are different. It is also rotationally invariant.
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Any questions? Get answers on any topic
) and is unique unless you have an even number of
collinear points and the middle two are different. It is also
rotationally invariant.
A good reference is
Christopher G. Small. A Survey of Multidimensional Medians.
International Statistical Review, 58(3):263-277. Dec. 1990.
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and Borda strategies for use with DSV.
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{A, C} is a better winner set
than {A, B} even though B is the Condorcet winner.
(I didn't suggest a name for the method when I proposed it, but it has
been called the orphan method, LeGrand IRV and BTR-IRV.)
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, thanks to Brian for pointing this out.
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approval DSV strategy-A equilibria (which also
turn out to be strong Nash equilibria):
49:A
21:B
30:CB
49:A
21:BC
30:C
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. I think it's my new favorite
ranked-ballot system.
(Or maybe slightly better, spread out the different voted rank
levels evenly over a range. For example, A=BCDE=F=GH=I would
give A and B 100 points, C 75, D 50, E, F and G 25 and H and I 0.)
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or winning-votes.
I think it would be a mistake to insist on winning-votes if it
turns out that margins is an easier sell for public elections.
Kevin, could you post an example that gives a favorite-betrayal
incentive under margins but not winning-votes?
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insincerely is NP-
hard. See
Bartholdi III, John J., Craig A. Tovey and Michael A. Trick. The
computational difficulty of manipulating an election. Social
Choice and Welfare, 6(3):227-241, 1989.
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ranking near the bottom even
when insincere (and even in the zero-info case!) that I prefer
margins to winning-votes.
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Condorcet methods, like Baldwin
(Borda-elimination) and Arrow-Raynaud (minimax-elimination), now
give C as the winner.
I'm sure someone else will post a more compelling example.
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problems would result.
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Election
(2005, forthcoming).
END OF STATEMENT
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to hurt B's chances. And
under a winning-votes system I'd strategize by voting A=BC even if
I knew nothing or expected it to be a close three-way race.
Following this intuitive Borda-style strategy under Approval or
Range Voting never requires expression of an insincere pairwise
preference.
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.
END OF STATEMENT
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Election-methods
Say in a Raynaud election the ranked ballots are
7:ABC
2:BAC
5:BCA
6:CAB
C is eliminated and A wins. But if the BAC voters uprank A,
giving
9:ABC
5:BCA
6:CAB
B is eliminated and C wins. So A went from winning to losing with
extra support.
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naturally from the
smart strategic moves. Declared Strategy Voting in ballot-by-
ballot mode running for many rounds using Approval and strategy A
elects them with approximate probabilities A 25.05%, B 12.99%, C
27.54% and D 34.42%.
Rob LeGrand, psephologist
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Citizens for Approval
to approve B. Plus, a majority
strictly prefers B to C.
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the intervals between leader changes become longer and longer as
the number of rounds increases.) To me, these results confirm my
intuition that ballot-by-ballot (with a random voter order in each
round) is a fairer way to find a winner than the batch modes given
a large number of rounds.
=
Rob
that has that property of weak sincerity.
Anyway, the point is that I think Approval has the best combination
of manipulation-resistance, convergence and quality of winners, not
to mention simplicity. A little divergence is worth the better
equilibria.
=
Rob LeGrand, psephologist
[EMAIL
. Thanks!
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of one-person-one-vote, but
instead a yes/no vote per choice.
I think some major-party voters would still want to keep others
from voting for many candidates, but it's hard to tell what would
happen.
=
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approvals. But allowing n approvals in a race would allow
n + 1 parties to compete fairly in that race, which is still a
strict improvement over plurality.
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like the Uncovered Set, Banks Set, Minimal Covering Set,
Tournament Equilibrium Set, Markov Set etc.
Jobst, could you post mathematical definitions and intuitive
explanations for each of these sets?
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the following example works:
98:ACEDB
64:BAECD
12:BAEDC
98:BEACD
13:BEADC
125:BEDAC
124:CAEDB
76:CEADB
21:DABEC
30:DBAEC
98:DBECA
139:DCABE
23:DCBAE
=
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elect A, the
Condorcet winner.
=
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), which is an unfortunate simplification.
=
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Election-methods mailing list - see http
Here's a question I thought about quite a bit a while ago but never posted
until now that there's talk of Bucklin on the list: Which candidate should
win the following Bucklin election?
25:BrownJonesDavisSmith
26:DavisSmithBrownJones
49:JonesSmithBrownDavis
Smith? Jones?
=
Rob
.
Oh, and I'd like to add one presidential nomination for the poll:
Congressman Ron Paul (http://www.house.gov/paul/).
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the winners of the
above methods if asked.
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for Libertarian presidential candidates. Support Approval Voting by
voting for Michael at http://cass.molp.org/polls.htm !
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by voting 0
for B. In fact, by doing so, they'd remove the possibility that the C
voters could elect B by voting 2 for B, which would be an improvement from
their point of view.
=
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representation scheme.
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Election-methods mailing list - see
by Steven Brams)
and strategy I (adjust your previous Approval strategy just enough to
differentiate between the latest top two candidates).
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and last own vote. If anyone has a better one, or even an
interesting new one, please let me know.
=
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an interesting
example, though. I'll investigate it further and get back to you again.
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could be extremely simple.
=
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Election-methods
,
only the Smith set is reported. Try
ACBFDE
BCEFDA
DBAFEC
EABCFD
EDABCF
FCDABE
or
ACDEB
BACED
BAEDC
DCEBA
and click Calculate all winners for examples of the sets' differing.
=
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Citizens for Approval Voting
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For anyone who uses my ranked-ballot voting calculator, it and my other
webpages have moved. Please see http://cec.wustl.edu/~rhl1/rbvote/ .
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proportionality (which improves as n increases).
So it's not obvious to me that the best multiwinner systems reduce in the
single-winner case to the best single-winner systems.
=
Rob LeGrand, psephologist
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Citizens for Approval Voting
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Note that Nanson eliminates all candidates that couldn't possibly be
Condorcet winners based solely on Borda score.
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of all Borda scores is zero, so a Condorcet winner's
Borda score is always above average. Therefore it won't be eliminated at
any stage of Baldwin or Nanson, so Baldwin and Nanson are Condorcet methods.
=
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Citizens for Approval Voting
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example effectively
demonstrates IRV's caprice, but I think he has the wrong remedy in mind.
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