Better quorum change proposal, with justification

[Nathanael Nerode <neroden@twcny.rr.com>]

Here's the nightmare scenario, under Manoj's amendment, which I think 
John Robinson may have been trying to come up with.  Consider two options,
A and B, and the default option D.  Let the quorum requirement R=20.
39 people show up to vote.  These are their preferences (most prefered 
on the left, = denotes two equally preferred options).

19x A=DB
19x ABD
1x BA=D

Look at the pairwise results:
A vs. B
38 to 1

A vs. D
19 to 0 (20 no preference)

B vs. D
20 to 19

A is the Condorcet winner.
  
Under Manoj's proposed amendment, A fails to make quorum and is dropped, 
and B wins (20 to 19).  

Now, with such a low vote, it may seem reasonable for the default option 
to win.  But it's certainly not reasonable for B to win.

If A had a supermajority requirement and B didn't, then it would be 
reasonable for B to win.  But this isn't the case.

This is a serious defect in A.6 part 2.

>     2. If the ballot has a quorum requirement R any options other
>        than the default option which do not receive at least R votes
>        ranking that option above the default option are dropped from
>        consideration.

--

I propose the following change.  First of all, move clause 3a up 
earlier so it can be used in clause 2:

>        a. Given two options A and B, V(A,B) is the number of voters
>           who prefer option A over option B.

Second, change clause 2 to read as follows:

     2. If the ballot has a quorum requirement R, any option A other
        than the default option D, where V(A,D) - V(D,A) < R,
        is dropped from consideration.

This should eliminate the truly perverse result given above, because B 
would *also* be dropped and D would win.  This gives a slight bias 
towards the default option (which seems to be desired).  It is parallel 
to the supermajority design.  It (hopefully) eliminates the nonsense 
results such as the one above.

(I welcome people who can discover similar defects in this rule.)

This isn't really a quorum rule (but then, neither is the one in Manoj's 
proposal) -- it's a margin-of-victory rule.  That seems to be what 
people actually want. :-)

--
FYI, A true quorum rule might look like this:

     2. If the ballot has a quorum requirement R any options other
        than the default option which do not receive at least R votes
        explicitly ranking that option are dropped from consideration.

This is closer to how quorum normally works (the people who "showed 
up" count), and yes, it means that showing up can cause you to lose.
This is why the Democrats in the Texas Legislature staged a walkout to 
prevent quorum.

I don't think this is what you're looking for.

--Nathanael