
who rank Clinton over Dole. Is that something that we want to
ignore? Not if we want to get rid of the lesser-of-2-evils
problem. Not if we want to get rid of the need of a majority
to use defensive strategy to get an ourcome that they all want.

***

Can Condorcet violate MM (Mutual Majority)? Not if we say:

"If there's a group of candidates who all beat everyone outside
the group, then apply Condorcet's rule withing that group."

If we say that, Condorcet, as I've said, meets all the academic
criteria that I've heard of that have any objective basis.

If we don't say that--if we apply Condorcet's least-beaten rule
to all the alternatives when none beats each of the others, then
what does it take to make Condorcet fail MM? Well, there would
have to be a circular tie among the set S alternatives, so that
everything in set S has something else preferred to it by a
full majority of all the voters. That seems to be reaching rather
far to make Condorcet violate MM.

***

More about the other academic criteria in a subsequent letter.

***

Mike Ossipoff





--

Reply | Threaded
Open this post in threaded view
|

MM wording correction

Craig Carey-2
Mike Ossipoff writes:

[In my example, I didn't say quite what I meant, and so I'm
correcting that here, under the place where the mis-statement
was made]


>
> As I understand it, the Mutual Majority Criterion says that if
> there's a group of voters, consisting of a full majority of all the
> voters, who all rank all of the candidates in some set, S, over
> all the other candidates, then the winner should be chosen from S.
>
> Since they all prefer everythng in S to everything else, then each
> of those voters has something in S as his favorite. So the members
> of that group all prefer eachother's favorites, perhaps along with
> some other alternatives too, to everything else. That's why I
> call it the Mutual Majority Criterion. That's a very special &
> particular kind of a majority, which is why I don't call that the
> Generalized Majority Criterion.
>
> Howabout the example that I've been using:
>
> 40%: Dole, Clinton, Nader
> 25%: Clinton
> 35%: Nader, Clinton, Dole
>
> The Clinton-Nader majority don't all rank _anyone_ over Dole.
> The Dole-Clinton majority don't all rank anyone over Nader.

That isn't what I meant to say. I meant that there isn't any set S
such that a full majority prefer everything in S to everything not
in S. {Clinton} isn't such a set because the Dole voters prefer
Dole to Clinton. {Dole, Clinton} isn't such a set because the
Clinton voters don't rank Dole over anyone. Likewise, of course,
for {Nader, Clinton}.

The point of that being that MM wouldn't object no matter what
we do in that election. We couldn't violate MM in that election
if we tried. Not even if we used the infamously, abyssmally
non-majoritarian MPV, which starts out by eliminating the Condorcet
winner. As a matter of fact, MPV never violates MM. Does this mean
that MPV is tolerable  



[That's all I'm writing in this copy of this message. The rest
is copied only because I don't have a way to delete lines or
blocs of text]

>
> So there's no particular candidate or set of candidates that
> Mutual Majority says to choose from here. We can do whatever
> we like without violating Mutual Majority. We, for instance,
> can use MPV, which immediately eliminates the Condorcet winner.
> In general, MPV meets Mutual Majority.
>
> But say the Clinton voters all rank Dole 2nd.
>
> Then we do have a set of candidates from which Mutual Majority
> says we must choose: We must choose either Dole or Clinton.
> Well, that's reasonable, but Mutual Majority doesn't say anything
> about which one we should choose. It quite ignores the majority
> who rank Clinton over Dole. Is that something that we want to
> ignore? Not if we want to get rid of the lesser-of-2-evils
> problem. Not if we want to get rid of the need of a majority
> to use defensive strategy to get an ourcome that they all want.
>
> ***
>
> Can Condorcet violate MM (Mutual Majority)? Not if we say:
>
> "If there's a group of candidates who all beat everyone outside
> the group, then apply Condorcet's rule withing that group."
>
> If we say that, Condorcet, as I've said, meets all the academic
> criteria that I've heard of that have any objective basis.
>
> If we don't say that--if we apply Condorcet's least-beaten rule
> to all the alternatives when none beats each of the others, then
> what does it take to make Condorcet fail MM? Well, there would
> have to be a circular tie among the set S alternatives, so that
> everything in set S has something else preferred to it by a
> full majority of all the voters. That seems to be reaching rather
> far to make Condorcet violate MM.
>
> ***
>
> More about the other academic criteria in a subsequent letter.
>
> ***
>
> Mike Ossipoff
>
>
>
>
>
> --
> .-
>


--