[EM] Smith Sets with >3 members

Markus Schulze markus.schulze at alumni.tu-berlin.de
Thu Feb 28 04:36:00 PST 2002

Dear Forest,

every election method that meets the majority criterion is
vulnerable to "compromising". In so far as a voter will
usually approve at least that candidate who gets this
voter's first preference, you cannot circumvent this
incompability by using "some hybrid method that requires
information outside of the pairwise comparisons, perhaps
information not available in preference ballots".

Example:

40 A > B > C.
35 B > C > A.
25 C > A > B.

Suppose that the used election method meets the majority
criterion.

Suppose that A wins the elections. Then the 35 BCA
voters can change the winner from A to C by voting CBA
(i.e. by "compromising").

Suppose that B wins the elections. Then the 25 CAB
voters can change the winner from B to A by voting ACB
(i.e. by "compromising").

Suppose that C wins the elections. Then the 40 ABC
voters can change the winner from C to B by voting BAC
(i.e. by "compromising").

Markus Schulze