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| In [[welfare economics]], a '''social welfare function''' is a [[function (mathematics)|function]] that ranks social states (alternative complete descriptions of the society) as less desirable, more desirable, or [[indifference curve|indifferent]] for every possible pair of social states. Inputs of the function include any variables considered to affect the [[economic welfare]] of a society.<ref>[[Amartya K. Sen]], 1970 [1984], ''Collective Choice and Social Welfare'', ch. 3, "Collective Rationality." p. 33, and ch. 3*, "Social Welfare Functions." [http://www.citeulike.org/user/rlai/article/681900 Description.]</ref> In using welfare measures of persons in the society as inputs, the social welfare function is [[methodological individualism|individualistic]] in form. One use of a social welfare function is to [[Mathematical problem|represent]] prospective patterns of collective choice as to alternative social states.
| | Those that are enduring hemorrhoids all agree that it is very painful. For those individuals even sitting is especially big trouble. This healthy condition will affect on a profession, method of living, even the social and personal life can quite agonizing, if not fix this issue. Curing it happens to be no issue today, since there are plenty of hemorrhoid treatments accessible to take care of it for we. If you don't have the means to take operation to quickly do away with piles or expensive painkillers to create the pain go away, then here are several natural techniques for this several all-natural hemorrhoid treatments you need to try.<br><br>Then that a hemorrhoids aren't getting worse, it's time to use [http://hemorrhoidtreatmentfix.com/prolapsed-hemorrhoid-treatment prolapsed hemorrhoid treatment] that can relieve itching plus pain. Soaking in a a sitz shower for about fifteen minutes at a time is one method to find relief. You are able to do this numerous occasions a day. You are able to equally heat a damp towel plus apply it to the hemorrhoid area. Ice for ten minutes, followed by a warm compress for an equal or slightly longer length of time is another way to relieve your pain and itching.<br><br>As a former hemorrhoid sufferer, I could tell we there are several all-natural hemorrhoid treatments that you are able to do on a daily life that can assist we or completely cure you when symptom is less serious. Try the following natural techniques before we search for alterantive treatment.<br><br>Venapro is really good considering there is not any need for awkward moments in the toilet wherein you need to place cream on the anus. Just spritz it and you're completed. In because short as 3 days, positive effects are felt.<br><br>Step 7 - Take A Sitz Bath. Fill the bath with approximately 8 or 9 inches of warm water, climb inside and bathe for 10 to 15 minutes. You are able to repeat this process three times a day. One cup of Epsom salts is added but when you are a diabetic or suffer from any different chronic disease, check with your general practitioner at the outset.<br><br>Ice is regarded as the simplest however the most efficient hemorrhoid treatments we can utilize to minimize swelling, inflammation, bleeding plus pain. Wrap it in chipped form in a piece of cheese fabric plus apply it onto the hemorrhoid itself.<br><br>The persons writing critiques from personal experience provide treatments like Venapro, Hem Relief and Avatrol low success ratings. The system plus products that receive the highest reviews is one called H magic by Holly Hayden. It appears to be a entire system which we sign up online for. After we pay a cash we get all the info about what treatments plus life-style changes function on your computer. It has consistently wise customer reports along with a 60 day cash back guarantee. Folks are composing about results in 2 to 10 days plus a 90% cure rate. It uses natural plus minimally invasive treatments and treatments thus it is actually worth striving. |
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| The social welfare function is analogous to the [[consumer theory]] of [[indifference curve|indifference-curve]]/[[budget constraint]] equilibrium for an individual, except that the social welfare function is a mapping of individual preferences or judgments of everyone in the society as to collective choices, which apply to all, whatever individual preferences are for (variable) constraints on factors of production. One point of a social welfare function is to determine how close the analogy is to an ordinal [[utility function]] for an individual with at least minimal restrictions suggested by [[welfare economics]], including constraints on the amount of [[factors of production]].
