[EM] another CR/Approval method

[Forest Simmons]

On Sun, 28 Sep 2003, [iso-8859-1] Kevin Venzke wrote:

> Forest,
>
> I wonder if a better name can be devised for it.  The notion of "gradual info
> approval" isn't so novel, and isn't very particular to this method.

But if this method is the best of this type, and nobody else has claimed
the name, why not use it?

Another possibility: "Concentrated Viability Approval"

Think of "viability" as a substance distributed uniformly among all of the
candidates at the start of the process.   This substance is gradually
concentrated among fewer and fewer candidates, until only one viable
candidate remains ... the winner!

>
> About your MMPO idea:
>
> > Find the two candidates whose max opposition is least.
> >
> > On each ballot that contributes to the max opposition of both of these
> > candidates, merge the top two levels.
> >
> > Recalculate the max oppositions of all the candidates to find the new
> > front runners.
>
> (I assume first of all that opposition is measured in terms of the number
> of voters, not in terms of the total rating difference on all ballots.)
>

Yes, that's what I meant.

This idea came to me because MMPO is one of the simplest ranked ballot
methods that satisfies the FBC when equal rankings are allowed at the top.

> It's interesting to me that the method seems unlikely to alter the MMPO scores
> of the original front-runners.  It seems it would pick new front-runners only
> because someone else's score went down far enough.  It also seems that those
> new front-runners would be likely to have been ranked near the top, along with
> their "opposition candidate."  Is that a deliberate effort to make Favorite
> less likely to sink Second-Favorite?
>

Yes.  So the voters don't have to start with equal rankings at the top.


Here's another version that attempts to minimize collapses by
incorporating a version of your viability concentration idea:

Initialize by calculating the max pairwise opposing vote total (mpovt) for
each candidate, and set the viability counter i to the total number of
candidates.

While i>1

    Mark the i candidates with the least (current) mpovt values as

    "viable".

    On each ballot that contributes to the mpovt of all viable candidates,
    temporarily merge the highest viable level (level containing a viable
    candidate) with levels immediately above it until there is some
    candidate whose mpvot cannot be blamed on this ballot.

    Erase the viability marks.

    Use the temporarily altered ballots to recalculate the mpovt's for the
    all of the candidates.

    Undo the temporary collapses on the ballots.

    Decrement i.

End While


The candidate with the (current) smallest mpovt (as calculated the last
time through the loop) is the winner.


This method is an attempt to preserve the FBC while minimizing the
necessary collapses.  I hope that it would not give incentive for the
voter to pre-collapse the top two levels.  I'm not sure if that goal is
attained.

This method doesn't take advantage of the CR values; it gives the same
answer for CR ballots as it does for merely ranked preference ballots, so
it is inferior to your method as far as I'm concerned.

However, perhaps it will stimulate a useful idea in the mind of somebody.


Forest