Pigou-Dalton principle

In social choice theory and economic policy , the Pigou-Dalton principle (also: transfer principle or transfer principle according to (Pigou-) Dalton ) describes a property of social prosperity measures , according to which an income transfer must increase social welfare whenever it moves from a richer to a poorer one Person takes place and as long as it does not change who is the richer and who is the poorer.

origin

The name of the requirement goes back to Arthur Pigou and Hugh Dalton . Dalton postulated the principle in an article in the Economic Journal in 1920, referring to Pigou, who had already pointed out a similar connection in the two-person case in Wealth and Welfare in 1912 :

“My second proposition can be stated in several ways. The most abstract form of it affirms that economic welfare is likely to be augmented by anything that, leaving other things unaltered, renders the distribution of the national dividend less unequal. If we assume all members of the community to be of similar temperament, and if these members are only two in number, it is easily shown that any transference from the richer to the poorer of the two, since it enables more intense wants to be satisfied at the expense of less intense wants, must increase the aggregate sum of satisfaction. "

presentation

Consider a society with n members. The endowment or prosperity of these members is given by a vector , where i,, stands for the endowment (prosperity) of the person . What exactly is to be understood by “equipment” has not yet been determined - in the simplest case, for example, it concerns the assets of the respective person. ${\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})}$ ${\displaystyle x_{i}}$ ${\displaystyle 1\leq i\leq n}$

(Pigou-Dalton transfer :) Consider any two individuals j and k with respective equipment and respectively . Be now . Then a transfer of the amount of equipment from k (the "richer") to j (the "poorer"), through which the equipment of the other members of society does not change and after which at least still applies, is called Pigou-Dalton transfer. ${\displaystyle x_{j}}$ ${\displaystyle x_{k}}$ ${\displaystyle x_{j}<x_{k}}$ ${\displaystyle \delta }$ ${\displaystyle x_{j}+\delta \leq x_{k}-\delta }$

First then, define a social welfare measure , . ${\displaystyle W(\mathbf {x} )}$ ${\displaystyle W:\mathbb {R} ^{n}\rightarrow \mathbb {R} }$

(Pigou-Dalton principle :) Let be and two equipment vectors, whereby from a Pigou-Dalton transfer resulted. Then the welfare measure satisfies the Pigou-Dalton principle, if . ${\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})}$ ${\displaystyle \mathbf {y} =(y_{1},\ldots ,y_{n})}$ ${\displaystyle \mathbf {y} }$ ${\displaystyle \mathbf {x} }$ ${\displaystyle W}$ ${\displaystyle W(\mathbf {y} )>W(\mathbf {x} )}$

Connection to individual welfare

If one assumes, in simplified form, that - that is, social welfare can be represented as the sum of the (sometimes also social) benefits from the prosperity of each individual - then the following two statements are equivalent: ${\displaystyle W(x_{1},\ldots ,x_{n})=u(x_{1})+u(x_{2})+\ldots +u(x_{n})}$

1. ${\displaystyle u}$is strictly concave on an interval . ${\displaystyle X\subset \mathbb {R} }$
2. ${\displaystyle W}$fulfills the Pigou-Dalton principle . ${\displaystyle X^{n}}$

literature

• Kristof Bosmans, Luc Lauwers and Erwin Ooghe: A consistent multidimensional Pigou-Dalton transfer principle. In: Journal of Economic Theory. 144, No. 3, 2009, pp. 1358–1371, doi : 10.1016 / j.jet.2009.01.003 .
• Hugh Dalton : The Measurement of the Inequality of Incomes. In: The Economic Journal. 30, No. 119, 1920, pp. 348-361 ( JSTOR 2223525 ).
• Peter C. Fishburn: Transfer Principles in Income Distribution. In: Journal of Public Economics. 25, 1984, pp. 323-328, doi : 10.1016 / 0047-2727 (84) 90059-8 .
• Marc Fleurbaey: Social welfare, priority to the worst-off and the dimensions of individual well-being. In: Francesco Farina and Ernesto Savaglio (eds.): Inequality and Economic Integration. Routledge, London 2006, ISBN 978-0-415-34211-7 , pp. 225-268.
• Hervé Moulin: Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge 1991, ISBN 978-0-521-42458-5 .
• Arthur C. Pigou : Wealth and Welfare. Macmillan, London 1912 (also online: http://archive.org/details/cu31924032613386 ).
• Johna Weymark: The normative approach to the measurement of multidimensional inequality. In: Francesco Farina and Ernesto Savaglio (eds.): Inequality and Economic Integration. Routledge, London 2006, ISBN 978-0-415-34211-7 , pp. 303-328.

Individual evidence

1. ^ Dalton 1920, p. 351.
2. ↑ Pigou 1912, p. 24 f., Internet http://archive.org/stream/cu31924032613386#page/n61/mode/2up , accessed on May 3, 2012.
3. ↑ Cf. Fleurbaey 2006, p. 226 f.
4. ↑ Cf. Fleurbaey 2006, p. 227.
5. ↑ Cf., also for evidence, Fleurbaey 2006, p. 227.