BENTHAM’S CALCULUS

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UTILITARIAN THOUGHT

"Greatest good for the greatest number."

The Pied Piper of Utilitarianism

Jeremy Bentham (1748 - 1832)

English jurist and reformer, Bentham attacked the conservative jurist Sir William Blackstone in his first book in his 1776 book, Fragment on Government.

He professed the belief that an action is moral to the degree that it is useful; hence the idea of utilitarianism that the utility of an action is determined by the happiness it promotes or the widespread benefits that come to people.

That is an action is understood in terms of how beneficial, or salutary the outcome is, or the pleasurable affect it has on the widest array or most number of people.

Bentham envisioned a system of decision making in civil affairs to reduce the power of prejudice, ignorance, passion, prestige and favoritism. Decisions should be made based on assigning values to different outcomes on a scale reflecting the utility, or beneficial properties of competing policies.

Problems with utilitarian thought:

• The product of measuring the amount of public happiness is not always the full reflective measure of the costs incurred by the process of measuring, or the impacts of policies we are trying to measure.

• Number is not the same as quantity. (Bateson)
  
  
• Ascribing values determines outcomes. (Hume)

• Calculations are misleading because widespread but not so intense misery and immense contentedness among a sizeable group could, according to strict utilitarianism, equally promote the greatest good.

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  Quality vs quantity | fractions | Utils | Sequences | Critics | Problems

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These are not synonymous:

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Percentages are actually decimals; that are fractions of a larger whole.

Percentage, Decimal, Fraction Tables

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What is a number?

Compare how the following sequences differ:

Sequences

Arithmetic progression; the increase here is by increments of one.

The increase occurs very slowly. Thomas Malthus argued the rate at which a food supply increases over time is an arithmetic progression.

 

Geometric (or exponential) progression; the increase here is obtained by doubling the number each time.

The increase occurs most rapidly and was attributed by Thomas Malthus to the rate at which population increases, thereby surpassing the food supply

 

 

Fibonacci progression; increases are obtained each time by adding the previous amount to get the subsequent sum.

The increase is not as fast, at first, but it nonetheless increases faster than an arithmetic progression and is characteristic of doubling times with respect to interest, natural growth rates for individuals, or entire populations.

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“It is virtually impossible to calculate the total distribution of happiness across a mixed group.” (Peter Marshall, 1996, 436 - 437)

Does scale affect values (defining what is good)? (Hardin pp. 128 - 137)

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Defining terms in utilitarian thought:

“the good ”, what does that mean?

While some have agrgued that this means happiness, or the reduction of pain, or great pleasure, better performance, and the best situation; should it imply optimal instead of most?

Quantities are a problem when assigning proper values to goods with varying capacities to promote pleasure that reflect the differences between necessities and luxuries; not just competing costs and varying benefits.

necessities versus luxuries

• necessities -- answers what must a person have -- needs that cannot be denied.

• luxuries -- answers what is surplus, expendable or not required to exist?

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Calculating the affect of scale:

"From Plato’s time to the present, professional philosophers have often tried to solve problems of 'the good ' without considering how potentialities, behavior and value are affected by scale.”

Galileo gave sound mathematical reasons why a mouse simply cannot be as big as an elephant. The weight of an animal goes up as the cube of its linear dimensions, whereas the strength of its supporting limbs goes up only as the square. From this simple mathematical difference profound practical conclusions follow. (Hardin, 1985, p. 128)

• ”The scale of things determines what is functionally best.”

• “A politico economic system that works well with small numbers may fail utterly with large.” (Ibid. p. 130)

If Hardin is correct, then the greatest good (Bentham's term) depends to a discernible extent on scale, that is the dimensions of a person, place, thing or problem.

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Calculating the assignment of value:

A radically egalitarian materialism

In his ‘felicific calculus’, Bentham insisted on the egalitarian principle of ‘Each to count for one and none for more than one’. Godwin also introduced the principle of impartiality as a beacon in dealing with competing interests in his utilitarian ethics.” (Marshal, 1996, p. 437.)

”When the hedonistic principle of utility is applied in practice, it is difficult to decide not only between competing claims of human communities, but also between different species. Does the happiness of foxes trump the happiness of sheep farmers?” (Marshal, 1996, p. 436.)

John Kenneth Galbraith on the 1929 Economic Depression

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Calculating for two variables at once:

It is not mathematically possible to maximize for two or more variables at the same time. This was clearly stated by Von Neumann and Morgenstern, but the principle is implicit in the theory of partial differential equations, dating back at least to D’Alembert (1717 - 1783).

Bentham’s goal is impossible. . . . unobtainable. (Hardin, Tragedy, 1968)

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