[EM] Fixing IRV

[Forest Simmons]

Excellent ideas!

I think they deserve further consideration.

Note that the candidate with lowest mean (as opposed to median) rank is
the Borda loser, so this method is similar to Nanson (if I remember
correctly).

The median is better than the mean in this context because it is more
majoritarian and less sensitive to the extremes.

The IRVies make big claims for a majority winner, but the Condorcet Winner
will always beat the IRV winner by a majority when the two differ.

Ask an IRV supporter this question.  Suppose that whenever methods X and Y
produce different winners, the X winner beats the Y winner by a majority.
Which method is better, X or Y ?

Let method Y be IRV. Let method X be the method that gives the win to the
CW if there is one, else picks the IRV winner.

Method X is obviously an improvement over method Y by the majority
criterion.

Roy's method is an improvement over both X and Nanson, in my opinion.

Forest

On Tue, 7 Aug 2001, Roy One wrote:

> Much has been made of the flaws of IRV. Notably, that it fails to
> find
> the Condorcet winner when there is one, which casts serious doubt on
> its claim of supporting majority rule.
> 
> I think we all know the source of the flaw: it doesn't use majority
> rule in elimination rounds. It uses (anti-)plurality. WHY???
> Proponents seem to have a great attachment to the notion of using
> only
> the first place votes. Of course, by eliminating the anti-plurality
> choice, they've eliminated a majority of people's lower choices
> before
> they ever had a chance to be considered.
> 
> There is a better way to eliminate candidates, based on majority
> rule:
> eliminate the candiate with the lowest median rank. The median rank
> is
> the level at which half consider the candidate that high or higher,
> and half consider him that low or lower. (If you like, you can take
> the vote after the median vote, for a true, minimal majority.)
> 
> A similar method would be to eliminate all candidates whose median
> rank is not in the top half -- i.e., a majority of people believe
> those candidates should be ranked in the bottom half. It works a
> little faster, and in my (admittedly rather limited) testing, has
> always resulted in the same winner as Ranked Pairs.
> 
> Notes: if the median point is, say 1.5 (because there are 3
> candidates), count half of the 2nd place votes as well as all of the
> 1st place votes for each candidate. If candidates can be ranked equal
> to each other, they all get ranked as the average of the positions
> they span, e.g., if 2 candidates tie for 2nd, they each rank 2.5; if
> 3
> share 2nd, they each get ranked 3rd. Similarly as before, half of the
> between-value votes count toward the rank a half-step up (half of
> 2.5's count toward a candidate's being in the top two). In case all
> candidates are equally divided in the top N spots, consider the
> median value of only those votes and discard the lowest.
> 
> Wouldn't it be nice if a system with the support of IRV could be
> patched to make it Condorcet-compliant?
> 
> Roy Johnson
> 
> 
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