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| There are two major distinct but related types of social welfare functions. A Bergson–Samuelson social welfare function considers welfare for a ''given set'' of individual preferences or welfare rankings. An Arrow social welfare function considers welfare across ''different possible sets'' of individual preferences or welfare rankings and seemingly reasonable axioms that constrain the function.<ref>Prasanta K. Pattanaik, 2008. "social welfare function," ''[[The New Palgrave Dictionary of Economics]]'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_S000172 Abstract.]</ref>
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| ==Bergson–Samuelson social welfare function==<!-- This section is linked from [[Paul Samuelson]] -->
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| In a 1938 article, [[Abram Bergson]] introduced the ''social welfare function''. The object was "to state in precise form the value judgments required for the derivation of the conditions of maximum economic welfare" set out by earlier writers, including [[Alfred Marshall|Marshall]] and [[A.C. Pigou|Pigou]], [[Vilfredo Pareto|Pareto]] and [[Enrico Barone|Barone]], and [[Abba Lerner|Lerner]]. The function was real-valued and [[differentiable]]. It was specified to describe the society as a whole. Arguments of the function included the quantities of different commodities produced and consumed and of [[factors of production|resources]] used in producing different commodities, including labor.
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| Necessary general conditions are that at the maximum value of the function:
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| * The marginal "dollar's worth" of welfare is equal for each individual and for each commodity
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| * The marginal "diswelfare" of each "dollar's worth" of labor is equal for each commodity produced of each labor supplier
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| * The marginal "dollar" cost of each unit of resources is equal to the marginal value productivity for each commodity.
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| Bergson showed how [[welfare economics]] could describe a standard of economic efficiency despite dispensing with ''interpersonally-comparable'' [[cardinal utility]], the hypothesizaton of which may merely conceal value judgments, and purely subjective ones at that.
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| {| style="border:1px solid #999; text-align:leftcenter; margin: auto;" cellspacing="20"
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| | Earlier [[Welfare economics|neoclassical welfare theory]], heir to the classical [[utilitarianism]] of [[Jeremy Bentham|Bentham]], had not infrequently treated the [[Law of diminishing marginal utility|Law of Diminishing Marginal Utility]] as implying interpersonally comparable utility, a necessary condition to achieve the goal of maximizing total utility of the society. Irrespective of such comparability, income or wealth ''is'' measurable, and it was commonly inferred that redistributing income from a rich person to a poor person tends to increase total utility (however measured) in the society.* But Lionel Robbins ([[An Essay on the Nature and Significance of Economic Science|1935]], ch. VI) argued that how or how much utilities, as mental events, would have changed relative to each other is not measurable by any empirical test. Nor are they inferable from the shapes of standard indifference curves. Hence, the advantage of being able to dispense with interpersonal comparability of utility without abstaining from welfare theory.
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| * A practical qualification to this was any reduction in output from the transfer.
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| |}
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| Auxiliary specifications enable comparison of different social states by each member of society in preference satisfaction. These help define ''[[Pareto efficiency]]'', which holds if all alternatives have been exhausted to put at least one person in a more preferred position with no one put in a less preferred position. Bergson described an "economic welfare increase" (later called a ''Pareto improvement'') as at least one individual moving to a more preferred position with everyone else indifferent. The social welfare function could then be specified in a ''substantively'' individualistic sense to derive Pareto efficiency (optimality). [[Paul Samuelson]] (2004, p. 26) notes that Bergson's function "could derive Pareto optimality conditions as ''necessary'' but not sufficient for defining interpersonal normative equity." Still, Pareto efficiency could also characterize ''one'' dimension of a particular social welfare function with distribution of commodities among individuals characterizing ''another'' dimension. As Bergson noted, a welfare improvement from the social welfare function could come from the "position of some individuals" improving at the expense of others. That social welfare function could then be described as characterizing an equity dimension.
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| Samuelson ([[Foundations of Economic Analysis|1947]], p. 221) himself stressed the flexibility of the social welfare function to characterize ''any'' one ethical belief, Pareto-bound or not, consistent with:
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| * a complete and transitive ranking (an ethically "better", "worse", or "indifferent" ranking) of all social alternatives and
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| * one set out of an infinity of welfare indices and cardinal indicators to characterize the belief.
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| He also presented a lucid verbal and mathematical exposition of the social welfare function (1947, pp. 219–49) with minimal use of Lagrangean multipliers and without the difficult notation of differentials used by Bergson throughout. As Samuelson (1983, p. xxii) notes, Bergson clarified how production and consumption efficiency conditions are distinct from the interpersonal ethical values of the social welfare function.
