[EM] Approval vs. IRV

[James Green-Armytage]

>could you explain the details of how ER-IRV (whole and fractional) are
>tabulated?  
>I searched the list, and found a few posts about ER-IRV from this
>spring/summer (including your humorous June 7 post), but none of them
>describe the method in detail.

	I don't know how detailed I can get about this; my understanding of
ER-IRV is relatively uncomplicated. Here are some ad hoc definitions;
probably they're not the most well-written, but hopefully the meaning is
clear. If not, let me know. The only difference between the methods is in
step 2.

ER-IRV(fractional):
1. Ranked ballots, with equal rankings allowed, but with the possibility
of giving all candidates distinct rankings.
2. Do a ballot count for each candidate as follows: Add 1 to the vote
total of a candidate for each ballot which ranks them alone in first
place. Add 1/n to the vote total of a candidate for each ballot on which
they are in an n-candidate tie for first place. (By first place, I mean
the highest ranking given to a non-eliminated candidate.)
3. Eliminate the candidate with the lowest vote total.
4. Repeat steps 2 and 3 until only one candidate remains.

ER-IRV(whole):
1. Ranked ballots, with equal rankings allowed, but with the possibility
of giving all candidates distinct rankings.
2. Do a ballot count for each candidate as follows: Add 1 to the vote
total of a candidate for each ballot which ranks them alone in first
place. Add 1 to the vote total of a candidate for each ballot on which
they are tied for first place. (By first place, I mean the highest ranking
given to a non-eliminated candidate.)
3. Eliminate the candidate with the lowest vote total.
4. Repeat steps 2 and 3 until only one candidate remains.

	You may notice that I don't bother to add a majority stopping rule to the
definition, because I don't think that it adds anything to the method;
rather, it is a heuristic, and not a very useful one. Also, it is
incompatible with ER-IRV(whole).
	As, I've said, ER-IRV(fractional) is probably a safer bet. Perhaps not
just for legal reasons, but also because it is more of a known quantity.
It should be expected to perform rather similarly to regular IRV, and is
also compatible with STV as a proportional representation method, which is
not true of the whole-votes version. That's why I said that
ER-IRV(fractional) has no drawbacks to plain IRV. Really, its almost the
same method, but with the added freedom for equal rankings. ER-IRV(whole)
is less of a known quantity, and might want some more theoretical and/or
empirical examination before it becomes a solid proposal.
	The advantage that I have seen for ER-IRV(whole) over ER-IRV(fractional)
is that it further-decreases the incentive for the compromising:reversal
strategy relative to the incentive for the less-severe
compromising:compression strategy. (See the link below for definitions of
those terms.) Even if there is an advantage there, I'd suggest that the
gain from plain IRV to ER-IRV(fractional) is much more significant than
the gain from ER-IRV(fractional) to ER-IRV(whole).
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-March/012515.html

my best,
James

P.S.	Perhaps the next step after ER-IRV(fractional) could be Condorcet
completed by IRV for single winner
http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2004-July/013450.html
and STV proportional representation for legislatures...
	... and then from there, maybe cardinal-weighted pairwise for single
winner??? 
http://fc.antioch.edu/~jarmyta@antioch-college.edu/voting_methods/weighted_pairwise.htm
	That's one possible progression, although it might take some years.