Discussion:
Single-winner election data from the OpenSTV database
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Greg
2008-12-03 07:43:35 UTC
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There are 65 real single winner elections in OpenSTV Database
(stv.sourceforge.net/stvdb).While the database doesn't list the
individual ballots, it does list the Smith Set for each of these
races. In 63 of these 65 races, there exists a dominant Condorcet
winner (the Smith set has a size of 1).

For 61 of the 65 races, the database also includes the results of
applying other single-winner methods to the ballots, including IRV,
Coombs, Borda, Supplementary Vote, Plurality, and Bucklin. 60 of these
61 have a Condorcet winner. Here is the Smith efficiency (frequency of
electing a candidate from the Smith Set) for each of the applied
methods, from best to worst:

IRV, Coombs: 100% Smith Efficiency (61 of 61 races)

Borda, Supplementary Vote: 96.7% Smith Efficiency (59 of 61 races)

Plurality: 95.1% Smith Efficiency (58 of 61 races)

Bucklin Voting: 91.8% Smith Efficiency (56 out of 61 races)

- Greg
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Steve Eppley
2008-12-03 14:34:07 UTC
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Hi,

I think it's misleading to compare voting methods pseudo-empirically the
way Greg did below, because the positions on the issues that the
candidates will take (assuming they want to win) depend (in part) on the
voting method, and the decisions by potential candidates whether to run
depend (in part) on the voting method.

It's not surprising that poor methods like plurality rule and single
winner STV (a.k.a. Instant Runoff) appear to usually elect Condorcet
winners given the overly simplistic analysis Greg cited, because with
those methods the elites try hard to organize into 2 large coalitions
that each nominate only one candidate.

Voting methods that make centrists appear relatively unpopular
(plurality rule, single winner STV a.k.a. Instant Runoff, etc.) not only
discourage politicians from taking centrist positions, they discourage
centrist candidates from competing. For example, recall John McCain's
decision not to compete as an independent in the 2000 general election
after the Republican Party nominated George W Bush. Under plurality
rule, McCain running as an independent would have cinched the election
for Al Gore. Under Instant Runoff, it probably wouldn't have changed
the outcome, but McCain would likely have been eliminated before Gore
and Bush and therefore would have appeared relatively unpopular, so why
bother running, and why would donors bother contributing campaign funds
to a likely loser? Under a Condorcetian voting method, McCain would
have won. (Of course, if the voting method had really been Condorcetian,
McCain would have faced different competition from candidates trying to
be the best centrist compromise.)

For another way that the voting method can affect who runs and the
positions taken by candidates trying to win, consider methods like
Voting for a Published Ranking (VPR). VPR can be expected to greatly
reduce the campaign money needed by good centrist candidates to win,
which would change who runs, their positions on the issues, and who wins.

Here's a quote from page 89 of Peter Ordeshook's book Game Theory and
Political Theory:

"... since it seems reasonable to require that democratic voting
procedures
elect Condorcet winners if they exist, scholars have proposed a
variety of
voting schemes as alternatives to plurality rule. But the problem
with most
analyses of these alternatives is that they take inadequate account
of the
possibility that voters might misrepresent their preferences and
candidates
might change their campaigns under different rules."

Ordeshook could have added that potential candidates might make
different decisions about whether to run, and that donors might make
different decisions about how much to donate and to whom. He could also
have added that, by the same reasoning that it seems reasonable to elect
a Condorcet winner if it exists, it also seems reasonable to elect a
member of the top cycle (a.k.a. Smith set).

Regards,
Steve
--------------------------
Post by Greg
There are 65 real single winner elections in OpenSTV Database
(stv.sourceforge.net/stvdb).While the database doesn't list the
individual ballots, it does list the Smith Set for each of these
races. In 63 of these 65 races, there exists a dominant Condorcet
winner (the Smith set has a size of 1).
For 61 of the 65 races, the database also includes the results of
applying other single-winner methods to the ballots, including IRV,
Coombs, Borda, Supplementary Vote, Plurality, and Bucklin. 60 of these
61 have a Condorcet winner. Here is the Smith efficiency (frequency of
electing a candidate from the Smith Set) for each of the applied
IRV, Coombs: 100% Smith Efficiency (61 of 61 races)
Borda, Supplementary Vote: 96.7% Smith Efficiency (59 of 61 races)
Plurality: 95.1% Smith Efficiency (58 of 61 races)
Bucklin Voting: 91.8% Smith Efficiency (56 out of 61 races)
- Greg
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