BENTHAM’S CALCULUS
&
UTILITARIAN
THOUGHT
"Greatest good for the greatest number."
* 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% 
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 
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 
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.
“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)
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?
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.
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)