James Green-Armytage wrote (20 Nov 2010):
<snip>
In addition to the nine methods listed above, I tried some of my
analyses with six other Condorcet methods: beatpath, ranked pairs,
Smith/Hare, alternative Smith, and two versions of cardinal pairwise.
Beatpath and ranked pairs generally seem to perform like minimax, and
cardinal pairwise usually but not always performs somewhat better than
these, but the really striking news in my opinion is how well the
Hare-Condorcet hybrids perform.
That is, given a preliminary analysis, they seem to be as resistant to
strategic voting as Hare (and possibly slightly more resistant), and
they are distinctly less vulnerable to strategic nomination (because
they are Smith efficient, and therefore only vulnerable to strategic
nomination when there is a majority rule cycle). So, for single-winner
public elections, alternative Smith and Smith/Hare seem to have a lot
to recommend them, i.e. the combination of Smith efficiency with
strong resistance to both types of election strategy.
I should define these methods here, for clarity. Smith/Hare eliminates
all candidates not in the Smith set (minimal dominant set, i.e. the
smallest set of candidates such that all members in the set pairwise
beat all members outside the set), and then holds an IRV tally among
remaining candidates. This method has been floating around this list
for a while, yes? Does anyone know of an academic publication that
mentions it? I seem to remember reading something that said that it
had been named after a person at some point, but I no longer know
where I read that.
Alternative Smith is a closely related method, which Nic Tideman made
up when he was writing Collective Decisions and Voting. It (1)
eliminates all candidates not in the Smith set, then (2) eliminates
the candidate with the fewest top-choice votes. Steps 1 and 2
alternate until only one candidate remains. (See page 232 of the
book.) I focus on this rule rather than Smith/Hare in the paper,
because I find it marginally more elegant, but the difference between
the two is very minor.
James,
We discussed these "Hare-Condorcet hybrids" on EM in the months of
October and
November 2005. Then I quoted Douglas Woodall's demonstration that both
the versions
you discuss fail Mono-add-Plump and Mono-append.
abcd 10
bcda 6
c 2
dcab 5
All the candidates are in the top tier, and the AV winner is a. But
if you add two extra ballots that plump for a, or append a to the two
ballots, then the CNTT becomes {a,b,c}, and if you delete d from all
the ballots before applying AV then c wins.
Translating to a more familiar EM format:
10: A>B>C>D
06: B>C>D>A
02: C
05: D>C>A>B
All candidates are in the Smith set (Woodall's "Condorcet-Net Top
Tier"), and the Hare
(aka "Alternative Vote", aka IRV) winner is A.
But if you add 2 ballots that bullet-vote (plump) for A, or change the
two C ballots to C>A,
the Smith set becomes {A B C}, and if you delete D from all the ballots
from all the ballots before
applying Hare (i.e. properly "eliminate" D and not just disqualify D
from winning) then C wins.
Smith,Hare (which Woodall called "CNTT,AV") meets those criteria and has
a simpler algorithm:
Begiinining with their most preferred candidate, voters strictly rank
however many candidates they wish.
Before each (and any) elimination, check for a candidate X that
pairwise beats all (so far uneliminated)
candidates. Until such an X appears, one-at-a-time eliminate the
candidate that is voted favourite
(among uneliminated candidates) on the fewest ballots. As soon as an X
appears, elect X.
So why put up with failures of mono-add-plump and mono-append? What
advantage (if any) do you think
the two versions you discuss have over Smith,Hare to compensate for that?
Chris Benham
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