Anonymity
if it treats all of the voters equaly.
Neutrality
Social Choice function is Neutral if it treats all of the candidates equaly.
Monotonicity
if moving up the ranks in a profile does not adversely affect a candidates chances to win.
Pareto
If everyone preferes one candidate to another, the second candidate can not win.
condorcet
If a candidate wins all head to head matchups he must win an election
anti-condorcet
if a candidate loses all head to head matchups he must lose the election.
Independence
If in two profiles A wins to B, and in profile 1 A is prefered to B then in profile 2 B can not be prefered to A and also B can not win the election.