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| Samuelson further sharpened that distinction by specifying the ''Welfare function'' and the ''Possibility function'' (1947, pp. 243–49). Each has as [[Function (mathematics)#The vocabulary of functions|arguments]] the set of utility functions for everyone in the society. Each can (and commonly does) incorporate Pareto efficiency. The Possibility function also depends on technology and resource restraints. It is written in implicit form, reflecting the ''feasible'' locus of utility combinations imposed by the restraints and allowed by Pareto efficiency. At a given point on the Possibility function, if the utility of all but one person is determined, the remaining person's utility is determined. The Welfare function ranks different hypothetical ''sets'' of utility for everyone in the society from ethically lowest on up (with ties permitted), that is, it makes interpersonal comparisons of utility. Welfare maximization then consists of maximizing the Welfare function subject to the Possibility function as a constraint. The same welfare maximization conditions emerge as in Bergson's analysis.
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| {| style="border:1px solid #999; text-align:leftcenter; margin: auto;" cellspacing="20"
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| | For a two-person society, there is a graphical depiction of such welfare maximization at the first figure of [http://cepa.newschool.edu/het/essays/paretian/paretosocial.htm#swf Bergson–Samuelson social welfare functions]. Relative to [[consumer theory#Indifference curves and budget constraints|consumer theory]] for an ''individual'' as to two commodities consumed, there are the following parallels:
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| * The respective hypothetical utilities of the two persons in two-dimensional utility space is analogous to respective quantities of commodities for the two-dimensional commodity space of the indifference-curve ''surface''
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| * The Welfare function is analogous to the indifference-curve ''map''
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| * The Possibility function is analogous to the budget constraint
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| * Two-person welfare maximization at the tangency of the highest Welfare function curve on the Possibility function is analogous to tangency of the highest indifference curve on the budget constraint.
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| |}
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| ==Arrow social welfare function (constitution)==
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| [[Kenneth Arrow]] ([[Social Choice and Individual Values|1963]]) generalizes the analysis. Along earlier lines, his version of a social welfare function, also called a 'constitution', maps a set of individual orderings ([[ordinal utility function]]s) for everyone in the society to a social ordering, a rule for ranking alternative social states (say passing an enforceable law or not, [[ceteris paribus]]). Arrow finds that nothing of behavioral significance is lost by dropping the requirement of social orderings that are ''real-valued'' (and thus cardinal) in favor of orderings, which are merely ''complete'' and ''transitive'', such as a standard [[consumer theory|indifference-curve map]]. The earlier analysis mapped any set of individual orderings to ''one'' social ordering, whatever it was. This social ordering selected the top-ranked ''feasible'' alternative from the economic environment as to [[production possibility frontier|resource constraints]]. Arrow proposed to examine mapping different sets of individual orderings to possibly different social orderings. Here the social ordering would depend on the set of individual orderings, rather than being ''imposed'' (invariant to them). Stunningly (relative to a course of theory from [[Invisible hand|Adam Smith]] and [[Jeremy Bentham]] on), Arrow proved the ''[[Arrow's impossibility theorem|General Possibility Theorem]]'' that it is impossible to have a social welfare function that satisfies a certain set of "apparently reasonable" conditions.
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| ==Cardinal social welfare functions==
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| In the above contexts, a social welfare function provides a '''societal preference''' based on only individual [[utility function]]s, whereas in others it also outputs cardinal measures of social welfare not aggregated from individual utility functions. Examples of such measures can be [[life expectancy]] and per capita income for the society. For the purposes of this article, income is adopted as the measurement of utility in this section.
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| The form of the social welfare function is intended to express a statement of objectives of a society. Consider the Utilitarian or [[Benthamite]] social welfare function which measures social welfare as the total or sum of individual incomes:
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| :<math>W = \sum_{i=1}^n Y_i</math>
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| where <math>W</math> is social welfare and <math>Y_i</math> is the income of individual <math>i</math> among <math>n</math> individuals in society. In this case, maximizing the social welfare means maximizing the total income of the people in the society, without regard to how incomes are distributed in society. Alternatively, society's welfare can also be measured under this function by taking the average of individual incomes:
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| :<math>W = \frac{1}{n}\sum_{i=1}^n Y_i</math>
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| In contrast, the Max-Min or Rawlsian social welfare function (based on the philosophical work of [[John Rawls]]) measures the social welfare of society on the basis of the welfare of the least well-off individual member of society:
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| :<math>W = \min(Y_1, Y_2, \cdots, Y_n)</math>
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| Here maximizing societal welfare would mean maximizing the income of the poorest person in society without regard for the income of other individuals.
