Adam Smith’s Advocacy and Support for His Theory of Imprecise Probability Means That It Was Impossible for Him To Be a Utilitarian of Any Type, Benthamite or other : Any and All Types of Utilitarianism Necessarily Require Precise Probability As Advocated by Bentham in Chapter Four of His 1787 the Principles of Morals and Legislation

Adam Smith demonstrated, repeatedly in his The Wealth of Nations in 1776 on, for example, pp.105-113,pp.227-244, pp.419-423,and p.714, his commitment and adherence to his theory of imprecise and inexact probability assessment that completely conflicted with Bentham’s exact, linear and additive approach based on precise probability. In chapter Four of his 1787 The Principles of Morals and Legislation, Bentham lays out an explicit and detailed account of precise probability. Bentham explains clearly how his Max Utility approach is to be implemented. Bentham’s Max U approach requires, as a necessary condition, the use of precise probabilities (what he calls uncertainties) and precise numerical outcomes that are linear and additive so that aggregate “happiness” (material goods) can be maximized. Of course, this is precisely what Adam Smith rejected in his virtue ethics approach. Smith’s integration of uncertainty into a decision making approach based on imprecise probability has apparently been overlooked by every single historian, economist, philosopher, sociologist, psychologist, political scientist, and decision theorist who has written on Smith in the 20th and 21st centuries. This ignorance is demonstrated in the sterile, ongoing controversy, engaged in by numerous academic writers on Adam Smith, as to whether or not he was a utilitarian, semi-utilitarian, nonutilitarian, or anti-utilitarian. A knowledge of Smith’s imprecise approach to probability immediately leads to the clear cut decision that he must have been either a nonutilitarian or an anti-utilitarian. There is no other possible conclusion once Smith’s imprecise view of probability is acknowledged, highlighted and brought to the attention of readers of The Wealth of Nations