How to Define 'Prioritarianism' and Distinguish It from (Moderate) Egalitarianism

In this paper, first the term 'prioritarianism' is defined, with some mathematical precision, on the basis of intuitive conceptions of prioritarianism, especially the idea that "benefiting people matters more the worse off these people are". (The prioritarian weighting function is monotonously ascending and concave, while its first derivation is smoothly descending and convex but positive throughout.) Furthermore, (moderate welfare) egalitarianism is characterized. In particular a new symmetry condition is defended, i.e. that egalitarianism evaluates upper and lower deviations from the social middle symmetrically and equally negatively (as do e.g. variance and Gini). Finally, it is shown that this feature distinguishes egalitarianism also extensionally from prioritarianism.