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Philosophy 302: Ethics
The Hedonistic Calculus
Abstract: A modified hedonistic
calculus is sketched along the lines first proposed by Bentham and
Mill. The major problem encountered is the quantification of
pleasure.
I. Bentham's method of estimating pleasures and pains can be applied to egoistic hedonism.
With the addition of the utilitarian factor "extent" of
pleasure, the hedonism can be extended to any number of persons.
- Utilitarianism is the moral theory that an action is morally right if and
only if it is productive of the most utility (happiness, pleasure) for the greatest
number of persons. Bentham believed the right act is the act
which of all those open to the agent, will actually or probably
produce the greatest amount of pleasure in the world-at-large.
Pleasure and pain form the basis of the standard of right and
wrong.
- Bentham lists benefit, advantage, good, or happiness as suitable
paraphrases of pleasure. The good of the community is simply the
sum of the pleasures of the individuals who compose it.
- The main problem for the calculus is calculating the interpersonal utility comparison using
cardinal
utility measurement rather than ordinal measurement.
- John Stuart Mill's addition of the quality of pleasures later ( in terms of higher and lower
pleasures) is neglected for the moment since his distinction is
patently qualitative rather than quantitative.
II. The Modified Hedonistic Calculus:
- The major factors of sensations of
pleasure and pain resulting from an action as outlined by Bentham are
summarized by these variables.
The first four variables (intensity, duration, certainty, and propinquity)
show the value of the pleasure or the pain "considered by itself."
This phrase implies Bentham did not see pleasure and pain as
polar concepts
or contraries.
The next two variables (fecundity and purity) are properties of the event or action
produced by the pleasure or pain-—not properties of the pleasure
or pain, itself..
- Intensity (I)--How intense is the pleasure or
pain?
- Duration (D)--How long does does the pleasure
of pain last?
- Certainty (C)--What is the probability that the pleasure
or pain will
occur?
- Propinquity (nearness or remoteness) (N)--How far
off in the future is the pleasure or pain?
- Fecundity (F)--What is the probability that the
pleasure will lead to other pleasures?
- Purity (P)--What is the probability that the
pain will lead to other pains?
- Extent (E)--How many persons are affected by
the pleasure?
- How are the individual factors to be quantified or measured?
- Intensity (I)--Bentham apparently thought intensity would
vary from zero to infinity, but
psychological data indicates an upper threshold of pleasure; hence, we
can use an ordinal relation from 0 to 10. Pain could be
measured in the same manner, where for both pleasure and pain,
0 represents indifference.
E.g., a contemporary approach in the psychophysics
of pain is reported by Price, et al.: "Someone who
is having pain is asked to match the perceived intensity of
the pain to a scale. This can be done in a variety of ways.
For example, one can match words or numbers to pain intensity,
or match an intensity of experimental pain to that of clinical
pain, or use more than one of these procedures. … The
clinician or investigator … provides the scaling procedures,
records the reported values, and uses a measurement method
that has been chosen to be reliable and valid." Donald C.
Price, et al. "Psychophysical Approaches to
Measurement of the Dimensions and Stages of Pain" in
Dennis C. Turk and Ronald Melzack, Handbook of Pain
Assessment (New York: Guilford Press, 2001) 54.
- Duration (D)--We can use increments of time: seconds, minutes,
and so forth. The time interval from the perceived beginning
of the pleasure until the end of the pleasure in question.
- Certainty (C)--The assigned probability can be drawn from
records of out past experience and records from persons similar to us.
What proportion of times has the pleasure followed actions of
the kind under consideration? E.g., as the Epicureans noted, many extreme pleasures
are not likely to be followed by other pleasures.
- Propinquity (nearness or remoteness) (N)--We can set up a
future indifference curve based on a "store of satisfaction" such as
money (q. v., below). Propinquity of pleasure
depends upon how long one must wait for the pleasure to
occur.
Homework Assignment: How does
the propinquity factor function in the modified hedonistic calculus?
Specifically how does an individual's propinquity indifference curve yield
an approximate weighting for a general equation of hedonism? (See below III,
D).
- Fecundity (F)--The probability that the
pleasure or pain will lead to other pleasure or pain of the same kind can be drawn from records
of our own past experience and the past experience of others like us.
- Purity (P)--Bentham writes, "Of the
value of each pain which appears to be produced by it after
the first. This constitutes the fecundity of the first pain,
and the impurity of the first pleasure"
- Extent (E)--The total amount of utility or pleasure can be
had by summing a similar calculation for every other
person who is affected by the action in question.
III. How can the general equation be set up?
- In setting up the calculus, we need to make a number of assumptions about
preferences and satisfaction in order to insure consistency. Initially, the
following assumptions or principles seem reasonable to assume when faced
with choices concerning pleasure and pain ...
- We can decide when we prefer one thing to another or whether we are
indifferent.
- Our preferences are transitive. (If I prefer activity A over
activity B, and activity B over activity C, then
I prefer activity A over activity C.)
- An egoistic hedonist prefers more pleasure to less pleasure and less
pain to more pain.
- The magnitude of a pleasure (the product of the dimension of pleasure) is the
duration multiplied by the intensity of the pleasure. (Try working out specific
examples for (1) studying, (2) sleeping late, (3) going to a small party.)
D ×
I
- The certainty is a factor of probability that the pleasure will occur.
The expected
pleasure value equals the probability multiplied by the
magnitude of the pleasure.
P × M
- How do we get a weighting for the propinquity? I.e.,
the nearness or remoteness of the pleasure? How
can we quantify our feelings about pleasures in the future? One possibility is
to set up a future indifference curve based on a "store of
satisfaction," i.e.,
money.
