BENTHAM’S CALCULUS

&
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:

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.

pie chart

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? atomic 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


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

 


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

 

cubecube

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:

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


 

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)


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

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