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Jeremy Bentham, in Chapter 4 of his 1781 An Introduction to the Principles of Morals and Legislation, defines what has become known as the Hedonic Calculus. He states,

Pleasures then, and the avoidance of pains, are the ends that the legislator has in view; it behoves [sic] him therefore to understand their value. Pleasures and pains are the instruments he has to work with: it behoves [sic] him therefore to understand their force, which is again, in other words, their value.

The model he provides seems to be intended to evoke the idea of a quantitative model, where one can (in theory) add up the relative merits of two competing ideas and determine the correct act by taking whichever has the higher score (if summing pleasures) or the lowest score (if summing pains), but he doesn't seem to actually provide such a model.

Presumably, such a system would allow utilitarian ethical judgments to be calculated. That is, once one "ran the numbers" on each potential act, the correct answer would appear, and one could be certain that that act/choice was the most ethical (under utilitarian/consequentalist thought) up to the confidence level of the underlying quantitative model.

I thought, at first, that this was ridiculous (such a model would need to integrate and make quantitatively comparable various disparate concepts - for example, which is more hurtful, getting lung cancer or losing the right to vote? Which carries more pleasure, learning two languages of my choice up to fluency, being elected governor, or receiving a financial annuity allowing me to live modestly without working for the rest of my life? If it came down to a choice between giving someone the Key to the City of Podunk and giving them an honorary doctorate from Podunk University, which would you say gives more pleasure to the average recipient?*) and that such a model as Bentham's must inherently remain a qualitative one, but I found some lecture slides from Dr. David Pattillo of the University of Notre Dame in which he states,

Some utilitarians even allow for there to be quantifiable units of pain and pleasure.

We can give an easy model of the value of an action. If hedons (H) are units of pleasue [sic] and pains (P) are units of pain, then the value of an action (A) is A=H-P.

Dr. Patillo here seems to be speaking specifically about a quantitative model, but then proceeds to give several examples that are primarily qualitative in nature (e.g. estimating conjugal happiness), and the only truly quantitative example turns out to be a restatement of the Trolley Problem.

Has anyone defined or created a framework for a quantitative model of the Hedonic Calculus, or is the existence of a quantitative form purely theoretical at this point?

*I can see these as great opinion questions, questions to use on a personality assessment, or "get to know you" questions to ask a potential romantic partner, but I'm at a loss to figure out how one would even begin to assign numerical scores to these items.

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    Bentham gave more detailed instructions on calculating "pleasure", Lander even attempts to arrange them into a mathematical formula. The idea does not have many takers due to the problems with cross-type and cross-personal comparisons of "pleasures". Even defenders do not profess to give a workable calculus, only argue that one abstractly exists, see e.g. Klocksiem's 2009 thesis On the Measurability of Pleasure and Pain.
    – Conifold
    Jun 5, 2019 at 2:49

2 Answers 2

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Yes, if you are interested in the mathematical foundations of utilitarianism, you should look at the literature on "Harsanyi's Theorem".

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You're talking about the Felicific Calculus

Here's a rough sketch from the article linked to above outlining what kinda quantitative measures need to be made:

  1. Intensity: How strong is the pleasure?
  2. Duration: How long will the pleasure last?
  3. Certainty or uncertainty: How likely or unlikely is it that the pleasure will occur?
  4. Propinquity or remoteness: How soon will the pleasure occur?
  5. Fecundity: The probability that the action will be followed by sensations of the same kind.
  6. Purity: The probability that it will not be followed by sensations of the opposite kind.
  7. Extent: How many people will be affected?
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    Well yeah, the OP obviously knows that. Yet, the dimensions are qualitative in nature. The question asks whether there is some quantified model of these dimensions, e.g. in terms of standardised interviews or surveys.
    – Philip Klöcking
    Nov 13, 2022 at 17:25
  • Excellent point! The seven points listed in the Wikipedia page on the felicific calculus are quantitative if you examine them closely. Nov 14, 2022 at 2:42
  • @PhilipKlöcking exactly. My question is about any proposed quantifications. For example, if me performing a concert brings 10 pleasure points to the population at the cost of 8 pain points (negative pleasure) for me to actually perform it on stage and either 6 pain pts for me to obtain the necessary land use permit or 1 pain pt to serve the night in jail for performing a concert without a permit we can calculate that it is ethical (10 pleasure - (8 pain+1 pain) = 1 pleasure) for me to perform it unlawfully and unethical (10 pleasure - (8 pain+6 pain) = 4 pain) to perform with a permit. Nov 14, 2022 at 11:18
  • I'm amazed at the simplicty of it all, but that's what makes me wanna question its validity Robert Columbia. Nov 16, 2022 at 8:03

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