|JOURNAL:||The Journal of political Economy|
Headline: Social Preferences can't Reflect Rationality as they can for Individuals
There is no possible way to choose among three or more options(he describes it as creating a social welfare function for choosing between distinct alternatives) while fulfilling the following reasonable conditions.
1. Defined for every ordering of individuals' preferences
2. Independence of Irrelevant Alternatives: If z is winning, removing y from consideration should not make x win.
3. Between two states, x not falling and possibly rising without any other change and x was preferred to y before the reordering, x should still be preferred to y.
4. The ordering must change as preferences change.
5. The ordering must not be dependent on the desires of one and only one person.
Symbolic manipulation. Pure and abstract mathematics. A list of axioms, conditions, and steps.