In response I will pick on LNH for not being a serious reason for
rejecting Condorcet - that such failure can occur with reasonable
voting choices for which the voter knows what is happening. Quoting
from Wikipedia:
For example in an election conducted using theCondorcet compliant
method Ranked pairs the following votes are cast:
49: A
25: B
26: C>B
B is preferred to A by 51 votes to 49 votes. A is preferred to C by
49 votes to 26 votes. C is preferred to B by 26 votes to 25 votes.
There is no Condorcet winner and B is the Ranked pairs winner.
Suppose the 25 B voters give an additional preference to their
second choice C.
The votes are now:
49: A
25: B>C
26: C>B
C is preferred to A by 51 votes to 49 votes. C is preferred to B by
26 votes to 25 votes. B is preferred to A by 51 votes to 49 votes.
C is now the Condorcet winner and therefore theRanked pairs winner.
By giving a second preference to candidate C the 25 B voters have
caused their first choice to be defeated.
Pro-A is about equal strength with anti-A. For this it makes sense
for anti-A to give their side the best odds with the second vote
pattern, not caring about LNH (B and C may compete with each other,
but clearly care more about trouncing A).
An aside: Note that the same strategy makes sense for IRV - A wins
the first vote while B or C wins the second (C as shown; B with a
trivial change in votes).
LNH may have made sense for the methods that inspired it, but cannot
compete for causing trouble for Condorcet, considering IRV's problems.
Dave Ketchum
On Jan 17, 2010, at 2:30 PM, Chris Benham wrote:
Abd Lomax wrote (17 Jan 2010):
<snip>
"Chris is Australian, and is one of a rare breed: someone who actually
understands STV and supports it for single-winner because of LNH
satisfaction. Of course, LNH is a criterion disliked by many voting
system experts, and it's based on a political concept which is, quite
as you say, contrary to sensible negotiation process."
<snip>
I endorse IRV (Alternative Vote, with voters able to strictly rank
from the top however
many candidates they choose) as a good method, much better than
Plurality or TTR,
and the best of the methods that are invulnerable to Burial and meet
Later-no-Harm.
Some of us see elections as primarily a contest and not a
"negotiation process".
I endorse IRV because it has a "maximal set" of (what I consider to
be) desirable
criterion compliances:
Majority for Solid Coalitions (aka Mutual Majority)
Woodall's Plurality criterion
Mutual Dominant Third
Condorcet Loser
Burial Invulnerability
Later-no-Harm
Later-no-Help
Mono-add-Top
Mono-add-Plump (implied by mono-add-top)
Mono-append
Irrelevant Ballots
Clone-Winner
Clone-Loser (together these two add up to Clone Independence)
As far as I can tell, the only real points of dissatisfaction with
IRV in Australia are
(a) that in some jurisdictions the voter is not allowed to truncate
(on pain of his/her
vote being binned as "invalid") and (b) that it isn't multi-winner
PR so that minor
parties can be fairly represented.
I gather the Irish are also reasonably satisfied with it for the
election of their President.
<snip>
"I've really come to like Bucklin, because it allows voters to
exercise full power for one candidate at the outset, then add, *if
they choose to do so*, alternative approved candidates."
<snip>
The version of Bucklin Abd advocates (using ratings ballots with
voters able to give
as many candidates they like the same rating and also able to skip
slots) tends
to be strategically equivalent to Approval but entices voters to
play silly strategy
games "sitting out" rounds.
It would be better if 3-slot ballots are used, in which case it is
the same thing as
(one of the versions of) "Majority Choice Approval" (MCA).
IMO the best method that meets Favourite Betrayal (and also the
best 3-slot ballot method)
is "Strong Minimal Defence, Top Ratings":
*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).
Interpreting top and middle rating as approval, disqualify all
candidates
with an approval score lower than their maximum approval-opposition
(MAO) score.
(X's MAO score is the approval score of the most approved candidate
on
ballots that don't approve X).
Elect the undisqualified candidate with the highest top-ratings
score.*
Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so
the voters have a less
strong incentive to truncate.
Unlike MCA/Bucklin this meets Irrelevant Ballots. In MCA candidate X
could be declared the
winner in the first round, and then it is found that a small number
of voters had been wrongly
excluded and these new voters choose to openly bullet-vote for
nobody (perhaps themselves
as write-ins) and then their additional ballots raise the majority
threshold and trigger a second
round in which X loses.
I can't take seriously any method that fails Irrelevant Ballots.
Compliance with Favourite Betrayal is incompatible with Condorcet.
If you are looking for a
relatively simple Condorcet method, I recommend Smith//Approval
(ranking):
*Voters rank from the top candidates they "approve". Equal-ranking
is allowed.
Interpreting being ranked above at least one other candidate as
approval, elect the most
approved member of the Smith set (the smallest non-empty set S of
candidates that pairwise
beat all the outside-S candidates).*
Chris Benham
----
Election-Methods mailing list - see http://electorama.com/em for list info
