[EM] Example of strategic Condorcet voters not electing honest-voter-Condorcet-winner

[Warren Smith]

There are 3 candidates A,B,C (or there could be more D,E,...; it'll still work).
C is the honest Condorcet winner, with slight pairwise victories over A,B,...
A has large pairwise victories over everybody but C.
The A-voters instead of honestly voting A>C>B>...  vote A>B>...>C.
This causes C no longer to be the Condorcet winner.  In fact C now
loses pairwise (by moderate margins) to every candidate except A.
A now wins pairwise over every candidate except C.
C beats A by slight margin.
Now A is the winner under all these popular Condorcet
methods (plus more too, if you do it right):
Schulze beatpaths, Tideman ranked pairs,
basic Condorcet, Simpson-Kramer minmax.

It has sometimes been falsely stated that, although Condorcet was vulnerable to strategic
voting, it was only vulnerable in cycle situations with no Condorcet winner.
In fact it is vulnerable in situations with an honest Condorcet winner too.
Strategic Condorcet voters an fail to elect a Condorcet winner.
Strategic range or approval voters will, however, elect an honest-voter Condorcet winner
under certain (in practice highly reasonable) assumptions:
   http://rangevoting.org/AppCW.html

Warren D Smith
http://rangevoting.org