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 '19 at 2:49

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