James,
You wrote:
Dear election methods fans,
In a recent message, I noted that there is no broad consensus among
Condorcet supporters as to which completion methods would be most
appropriate for a few key scenarios. I don't really expect to establish
such a consensus, but I would at least like to address some of the issues
involved, and hear where some of the other Condorcet supporters are coming
from.
There are at least three areas of possible divergence:
1. The base method: Minimax (candidate whose worst loss is least bad),
sequential dropping (drop the weakest defeat that's in a cycle until a
candidate is unbeaten) ranked pairs, river, beatpath, Condorcet completed
by another method, approval hybrids, etc.
Like many others here, I'm a big fan of Ranked Pairs (RP), Schulze, and River. To a great extent this is because I value approximations of IIA, so I want a method that meets Smith-IIA and Independence of Clones.
2. Measures of defeat strength: margins, winning votes, or something else
(cardinal-weighted pairwise (CWP), approval-weighted pairwise (AWP), etc.)
I recently re-read your paper on CWP. I must confess that I didn't see much justification for it at first, but I now find it to be well justified and elegant. Unfortunately, there's the matter of the complications this will create when it comes to creating and using ballots. Perhaps over time I'll come to appreciate CWP more and think it's worth the trouble, but for now I remain partial to margins.
To what I've said in regards to (1) and (2) so far I'd like to add that
for some time I've had difficulty deciding which of the aforementioned three methods I prefer. Similarly I've had trouble finding any criterion that makes either margins or winning votes the obvious choice. However, I've recently become partial to RP(m). I'll post more about this in the days to come.
3. Whether to use an anti-strategy measure (candidate withdrawal option
(CWO), CWP, AERLO/ATLO, iterative procedure, etc.)
I'm not about to advocate AERLO or ATLO, largely for the reasons you've already mentioned. I also feel that CWO would give too much power to candidates.
What do I propose? I'll briefly reiterate an idea I presented to this list some time ago: Make runners-up matter. One modest example would be that the bylaws of an organization could state that when an officer becomes incapacitated, the runner-up will assume the role until re-election or the officer is able to serve again. This might dissuade people from (some) insincere ranking and truncation. Ranked Pairs could be used to find the social ranking.
(The rest of your letter follows):
Area (1) is not necessarily the most contentious; i.e. most people who
like beatpath like ranked pairs just about as much, and so on. However, I
would not feel especially good about a method that isn't Smith-efficient,
even to start out with. So that cuts out plain minimax as far as I'm
concerned.
I prefer winning votes for area (2), entirely for anti-strategic reasons.
This starts to bring us toward area (3), i.e. strategy. I agree that
winning votes has a better protection against the burying strategy than
margins, but I still suspect it to be somewhat unstable in certain
situations. If I am correct (which is debatable, of course), this brings
us into slightly uncomfortable terrain. CWO is the simplest anti-strategy
method, but some voters might be intuitively uncomfortable with the idea.
CWP has an intuitive interface, but one which requires very sophisticated
ballots, and the tally rule is complex. AWP, AERLO/ATLO, and similar
methods have a somewhat confusing interface, and while the tally rules are
not terribly complex, they are not brilliantly easy to explain, either.
I know that Mike Ossipoff has said that we should all come together
around a winning votes method without an additional anti-strategy measure.
But I'd like to hear what some other people think. I'm not even sure what I would recommend, if I was in a position to
recommend something for public elections. I lean towards starting out with
a winning votes version of sequential dropping (or any one of ranked
pairs, beatpath, river, if there isn't an intense need for simplicity)
with a CWO. But that's subject to change, with further discussion.
my best, James
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Sincerely, CF
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