[EM] Quinn & LeGrand's puzzle about 2-long beatpaths; and "kingly" Condorcet methods

[Warren D Smith]

A solution the Quinn's puzzle, which greatly generalizes LeGrand's,
is now available here:
  http://rangevoting.org/PuzzKingTourn.html

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The "existence of king" theorem stated in part (a) there
suggests that it might be interesting
for Condorcetists to demand that
the winner always must be a "king."

For example, the king-variant of Markus Schulze's beatpath
method would be to demand that the winner W is the candidate
who
(i) is a king
(ii) beats every rival via the strongest <=2-hop beatpath
i.e. choose the king W such that the minimum defeat margin
used in all its (<=2)-hop beatpaths, is maximized.

There similarly would be king-variants of virtually every
Condorcet method ever proposed.
These king-variants might have advantages, such as speedier
algorithm; and disadvantages, such as losing some of the properties
Schulze's (original) beatpath method enjoyed.  I have not attempted
to check which properties survive/not.

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)