If a candidate receives a majority of the first-place
votes, then that candidate should be declared the winner.
If a candidate is favored when compared one-one-one
with every other candidate, then that candidate should
be declared the winner.
A candidate who wins a first election and
then gains additional support, without losing any of the
original support, should also win the second election.
If a candidate is declared the winner of an election,
and in a second election one or more of the other candidates
is removed, then the previous winner should still be declared
the winner.
The four criteria listed above: majority criterion, Condorcet
criterion, Monotonicity criterion, and irrelevant alternatives
criterion are referred to as the fairness criterion.
No social choice rule satisfies all six of the following
conditions:
(1) Unrestricted domain; Any set of rankings is
possible.
(2) Decisiveness; Given any set of individual rankings,
the method produces a winner.
(3) Symmetry and transitive; The voting system
should be symmetric and transitive over
the set of all outcomes.
(4) Independence of irrelevant alternatives; If
a voter prefers A to B with C as
a possible
choice, then the voter
still prefers A to B when C is not
a possible choice.
(5) Pareto principle; If each voter prefers A
over B, then the group chooses A over B.
(6) There should be no dictator.