- Ask yourself the following questions: Would you rather
receive $1 in one
week or $10 in one month?
- If you prefer $10 in one month, then ask yourself about $9, $8, and
so forth, until you are indifferent about when you
receive the money.
- If you would prefer $1 in one week to $10 in one month, then ask
yourself about $11 in one month, $12, $13, and so forth until you are
indifferent about whether you receive the money
in one week or one month.
- Ask the similar question about whether you prefer $1 in one week
to x dollars in six months. Continue the questioning
for one year,
five years, ten years, twenty years.
- When you are finished, you should have a set of amounts of money corresponding
to the various time periods. Each item numbered below represents one student's values:
Question |
Time |
Amount
in Dollars |
1. |
one
week |
1 |
2. |
one
month |
10 |
3. |
six
months |
44 |
4. |
one
year |
110 |
5. |
five
years |
700 |
6. |
ten
years |
5,000 |
7. |
twenty
years |
12,000 |
- The student is indifferent about questions 1 through 7.
That is,
The student is unable to decide which one of these is preferred.
Obviously, your list will differ in the amounts in dollars, and you
should also be indifferent about the values you adopt.
- After you have finished a chart like the one in 2 above, plot
these values on a sheet of graph paper. (Note the nonlinear
scales.)
The graph is your proximity indifference curve. How can the
information in this graph be used in the general equation
on which we are working? Let's use the
slope of the curve at the same time period under
consideration? (Note the similarity to marginal
utility of interest rates in economics.)
The fecundity of the action for that individual could be determined by the
summation of the measure of the sensations of pleasure and pain for that individual
which follow the initial sensation of pleasure and pain.
The purity of the sensation of pleasure and pain
resulting from the action would be the summation of the measures
from the complex of individual pleasures and pains resulting from the action.
This factor might be expresses as a ratio of pleasure to
pain. Since pleasure is scaled from 0 to 10 and pain is
scaled from 0 to -10 a positive ratio would represent an aggregate
purity value in the pleasure range, and a negative ratio would
represent a purity value in the negative range. It's quite
possible that empirical measurements of pain and pleasure would
result in a logarithmic relation rather than a scalar one.
The factor of the extent is employed by repeating the above calculation for
each person affected by the original action in question. The result would be the sum
of the results of the each calculation with respect to the number of the individuals
in the community under examination.
(If we were to assume deterministic
natural laws, then there would have to be a calculation not
only for each person who is alive at the time of the action but
also for every person who will live in the future—a calculation
that could only be vaguely estimated.)
IV. What would the final equation look like? Add to and develop the following first
suggestion;
{ N [ C (I × D) ] +
Nf [ Cf ( If
×
Df ) ] }
where the subscript "f"
indicates future assignments. How is the purity factor
to be assessed?& How do we assess extent?
Recommended Sources
On this site:
"Happiness
the Greatest Good": Edited reading from Jeremy Bentham's
Principles of Morals and Legislation in
Introduction
to Ethical Studies.
"Happiness
is the Greatest Good": Tutorial notes on the Bentham
reading cited above.
Quiz on Bentham: True-False quiz
on the reading and notes on Bentham.
Recommended Readings
On the Web:
Anderson, Michael and Susan Leigh Anderson, eds.
Machine
Ethics (Cambridge: Cambridge University Press, 2011).
Papers on the nature, importance, approaches, and main issues
in computational ethics. doi:10.1017/CBO9780511978036. https://books.google.com/books?id=N4IF2p4w7uwC
(preview)
Fox, James R.
“Utilitarianism.”
Brief but useful discussion of the history of utilitarian and
hedonistic theories from the Catholic
Encyclopedia. http://www.newadvent.org/cathen/15241c.htm
Hibbard, Bill. Ethical
Artificial Intelligence 1st. ed., version 9(17 November 2015).
The definition and creation of ethical AI is discussed in terms
of its nature and problems. Utilitarian ethics for AI is discussed
in Chapter 2, ”How Should We instruct AI.” https://arxiv.org/pdf/14111.1373.pdf
Loukides, Mike. “On
Computational Ethics.” O'Reilly AI
Interesting, concise outline of some of the computational problems
involved in developing utility functions in computational ethical
computing. https://www.oreilly.com/ideas/on-computational-ethics
Mitchell, Wesley C. “Bentham's
Felicific Calculus.” Political Science Quarterly
33 no.2 (June 1918), 161-183. In Parts II-III an examination,
interpretation, and criticism of the felicific calculus and in
Part IV a construction of Bentham's functional psychology. http://www.jstor.org/stable/2141580
Rzepka, Rafal and Kenji Araki. “Possible
Usage of Sentiment Analysis for Calculating Vectors of Felific
Calculus.” IEEE 13th International Conference
on Data Mining Workshops (2013) doi:10.1109/ICDMW.2013.70.
Using a hedonic calculus algorithm for sentiment analysis in order to
understand reasons and consequences of human action for use with
machines. http://arakilab.media.eng.hokudai.ac.jp/~araki/2013/2013-A-15.pdf
Sinnott-Armstrong, Walter. “Consequentialism.” A discussion from the
Stanford Encyclopedia of
Philosophy on the doctrine that the rightness of an action
depends upon the consequences of the action. The classic
utilitarianism of Bentham and Mill is discussed as a paradigm
case. http://plato.stanford.edu/entries/consequentialism/
Sturt, Henry. Utilitarianism
The entry from the classic 1911
Encyclopedia Britannica discussing the ethical doctrine and
history of utilitarianism. https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Utilitarianism
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