BENTHAM’S CALCULUS

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UTILITARIAN THOUGHT

"Greatest good for the greatest number."

Quality versus quantity of happiness | defined | scale | equality | fractions | Utils | Sequences | Critics | Problems

* good is envisioned as pleasure (diminished pain) or happiness.

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)

These are not synonymous:

 Quality Quantity ~~~~~~~~~~~~~ ~~~~~~~~~~~~~ 1 to 10 .01 to 99.9%

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

Percentage, Decimal, Fraction Tables

 Name one one tenth twenty thirty forty half sixty seventy eighty ninety all Decimal .01 .1 .20 .30 .40 .50 .60 .70 .80 .90 1.0 % 1 10 20 30 40 50 60 70 80 90 100 fraction 1/100th 1/10 1/5 <1/3 2/5 1/2 3/5 > 2/3 4/5 9/10 1

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Numbers

Utilitarians assign units to different desired outcomes based on their utility, or usefulness, and the quantity assigned is called autil. The value of something is greater if it is more useful than something else.

This util refers to the benefits anticipated from the desirability based on the amount of pleasure the outcome is expected to generate. The number of people benefited is then multiplied by the assigned value represented by the util.

What is a number?

 units 10 20 30 40 50 60 70 80 90 100 1 10 20 30 40 50 60 70 80 90 100 2 20 40 60 80 100 120 140 160 180 200 3 30 60 90 120 150 180 210 240 270 300 4 40 80 120 160 200 240 280 320 360 400 5 50 100 150 200 250 300 350 400 450 500 6 60 120 180 240 300 360 420 480 540 600 7 70 140 210 280 350 420 490 560 630 700 8 80 160 240 320 400 480 560 640 720 800 9 90 180 270 360 450 540 630 720 810 900 10 100 200 300 400 500 600 700 800 900 1000

Compare how the following sequences differ:

 1 2 3 4 5 6 7 8 9 10 ? 1 2 4 8 16 32 64 128 256 512 ? 1 1 2 3 5 8 13 21 34 55 ?

Quality versus quantity of happiness | defined | scale | equality | fractions | Utils | Sequences | Critics | Problems

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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Quality versus quantity of happiness | defined | scale | equality | fractions | Utils | Sequences | Critics | Problems

“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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Quality versus quantity of happiness | defined | scale | equality | fractions | Utils | Sequences | Critics | Problems

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)

 linearity 1 2 3 4 5 6 units strength 1 4 9 16 25 36 squared mass 1 8 27 64 125 216 cubed

• ”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:

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

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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