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The Pitfalls of Cardinal Utility

A recent article by David Gordon [1] discussing What We Owe the Future by William MacAskill on utilitarian ethics got me thinking about the absurdity of cardinal utility theory. Even from a layman’s perspective, the strangeness of cardinal utility seems like a good reason to believe there is something seriously wrong with its premises. It leads to ideas such as a dictator made so happy by enslaving others that he outweighs all negatives, as well as other bizarre conclusions, including the “sadistic conclusion [2],” and the “repugnant conclusion [3],” which both involve optimizing utility in groups. However, academics persist at papering over these conclusions and justifying all kinds of horrifying policies. This suggests some kind of perverse desire that I don’t fully understand. I suppose the title “Professor of Ethical Philosophy” is more attractive than “Professor of Genocide Planning,” but aside from that I don’t see the appeal.

To define our terms, cardinal utility states that the utilities of bundles of goods to people can be measured numerically, in a unit often called the util. For example, three bananas and one apple might provide seven utils to someone, and two bananas and two apples might provide eight. Another person might get different numbers for the same goods. The alternative is called ordinal utility, which says that utility is a ranking, not a number. Using the previous example, the person in question prefers two bananas and two apples to three bananas and one apple, but there is no unit shared between the goods or another person’s valuations.

Even neoclassical economists seem to admit that ordinal utility is the correct point of view[4], but the attractiveness of cardinal value is that it permits them to devise mathematical theories and models from which they can understand the economy and make predictions. However, as William Barnett II notes, there are serious logical issues with how the neoclassicals convert ordinal scales to cardinal ones [4]. A simpler way to put it is that the real world does not exist for the convenience of neoclassical economists–and it shows.

Indeed, aside from the logical problems with converting ordinal scales to cardinal scales, we observe even more issues with cardinal utility. First, it is arbitrary and unmeasurable. Preference is revealed by action, and Rothbard observes that attempts to show preference from inaction lead to absurdity [5]. Moreover, people’s valuations vary in time, so a collection of exchange data from different times may not even describe the same value scale. Therefore, it is impossible to measure or deduce numerical differences in utility after a trade, even given a large dataset, which–by the way–we usually don’t have.

In fact, the creation of numerical value scales by theorists is often a tool to hide or avoid considering certain goods or perceptions. In a classic example, the cardinal utilitarian argues that taking $100 from a millionaire and giving it to a poor person increases net utility, since the poor person values that $100 more than the millionaire does. The usual justification is a corruption of diminishing returns–the millionaire has many dollars, so that top $100 is worth little to him, compared to the poor person. However, this comparison focuses only on these two and ignores others–for instance, the $100 invested by the millionaire provides long-term utility to a business serving a large number of customers, as compared to immediate consumption. Even worse, the complexities of time-preference are often ignored. Going a step further, the comparison ignores the need for some agent to force the transfer, and the last thing the cardinal theorist wants is for you to consider how much satisfaction the millionaire might gain from stopping a thief.

Another problem with cardinal utility scales is that they effectively eliminate moral precepts. A cardinal theorist would argue that what needs to be done is to choose a larger negative number to represent fraud, theft, and violence (up to and including murder!), but since the numbers are all arbitrary, that doesn’t actually solve the problem. All a determined statist must do is imagine more positive aspects of the aggression. In the extremes we find another problem: how do we describe the utility of a person who is no longer alive? Clearly, the dead man experiences no psychological trauma, which suggests a value of zero. How do we square that with the assumed large negative value of killing someone? It suggests that the negatives from murder are merely the psychological effects it has on others–and this idea leads to more awful conclusions. What about someone who is seriously depressed? Calculating numerical utilities leads to a number of perversities, one being the movement of Canada’s health care system to not just allow, but to embrace and encourage doctor-assisted suicide for people with mental and other non-terminal illnesses [6].

In reality, the only way to be sure that a transaction increases net utility is to show that it is voluntary. In a voluntary transaction, both parties independently, through their own interpretations of their own value scales, including psychological effects and time preference, decide that the exchange makes them better off. There are no utils to measure and no room for anyone to apply force. And since each party’s value scale may shift between this exchange and the next, there is no way to compare this exchange with others. The best a third party could do would be to provide information to those trading to make sure they are both fully aware of the consequences. But this provides no room for a coercive state to meddle, so it seems likely that state-funded academics will continue to count the angels on the head of this pin for the foreseeable future. Our best bet is to remind everyone, loudly and frequently, of the bankruptcy of their theories.

Videos available on Bitchute and Odysee.

References

[1] David Gordon, “Ethics for Inhumans,” Mises Wire 2022-12-30. Retrieved 11 January 2023 from https://mises.org/wire/ethics-inhumans

[2] Gustaf Arrhenius, “An Impossibility Theorem for Welfarist Axiologies,” Economics and Philosophy, Issue 02, pp. 247-266, October 2000. Retrieved 23 January 2023 from https://niplav.github.io/doc/population_ethics_impossible/an_impossibility_theorem_for_welfarist_axiologies_arrhenius_2000.pdf

[3] Derek Parfit, “Can We Avoid the Repugnant Conclusion?” Theoria 82, pp. 110-127, 2016. Retrieved 11 January 2023 from http://www.stafforini.com/docs/Parfit%20-%20Can%20we%20avoid%20the%20repugnant%20conclusion.pdf

[4] William Barnett II, “The Modern Theory of Consumer Behavior: Ordinal or Cardinal?” The Quarterly Journal of Austrian Economics 6, No. 1, pp. 41-65, Spring 2003. Retrieved 11 January 2023 from https://cdn.mises.org/qjae6_1_3.pdf

[5] Murray N. Rothbard, “Toward a Reconstruction of Utility and Welfare Economics,” 1956. Retrieved 11 January 2023 from https://cdn.mises.org/Toward%20a%20Reconstruction%20of%20Utility%20and%20Welfare%20Economics_3.pdf

[6] “Canada’s new medical assistance in dying (MAID) law,” Retrieved 11 January 2023 from https://www.justice.gc.ca/eng/cj-jp/ad-am/bk-di.html

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