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| These two social welfare functions express very different views about how a society would need to be organised in order to maximize welfare, with the first emphasizing total incomes and the second emphasizing the needs of the worst-off. The max-min welfare function can be seen as reflecting an extreme form of [[uncertainty aversion]] on the part of society as a whole, since it is concerned only with the worst conditions that a member of society could face.
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| [[Amartya Sen]] proposed a welfare function in 1973:
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| :<math>W_\mathrm{Gini} = \overline{\text{Income}} \cdot \left( 1-G \right)</math>
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| The average per capita income of a measured group (e.g. nation) is multiplied with <math>(1-G)</math> where <math>G</math> is the [[Gini index]], a relative inequality measure. James E. Foster (1996) proposed to use one of [[Anthony Barnes Atkinson|Atkinson]]'s Indexes, which is an entropy measure. Due to the relation between Atkinsons entropy measure and the [[Theil index]], Foster's welfare function also can be computed directly using the Theil-L Index. | |
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| :<math>W_\mathrm{Theil-L} = \overline{\text{Income}} \cdot \mathrm{e}^{-T_L}</math>
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| The value yielded by this function has a concrete meaning. There are several possible incomes which could be earned by a ''person'', who randomly is selected from a population with an unequal distribution of incomes. This welfare function marks the income, which a randomly selected person is most likely to have. Similar to the [[median]], this income will be smaller than the average per capita income. | |
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| :<math>W^{-1}_\mathrm{Theil-T} = \overline{\text{Income}} \cdot \mathrm{e}^{T_T}</math>
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| Here the Theil-T index is applied. The inverse value yielded by this function has a concrete meaning as well. There are several possible incomes to which an ''Euro'' may belong, which is randomly picked from the sum of all unequally distributed incomes. This welfare function marks the income, which a randomly selected Euro most likely belongs to. The inverse value of that function will be larger than the average per capita income.
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| The [[Theil index|article on the Theil index]] provides further information about how this index is used in order to compute welfare functions.
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| ==Notes==
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| {{Reflist|1}}
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| == See also ==
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| * [[Aggregation problem]]
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| * [[Arrow's impossibility theorem]]
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| * [[Community indifference curve]]
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| * [[Distribution (economics)]]
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| * [[Economic welfare]]
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| * [[Extended sympathy]]
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| * [[Justice (economics)]]
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| * [[Liberal paradox]]
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| * [[Social choice theory]]
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| * [[Welfare economics]]
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| * [[Production-possibility frontier]]
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| == References ==
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| *[[Kenneth Arrow|Kenneth J. Arrow]], 1951, 2nd ed., 1963, ''[[Social Choice and Individual Values]]'' ISBN 0-300-01364-7
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| * [[Abram Bergson]] (Burk),"A Reformulation of Certain Aspects of Welfare Economics," ''Quarterly Journal of Economics'', 52(2), February 1938, 310-34
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| * [http://cepa.newschool.edu/het/essays/paretian/paretosocial.htm#swf Bergson–Samuelson social welfare functions] in Paretian welfare economics from the New School.
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| * James E. Foster and [[Amartya Sen]], 1996, ''On Economic Inequality'', expanded edition with annexe, ISBN 0-19-828193-5).
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| * [[John C. Harsanyi]], 1987, “interpersonal utility comparisons," ''[[The New Palgrave: A Dictionary of Economics]]'', v. 2, 955-58
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| * Prasanta K. Pattanaik (2008). "social welfare function." ''[[The New Palgrave Dictionary of Economics]]'', 2nd Edition [http://www.dictionaryofeconomics.com/article?id=pde2008_S000172&q=social%20welfare&topicid=&result_number=1 Abstract.]
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| * [[Jan de Van Graaff]], 1957, "Theoretical Welfare Economics", 1957, Cambridge, UK: Cambridge University Press.
