| U | Unrestricted Domain: The SWF must assign a social preference
ordering for any possible preference profile. This condition is violated by majority rules. |
| I |
Independence of Irrelevant Alternatives:
If each citizen's pairwise ranking of alternatives x and y in profile P2
is the same as it is in profile P1, then x and y must be in the same order
in the social preference orderings that the SWF yields for P1 and P2. |
| PA |
Positive Association: If a SWF ranks an
alternative x above an alternative y for a given profile, it must also rank
x above y in any profile that is exactly like the original one except that
one or more citizens have moved x up in their own rankings. |
| D | Nondictatorship: For each citizen there must exist
at least one profile whose social preference order does not match that citizen's.
In other words, anyone may be outvoted. |
| CS | Citizens' Sovereignty: For each pair of distinct alternatives
x and y there is at least one profile for which the SWF ranks x above y.
For example, if everyone ranks x first & y last. |
| P | Pareto: The SWF must rank x above y for a given profile
if every citizen ranks x above y in that profile. Also called Unanimity rule. |