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 candiate 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) Decisisiveness; 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.