Friday, July 27, 2007

Utilitarian Calculus

While reviewing the literature of mathematical methods in utilitarian ethics, I came across a summary of perhaps the original utilitarian calculus, formulated by Jeremy Bentham. His is a hedonistic model similar to my own. Here is Bentham's felicific calculus.

One of the things I saw missing, though, was a metric of quantifying pleasure. I had quantified pleasure, or so I thought. As I looked at an overview of utilitarianism, I found that the metric of quantification of well-being I had employed was a form of the more general notion of preference (not just of psychological pleasure), which in the 1950s Kenneth Arrow had already suggested for utilitarian evaluation. That is, what one prefers ought to be the axis of ethical evaluation.

To give the numerical value a scale, my own quantitative approach modeled such preferences through a scale that (as Rob Bass brought to my attention) resembled quality-adjusted life years, but goes on more generally to allow for better than normal health conditions. Since it is posed as a thought experiment, it is also based on individual preference rather than systematic one-size-fits-all assumptions of what diverse members of a population might prefer.

Encouraged by this interesting and compatible prior art, I was about to update my own arithmetic model of comparative ethical calculus when I stumbled upon a resource that showed clearly, someone had beaten me to a definitive mathematical model of utilitarian ethics. Not just in theory but in actual application, boiled down to a form in the style of one of the greatest institutions of utilitarianism. From Swift magazine, here is the definitive utilitarian calculus.

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