The Pigou–Dalton principle (PDP) is a principle in

welfare economics Welfare economics is a branch of economics that uses microeconomic techniques to evaluate well-being (welfare) at the aggregate (economy-wide) level. Attempting to apply the principles of welfare economics gives rise to the field of public econ ...

, particularly in

cardinal welfarism In welfare economics, a social welfare function is a function that ranks social states (alternative complete descriptions of the society) as less desirable, more desirable, or indifferent for every possible pair of social states. Inputs of the fu ...

. Named after

Arthur Cecil Pigou Arthur Cecil Pigou (; 18 November 1877 – 7 March 1959) was an English economist. As a teacher and builder of the School of Economics at the University of Cambridge, he trained and influenced many Cambridge economists who went on to take chair ...

and

Hugh Dalton Edward Hugh John Neale Dalton, Baron Dalton, (16 August 1887 – 13 February 1962) was a British Labour Party economist and politician who served as Chancellor of the Exchequer from 1945 to 1947. He shaped Labour Party foreign policy in the 1 ...

, it is a condition on

social welfare function In welfare economics, a social welfare function is a function that ranks social states (alternative complete descriptions of the society) as less desirable, more desirable, or indifferent for every possible pair of social states. Inputs of the fu ...

s. It says that, all other things being equal, a

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,\dots,u_n)

and

u'=(u'_1,u'_2,\dots,u'_n)

be two utility profiles. Suppose that at the first profile: :

u_1 and at the second profile:
: u_1'+u_2' = u_1+u_2 and
: u'_3=u_3, u'_4=u_4,\dots,u'_n=u_n and
: u_1 < u_1' < u_2 and u_1 < u_2' < u_2 ::(so u_1 < u_1' < u_2' < u_2 or u_1 < u_1' = u_2' < u_2 or u_1 < u_2' < u_1' < u_2)
Then, the social-welfare ordering should weakly prefer the second profile 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

and developed by

Dalton, H. ''The measurement of the inequality of incomes'', Economic Journal, 30 (1920), pp. 348–461. (see, e.g.,

Amartya Sen Amartya Kumar Sen (; born 3 November 1933) is an Indian economist and philosopher, who since 1972 has taught and worked in the United Kingdom and the United States. Sen has made contributions to welfare economics, social choice theory, econom ...

, 1973 or Herve Moulin, 2004).

Examples

* The egalitarian function:

W(u) = \min(u_1,u_2)

satisfies PDP in a strong sense: when utility is transferred from the rich to the poor, the value of

W

strictly increases. * The

utilitarian In ethical philosophy, utilitarianism is a family of normative ethical theories that prescribe actions that maximize happiness and well-being for all affected individuals. Although different varieties of utilitarianism admit different charac ...

function:

W(u) = u_1 + u_2

satisfies PDP in a weak sense: when utility is transferred from the rich to the poor, the value of

W

does not increase, but also does not decrease. * The function

W(u) = u_1^2 + u_2^2

violates PDP: when utility is transferred from the rich to the poor, the value of

W

strictly decreases. * The

Atkinson Index The Atkinson index (also known as the Atkinson measure or Atkinson inequality measure) is a measure of income inequality developed by British economist Anthony Barnes Atkinson. The measure is useful in determining which end of the distribution cont ...

and the related

generalized entropy index The generalized entropy index has been proposed as a measure of income inequality in a population. It is derived from information theory as a measure of redundancy in data. In information theory a measure of redundancy can be interpreted as no ...

satisfy the principle - any transfer from someone relatively poorer to someone relatively richer will increase inequality as measured by the index. For the Atkinson index, this holds when the inequality aversion parameter is nonnegative, which is the defining case.

References

{{DEFAULTSORT:Pigou-Dalton principle Welfare economics