Just for the record, GDP - and indeed any purported cardinal measures of well-being in the absence of other assumptions - are "theological" in nature.



If we are to be rigorous we must address the whole issue of “Cardinalism” in Economics and ask if the cardinal values beloved of economists have any objective reality at all.



“The Church of Cardinal Preferences” is a belief system which holds that ordinal preferences can be mapped onto cardinal numbers in such a way as to allow the cardinal numbers of one individual’s preferences to be compared against the cardinal preferences of another individual’s preferences using the operations of cardinal arithmetic (“plus”, “minus”, “greater than”, “less than” and “equal to”).



This is, of course, the basis of Utilitarianism, the idea that there is some objectively real thing (call it “Utility”) that can be “added” and “subtracted” using the laws of cardinal arithmetic.



In fact it pre-dates Bentham by at least half a century. We see it referred to obliquely in Rousseau’s famous line:



. . . the general will studies only the common interest while the will of all studies private interests, and is indeed no more than the sum of individual desires. But if we take away from these same wills, the pluses and minuses which cancel each other out, the balance which remains is the general will.



This assumes of course that the “wills” (or today we might call them “preferences”) are defined under the operators “plus” and “minus”, the operators of cardinal arithmetic. If they were, economics would indeed be a simple matter of maximising the sum of cardinal utility.



But not all measures are cardinal. Vectors are not cardinal. For example, you can’t “plus” and “minus” vectors using simple cardinal arithmetic. They may point in different directions. You can’t say that “north” is greater than “east”. (For any particular vector the northern component may be greater than the eastern component, but that tells us nothing about whether north “outweighs” east.)



Likewise with preferences. It is tempting to believe that we can somehow “add” one individual’s preference for faster flight times and “subtract” another individuals distaste for aircraft noise, to get an objectively real “answer”.



This conceit is reinforced by the use of monetary values to do the bookkeeping for transactions in the marketplace. Believers who haven’t stopped to consider the issue carefully believe that they may extend this bookkeeping to the aggregation of preferences in general.



However, we can demonstrate quite easily that such comparison is possible only under very narrow assumptions.



If we go back to the foundations of Economics we may start with the observation of Ronald Coase (in his Alfred Nobel Memorial Lecture):



“ . . . what are traded on the market are not, as is often supposed by economists, physical entities but the rights to perform certain actions.”



[We could go back one step further and define a “right” as an “enforceable preference”, where the enforcement is carried out by a “State-like Entity”. A State-like Entity is an entity which de facto is able to enforce preferences. It may be a sovereign state, but it might also be sub-national polity like a federal state of an elected local council. It might be the judiciary of a sporting league. It might be a mafia. Under feudalism it might have been a baronial court operating independently of the monarch. It might have been the Church exercising its jurisdiction over certain matters (such as marriage, or the regulation and punishment of the clergy). It might even be a family. (As a child I have a “right” to sit at the head of the table if my preference to do is enforced by my parents who are the de facto State-like Entity in this regard.)]



When Cardinalism is applied to State-like Entities themselves itself it can be shown to yield no unambiguous solution.



The exchange value of any bundle of rights is determined by the marginal seller and the marginal buyer (or a hypothetical marginal seller and buyer). For both marginal seller and marginal buyer, the indifference point between the bundle and an amount of cash (i.e. the cardinal “value” they place on it) depends on their initial endowment of wealth. Richer buyers are prepared to pay more to buy while rich seller require more to sell. The opposite is true for poorer buyers and sellers.



In other words, the value determined by any such transaction is biased towards the initially well-endowed. If we were prepared to accept these initial endowments a priori then we might – perhaps – be able to attribute cardinal values to bundles of rights.



But . . . . one of the capabilities of State-like Entities is that they can alter initial endowments of buyers and sellers through their taxing and spending powers, and thus, in principle, the values of all bundles of rights.



Any proposal for which it is proposed to determine a “cardinal value” (as in a cost-benefit analysis) may – in principle – be “stapled” to a taxing and spending measure that would enrich those who support it (at the expense of those who do not) so that the supporters may bid up the value of the outcome.



Of course, their opponents may put forward a counter-proposal that does exactly the opposite!



The result is a theoretical bidding war in which the taxes and subsidies proposed by each side do not converge to any unambiguous finite solution but escalate to infinity.



Thus, any attempt to apply Cardinalism to a State-like Entity leads to a divergent bidding war which cannot determine an unambiguous result.



Now, committed Cardinalists might argue that such adjustment of initial endowments ought to be prohibited a priori. But that suggestion is itself nothing but a preference (one which would, incidentally, benefit the present rich at the expense of the present poor). Before it could be accepted, it would – by the logic of Cardinalism itself – need to validated by comparing its cardinal value against the cardinal value of other preferences (for example, the preference not to prohibited endowment adjustments) . . . . something we have just shown to be impossible!



When Cardinalists ask us to assign a “value” to something (especially aesthetic intangibles or things such as "equality"), they are actually pulling a very subtle rhetorical sleight-of-hand which most people don’t notice: they are subtly and implicitly limiting the “target space of available options”. They are implicitly asking: “What value would you place on this assuming that you actually had to pay for it from your current endowment of wealth and could not employ taxes-and-subsidies to your opponents to cover the cost?”



But we need not accept having our target space of options limited thus. If we refuse to be tricked, we can assign any value we please and Cardinalism collapses.



The assignment of arbitrary cardinal values (especially to aesthetic preferences) is not just a problem of measurement. It raises serious epistemological issues. In the absence of an in-principle method of determining unambiguously what those cardinal values are, it cannot be expected that other people should agree to their being attributed any objective reality. Cardinal preferences are akin to “Gods” which some people believe in and other people do not.



I should note that I am not here to promote religious intolerance. If some people find belief in cardinal preferences a helpful way to deal with the world, far be it from me to suggest that their belief is “wrong”. Likewise, if there are any who believe that certain preferences are “The Will of God”, far be it from me to suggest that they are “wrong”. I have no Monopoly on Wisdom.



But any suggestion that the assignment of arbitrary cardinal values to preferences gives them some sort of “objective truth” or “superiority” is theological nonsense.