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| * [[Lionel Robbins]], 1935, 2nd ed.. ''[[An Essay on the Nature and Significance of Economic Science]]'', ch. VI
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| * ____, 1938, "Interpersonal Comparisons of Utility: A Comment," ''Economic Journal'', 43(4), 635-41
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| * [[Paul A. Samuelson]], 1947, Enlarged ed. 1983, ''[[Foundations of Economic Analysis]]'', pp. xxi-xxiv & ch. VIII, "Welfare Economics," ISBN 0-674-31301-1
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| * _____, 1977. "Reaffirming the Existence of 'Reasonable' Bergson–Samuelson Social Welfare Functions," ''Economica'', N.S., 44(173), p [http://www.jstor.org/pss/2553553 p. 81]-88. Reprinted in (1986) ''The Collected Scientific Papers of Paul A. Samuelson'', pp. [http://books.google.com/books?id=UKeJEc46R9AC&printsec=fnd&pg=PA47=gbs_atb#v=onepage&q&f=false 47-54.]
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| * _____, 1981. "Bergsonian Welfare Economics", in S. Rosefielde (ed.), ''Economic Welfare and the Economics of Soviet Socialism: Essays in Honor of Abram Bergson'', [[Cambridge University Press]], Cambridge, pp. 223–66. Reprinted in (1986) ''The Collected Scientific Papers of Paul A. Samuelson'', pp. 3 [http://books.google.com/books?id=UKeJEc46R9AC&printsec=fnd&pg=PA225=gbs_atb#v=onepage&q&f=false -46.]
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| * [[Amartya Sen|Sen, Amartya K.]] (1963). "Distribution, Transitivity and Little's Welfare Criteria," ''Economic Journal'', 73(292), [http://links.jstor.org/sici?sici=0013-0133%28196312%2973%3A292%3C771%3ADTALWC%3E2.0.CO%3B2-1&size=LARGE&origin=JSTOR-enlargePage p. 771]-78.
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| * _____, 1970 [1984], ''Collective Choice and Social Welfare'' [http://www.citeulike.org/user/rlai/article/681900 (description)], ch. 3, "Collective Rationality." ISBN 0-444-85127-5
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| * _____ (1982). ''Choice, Welfare and Measurement'', MIT Press. [http://mitpress.mit.edu/catalog/item/default.asp?tid=6747&ttype=2 Description] and scroll to chapter-preview [http://books.google.com/books?id=u8GPYeT1qAUC&printsec=frontcover&dq=false links.]
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| * [[Kotaro Suzumura]] (1980). "On Distributional Value Judgments and Piecemeal Welfare Criteria," ''Economica'', 47(186), p [http://links.jstor.org/sici?sici=0013-0427%28198005%292%3A47%3A186%3C125%3AODVJAP%3E2.0.CO%3B2-I&size=LARGE&origin=JSTOR-enlargePage p. 125]-39.
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| * _____, 1987, “social welfare function," ''The New Palgrave: A Dictionary of Economics'', v. 4, 418-20
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| [[Category:Welfare economics]]
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| [[Category:Social choice theory]]
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Then that a hemorrhoids aren't getting worse, it's time to use prolapsed hemorrhoid treatment that can relieve itching plus pain. Soaking in a a sitz shower for about fifteen minutes at a time is one method to find relief. You are able to do this numerous occasions a day. You are able to equally heat a damp towel plus apply it to the hemorrhoid area. Ice for ten minutes, followed by a warm compress for an equal or slightly longer length of time is another way to relieve your pain and itching.
As a former hemorrhoid sufferer, I could tell we there are several all-natural hemorrhoid treatments that you are able to do on a daily life that can assist we or completely cure you when symptom is less serious. Try the following natural techniques before we search for alterantive treatment.
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Step 7 - Take A Sitz Bath. Fill the bath with approximately 8 or 9 inches of warm water, climb inside and bathe for 10 to 15 minutes. You are able to repeat this process three times a day. One cup of Epsom salts is added but when you are a diabetic or suffer from any different chronic disease, check with your general practitioner at the outset.
Ice is regarded as the simplest however the most efficient hemorrhoid treatments we can utilize to minimize swelling, inflammation, bleeding plus pain. Wrap it in chipped form in a piece of cheese fabric plus apply it onto the hemorrhoid itself.
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