Re: Don't allow ranking of options equal to default?
On Tue, 27 May 2003 14:02:19 -0400, Nathanael Nerode <email@example.com> said:
I've been trying to construct an example of perverse results of the
sort I want (where A beats D, B beats D, A beats B, and B wins
because of quorum). All the correct examples (which I can find,
anyway) depend on ranking options equal to the default option.
Do all these perverse cases also require less than 2Q votes to
Sadly, no. They do require less than Q votes to be cast with A above
the default, and nearly all of the other votes to be cast with A equal
to the default. They also require an electorate with strongly divided,
balanced views on at least two options, and another option which lots of
people rank equal to the default (which gets kicked out).
I see some value in it. Suppose I like A, enough to want A to
win, but do not feel too strongly about that. I certainly do not want
B to win; by I am really indifferent to C winning, if C can get the
required support from my fellow developers (I trust my fellow
developers, perhaps they have seen things in option C i did not).
A = 1;
B = 4;
C = 2;
D = 2; <default>
So, in this situation, how would you feel if only Q-1 developers voted
for C, but lots of other people voted C at equal rank to D? Would you
feel that C should be dropped (even if this might give the election to B)?
Here's a generalized example:
* Q-1 (or fewer) of the voters vote C as the only acceptable option:
C = 1
D = 2 <default>
A = 3
B = 3
* Slightly less than one-half of the remaining voters vote like you.
* Slightly more than one-half of the remaining voters vote:
A = 4;
B = 1;
C = 2;
D = 2; <default>
* (There are no other vote patterns)
(For those interested in the details, the "slightly"s above require that
the margin of victory of B over A is smaller than the number of pro-C
voters, so a margin of less than Q-1.)
Without quorum, C wins. (There is a majority preferring it to each
other option; a different majority in each case, admittedly.)
With quorum, C is thrown out and B wins.
If this is generally considered desirable, under your interpretation of
ranking something equal to the default (and it may well be), then there
is no problem at all with your proposal.
I just want to make it clear what the example which I found perverse is. :-)