[EM] Thorough Expeditious Elimination

[Forest Simmons]

In a way the thing that bothers me the most about IRV is how
computationally wasteful it is. Once the ballots (or their facsimiles) are
collected, the most computationally expensive aspect of the election is the
necessity of repeated passes through the ballots to access the information
required for each elimination step.

That wouldn't be so bad  ... except that some of the most valuable
information that surfaces at each pass through the ballots ... is ignored
or otherwise wasted ... like valuable food not only left uneaten but also
denied to starving people.

We're talking about information that could increase the accuracy of each
elimination judgment, as well as reduce the required number of these
expensive steps.

Nanson must have been thinking the same thing about Baldwin when he cut the
number of required passes through the ballots from O(n) to O(log n) on
average. From 63 passes down to six in the case of 64 candidates.

And Baldwin was surely thinking about squandered information, when he
decided to base elimination judgments on Borda scores... taking advantage
of newly available ranked ballot information at each step ... information
unavailable on traditional runoff ballots.

But while addressing the waste and efficiency issues, Baldwin and Nanson
unwittingly introduced two subtle problems not found in traditional runoff
elections ... the problems of clone distortion and burial strategy
incentive.

Coombs also (unwittingly) introduced the burial strategy incentive in his
attempt to reduce first place compromising incentive by basing elimination
judgments on Bottom counts instead of Top counts.

In perfect hindsight, it is now obvious that Nanson should have based his
method on a difference of Top and Bottom (equal whole) counts rather than
Borda to increase both efficiency and accuracy of elimination judgment
....without  introducing clone distortion or undue imbalance of
burial/compromise incentive.

A judgment improvement available at zero extra cost per elimination step
... is an instant elimination runoff between the two most likely suspects
... an elimination based on a democratic majority judgment ... as opposed
to some superficial statistical standard.

This is the idea of BTR-IRV. Too bad the BTR-IRV folks didn't combine their
idea with Nanson's efficiency idea.

But now we have an even better efficiency idea that increases computational
efficiency while taking advantage (at zero computational cost) of
information inherent in the settled eliminations ... to improve statistical
reliability of the elimination judgments.

If candidate Y has already been eliminated (as in BTR-IRV elimination) by a
settled majority decision between the two statistically weakest candidates
X and Y, and ... on top of that ... a majority of voter ballots opine Z to
be inferior to Y, then this information adds to the posterior likelihood
that X itself is a candidate worthy of elimination: when majorities say Z
is inferior to Y which is inferior to X ... both X and Y being a-priori
weak candidates ... then that is much better grounds for elimination of Z
than some superficial (non majority) statistic.

So, suppose in BTR-IRV at each stage of elimination, after eliminating Y
because it was (between the two minTop count candidates X and Y) the
majority loser ... then instead of wasting that information, before going
on to the next step, you also eliminate each and every candidate deemed
(also by majority vote) to be inferior to Y ... how many expensive steps
might that save at zero cost?

It's important to know that when there are a million ballots, it five
million times more costly to make five extra passes through ballots to
effect the next five eliminations than to eliminate them immediately before
proceeding to the next step.

Not only that ... the democratic information on which these immediate
decisions are made is more reliable than they would be without it ..
having ingnored or discarded that valuable information.

Based on these considerations ... here is one possible path to an ideal
voting method:

Step 1 ... go from IRV to BTR-IRV by using instant majority vote at each
step to decide which of the two statistically weakest candidates to
eliminate at that step.

Step2 ... go from BTR-IRV to BTR-BTR-IRV by eliminating the friends of the
pivot candidate for each step ... the friends of the pivot candidate are
those who do not majority beat it, including the pivot candidate itself.

[Always, at each step the pivot candidate is the democratic majority loser
between the two nominally weakest among those not yet eliminated.]

Step3... Determine the two statistically weakest candidates from the
pairwise support information so that more than one pass through the ballots
is never needed again!

Before this step I strongly suggest using the minTop and MaxBottom
candidates as the two statistically weak candidates (whose pairwise Loser
becomes the povot). If minTop and MaxBottom are the same candidate, then
that candidate is the pivot.

>From this step onward I recommend the respective pairwise analogues of
minTop and MaxBottom for the two statistically weak contenders for
elimination pivot ... the minminPS and the MaxMaxPO candidates respectively.

The first of these is the candidate whose minimal pairwise support is
smaller than any other candidate's minPS.

The second of these is the candidate whose Max pairwise opposition is
greater than any other candidate's MaxPO.

Of these two, the mmPS candidate is like the tennis player whose worst game
score was the worst one of any game in the whole yournament.

The MMPO candidate is the player with the single best defensive game in the
tournament.

Which brings up another huge advantage of the Step 3 transition ... this
transition enables deciding tournament championships on the basis of their
pairwise scores ... without reference to external "seeding."

I'll stop here ... hoping that you can take these basic ideas and run with
them ... there are so many ways to use your own creativity to branch out!

-Forest
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