Re: Supermajority requirement off-by-one error, and TC chairmanship

```On Fri, Feb 15, 2008 at 02:11:12PM -0800, Don Armstrong wrote:
> With 6 people, 1/2 of the votes is 3 votes, with no error. "more than
> 1/2" needs 4 votes, or 4/6th. So even though the stated requirement is
> "more than 1/2", the actual requirement is "at least 4/6th". The
> difference is 1/6th of the votes, or 16 2/3%. In other words, due to
> the small sample, the requirement is more than 16% higher than
> intended.

Yes, that too. :-)  But as I wrote, for the 50% situation, there is a
reason we want that.  We want to say "there are more people in favour
than against".  With the supermajority, we want to say "there are many
more people in favour than against".  What exactly is the value of
"many" is arbitrary.  If it means 2/3, or 2/3-ε, is therefore not very
important.  If using "2/3" gives an error of 16%, then that is a small
problem.  When the actual value is arbitrary anyway, it makes sense to
solve it.  When we're talking about the 50%, the value is not arbitrary,
and changing it really changes the meaning.

> [Wonderous how the numbers work out exactly the same.]

Because that "1/6th" is "one voter", which is the same fraction as long
as you don't change the number of voters. :-)

On Sat, Feb 16, 2008 at 02:38:05AM +0100, Josselin Mouette wrote:
> On ven, 2008-02-15 at 22:49 +0100, Bas Wijnen wrote:
> > On Fri, Feb 15, 2008 at 10:09:57PM +0100, Josselin Mouette wrote:
> > > On ven, 2008-02-15 at 15:50 +0100, Wouter Verhelst wrote:
> > > > Having said that, I agree with you that it makes sense for the
> > > > TC to not require 'X + 1', since the electorate is so small
> > > > anyway;
> > >
> > > I don’t understand why the previous argument wouldn’t apply to a small
> > > number of voters.
> >
> > Because of the error you're making.  With 6 people, 2/3 of the votes is
> > 4 votes, with no error.  "more than 2/3" needs 5 votes, or 5/6th.  So
> > even though the stated requirement is "more than 2/3", the actual
> > requirement is "at least 5/6th".  The difference is 1/6th of the votes,
> > or 16 2/3%.  In other words, due to the small sample, the requirement is
> > more than 16% higher than intended.
>
> I know that, but I don’t think this is an “error”. The concept of
> supermajority is here for things that require a strong consensus;

Sure.  And it's fine to say "for these decisions, we want a 5/6-ε
majority" if we want.  Or any other fraction which seems appropriate.
That's the whole point: the actual value of how strong the consensus
needs to be is arbitrary.  If we say "2/3", then it makes sense to
adjust that according to the number of voters so that we're not really
saying something different.

For 50%, I agree that we don't want to make such adjustments, because
that number is not arbitrary.

> in a body like the TC, which is supposed to base its decisions on
> technical ground, I don’t think we can say there is strong consensus
> if only 3 people agree, 1 disagrees and 2 don’t care.

This is an argument for raising the arbitrary value of what is a
supermajority.  And an argument for saying "don't care means no".  It's
fine to make these arguments, but IMO they're not appropriate in this
discussion.  This is about the technical point of lowering the
requirement by ε to make it closer to the possible results of the vote.

This obviously would lower the barrier, and I understand you don't want
that.  I think the most appropriate thing to do (assuming you do agree
with me on the ε part) is to add an option, which not only does this,
but also raises the majority we're requiring.

Thanks,
Bas

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