James Green-Armytage
Anti-strategy enhancements for Condorcet methods
Here is a brief list of measures that have been proposed to reduce the vulnerability of Condorcet to the burying strategy.
Iterative procedure:
Ranked vote. Pairwise tally. Provisional completion method winner declared.
Up-down vote on provisional winner. If majority up, process is complete. If
majority down, begin again.
Comments:
This method is recommended for small groups, but unlikely to be practical in a
public election.
http://fc.antioch.edu/~james_green-armytage/vm/iterative.htm
Two round procedure:
Ranked vote. Pairwise tally. If there is a Condorcet winner, the procedure ends. If not, another round of voting will be held. The completion method winner of the second round will be binding. Candidates will be allowed to withdraw in between rounds, and candidates who were not members of the Smith set in the first round will not be eligible for the second.
Comments: May provide a fairly robust line of defense against manipulation, but at the cost of a second balloting.
http://fc.antioch.edu/~james_green-armytage/vm/iterative.htm
Candidate withdrawal option (CWO):
Ranked vote. Pairwise tally. Provisional completion method winner declared.
Non-winning candidates have the option of withdrawing from the race and ordering
a re-tally with their names deleted from the ballot.
Comments:
A simple method that is practical for public elections, although some people
tend to find it counterintuitive. It is possible that CWO could produce a
strange result in the event of a sincere cycle.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-February/014703.html
AERLO/ATLO:
AERLO (automatic equal ranking line option) allows a voter to specify that all
preferences between candidates ranked above a certain line should be changed to
equalities in the event of a majority rule cycle. ATLO (automatic truncation
line option) allows a voter to specify that all preferences between candidates
ranked below a certain line should be changed to equalities in the event of a
majority rule cycle.
http://en.wikipedia.org/w/index.php?title=Voting_system&oldid=11617838
Comments: The AERLO feature can be used to help protect candidates from being buried, while the ATLO feature can be used in an attempt to deter a burying strategy. AERLO/ATLO may be somewhat difficult to explain to voters.
Strong/weak preference option (S/WPO):
Voters can express both strong and weak preferences. The direction of pairwise
defeats are determined by both strong and weak preferences, and the strength of
pairwise defeats are determined only by strong preferences.
Comments:
Slightly more flexible variant on AERLO/ATLO.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015217.html
Cardinal pairwise (a.k.a. cardinal-weighted pairwise or CWP):
Voters rate candidates from 0-100. Separate rankings are optional (otherwise
they can be inferred from ratings). The directions of pairwise defeats are
determined by rankings information, and the strength of pairwise defeats are
determined by ratings information, according to the procedure described in the
links below:
http://fc.antioch.edu/~james_green-armytage/cwp13.pdf
http://fc.antioch.edu/~james_green-armytage/cwp13.htm
http://fc.antioch.edu/~james_green-armytage/cwp21.pdf
Comments: I currently advocate this as the best single-winner method for public elections, for two primary reasons. (1) It provides relatively strong anti-strategic protection, without requiring the majority of voters to be strategically sophisticated in order to defend against incursion. (2) I claim that it provides a more meaningful resolution to sincere cycles than strictly ordinal methods.
Approval-weighted pairwise (AWP):
Similar to cardinal pairwise, but with a ranked ballot and an approval cutoff
rather than a continuous 0-100 cardinal scale.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-June/013241.html
Comments:
Provides many of the benefits of cardinal pairwise, with a less complex
interface. Differs from AERLO/ATLO in that the two lines are combined into one, and that
voters do not have the option of lending maximum strength to all preference gaps
in the event of a majority rule cycle.
Smith/IRV:
If there is no Condorcet winner, candidates outside the Smith set are eliminated, and there is an IRV tally between the remaining candidates.
Comments: If there is a Condorcet winner with more than one third of the vote, then the result will be essentially strategy-proof. On the other hand, if the Condorcet winner differs from the IRV winner, those who prefer the IRV winner will often have an opportunity to elect him by burying the Condorcet winner. I view this is an interesting method, as it combines Smith efficiency with a reasonable robustness against the more flagrant types of strategic incursion. This is probably a good proposal for an electorate that is already somewhat familiar with the IRV method, as it offers the obvious benefit of Smith efficiency, with no obvious drawbacks.