The Pigou–Dalton principle (PDP) is a principle in welfare economics, particularly in cardinal welfarism. Named after Arthur Cecil Pigou and Hugh Dalton, it is a condition on social welfare functions. It says that, all other things being equal, a social welfare function should prefer allocations that are more equitable. In other words, a transfer of some defined variable (for example utility or income) from the rich to the poor is desirable, as long as it does not bring the rich to a poorer situation than the poor. Formally, let u = ( u 1 , u 2 , … , u n ) {\displaystyle u=(u_{1},u_{2},\dots ,u_{n})} and u ′ = ( u 1 ′ , u 2 ′ , … , u n ′ ) {\displaystyle u'=(u'_{1},u'_{2},\dots ,u'_{n})} be two utility profiles. Suppose that at the first profile:
u 1 < u 2 {\displaystyle u_{1}<u_{2}}
and at the second profile:
u 1 ′ + u 2 ′ = u 1 + u 2 {\displaystyle u_{1}'+u_{2}'=u_{1}+u_{2}} and
u 3 ′ = u 3 , u 4 ′ = u 4 , … , u n ′ = u n {\displaystyle u'_{3}=u_{3},u'_{4}=u_{4},\dots ,u'_{n}=u_{n}} and
u 1 < u 1 ′ < u 2 {\displaystyle u_{1}<u_{1}'<u_{2}} and u 1 < u 2 ′ < u 2 {\displaystyle u_{1}<u_{2}'<u_{2}}
(so u 1 < u 1 ′ < u 2 ′ < u 2 {\displaystyle u_{1}<u_{1}'<u_{2}'<u_{2}} or u 1 < u 1 ′ = u 2 ′ < u 2 {\displaystyle u_{1}<u_{1}'=u_{2}'<u_{2}} or u 1 < u 2 ′ < u 1 ′ < u 2 {\displaystyle u_{1}<u_{2}'<u_{1}'<u_{2}} ) Then, the social-welfare ordering should weakly prefer the second profile u ′ {\displaystyle u'} , since it reduces the inequality between agent 1 and agent 2 (and may switch which is richer), while keeping unchanged the sum of their utilities and the utilities of all other agents. PDP was suggested by Arthur Cecil Pigou and developed by Hugh Dalton (see, e.g., Amartya Sen, 1973 or Herve Moulin, 2004).
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