[EM] Condorcet Enhancement
fsimmons at pcc.edu
Sun May 19 16:10:17 PDT 2019
There are various ways to enhance a given method to make it Condorcet
1. One can elect the ballot CW if there is one, and otherwise fall back on
the given method.
2. One can apply the given method to the Smith set.
3. One can use the given method winner as the starting point in a seamless
process that leads to a member of the Smith Set (or better).
Here is such a process:
First, create a directed graph whose vertices are the candidate names as
For each covered candidate X, draw an arrow to that candidate Y (among
those that cover X) which is ranked or rated strictly below X on the fewest
number of ballots.
To enhance the winner A of any method, start at candidate A and follow the
arrows as far as possible in the directed graph. The enhanced winner W' is
the one at the end of the directed path.
This W' covers W, but is itself uncovered (a member of the Landau Set), and
so also a member of Smith.
If the original method elects monotonically, then so does the enhanced
If the original method satisfies the FBC or in any case lacks vulnerability
to compromise, then the enhanced method gives little incentive for burying
Favorite because when there is an arrow from Favorite to Y, candidate Y is
already the natural compromise candidate for the supporters of Favorite,
the one that is rated strictly below Favorite on the fewest ballots among
those that cover Favorite.
A. Enhanced Approval.
B. Enhanced Majority Judgment
C. Enhanced Random Ballot
D. Enhanced Asset Voting (different possible versions)
E. Enhanced Chiastic Approval
If method M is Chicken Resistant, does it follow that the Enhanced version
of Method M also Chicken Resistant?
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