Sen's Paretian Liberal is nonsense

 

In 'On Liberty' JS Mill argued that 

“....the only part of the conduct of any one, for which he is amenable to society, is that which concerns others.

In which case no part of the conduct of anyone can be known a priori to be not 'amenable' to society.  

In the part which concerns himself, his independence (of choice) is, of right, absolute

Rights are meaningless save in relation to remedies including those a person is permitted to apply in her own defense- e.g. the right to kill someone who is trying to kill her. But, even here, the right isn't absolute at all. She may prefer to be killed because she knows killing the assailant will cause his clan to wipe out her family.  

......I forgo any advantage which could be derived to my argument from the idea of abstract right, as a thing independent of utility.

In which case, you wasted your own and the reader's time. An abstract right may be something willed by God. Violating it may cause you to burn in Hell for all eternity. Equally, it may be founded on some higher type of intellectual development which future generations are bound to have. In this case, violating such abstract rights would cause you eternal infamy. Your name would become a byword for evil conduct.  

I regard utility as the ultimate appeal on all ethical questions; but it must utility in the largest sense, grounded on the interests of man as a progressive being...”

in which case it is is unknowable.  

Consider the following, not untypical, way of representing Sen's Paretian Liberal paradox. 

Suppose there is a society N consisting of two or more individuals and a set X of two or more social outcomes. 

If individuals have preferences over outcomes, they can also have preferences over preferences and preferences over preferences etc. In other words, even if there is only one outcome one either likes it or dislikes it, then there are an infinite number of outcomes based on your liking the liking of liking etc.  

Moreover, if people can have multiple identities, as Sen would later argue, then there are always an infinite number of individuals even if there is only one. This is also the problem with a 'multiple utilities' framework. 

Suppose each individual in the society has a total and transitive preference relation on the set of social outcomes X.

We have seen that X is infinite. If we assume there is a total and transitive preference relation then we are assuming that X is well ordered. The problem is that X may have no least preferred option- i.e. which ever element looks most horrible could, with a little thought, shown to be less horrible than what it might be. In this case, X is not isomorphic to the natural numbers. This means you have to use the axiom of choice to get a well-ordered X. But, in that case, you get Banach Tarski weirdness (e.g. infinite multiple identities) and then, sooner or later, run into the problem of ordinals with higher cardinality than the continuum. Basically, this means whatever you are proving only has to do with some bizarro mathematical universe. It can have nothing to do with Economics or Jurisprudence where everybody has only one identity which is tied to a particular body.  

For notation, the preference relation of an individual i∊N is denoted by ≼i. Each preference relation belongs to the set Rel(X) of all total and transitive relations on X.

However, since preferences are impredicative or epistemic and often depend on what smarter people are choosing or else on strategic considerations, the 'intensional fallacy' arises. The extension of the 'intension' 'preference' is not well defined. It does not obey Leibniz's law of identity. Indeed, it may be wholly unknowable. Consider my preference for chocolate ice-cream over vanilla ice-cream which is conditional upon there being a proof that P is less than NP. That is an open problem. Once it is solved, we can say my preference is for chocolate ice-cream. But will the question ever be solved? We don't know.  

A social choice function is a map which can take any configuration of preference relations of N

which are unknown. If the domain is unknown, there is no fucking mathematical function 

as input and produce a subset of ("chosen") social outcomes as output.

Again 'social outcomes' are unknown because anybody can prefer to prefer, because they enjoy preferring stuff, whatever they had previously preferred.  There is no mathematical function here. 

Utilitarianism seemed 'sciencey', back when it was thought that the thing was objective and could be measured in the same way we measure height and weight. But it can't. Pretending otherwise may let you do mathsy stuff but Mathematics itself says 'stop being so silly. There is no Set here- the thing is not well enough defined- and there are no functions here and there is no fucking topology for fixed point theorems to sink their teeth into. What you are doing isn't math. It is masturbation.

Economics has been defined as the science of choice under scarcity. The problem is that feelings of regret or anticipated regret aren't 'scarce' at all. The more you think about a choice the more fucking agonizing it becomes. Suppose an angel from Heaven appeared any time Society made a choice and confirmed that it was the best possible choice and the one God was hoping we would make. We would experience great satisfaction. Similarly, political philosophy tries to give us this reassurance that the way decisions are made in our polity really are the best possible. But political philosophy is a sort of secular theology or theodicy. It has no mathematical representation. True, it may invoke mathematical ideas, but then it may also invoke Lesbian Walruses. 

 (Intuitively, the social choice function represents a societal principle for choosing one or more social outcomes based on individuals' preferences. By representing the social choice process as a function on Rel(X)N, we are tacitly assuming that the social choice function is defined for any possible configuration of preference relations; this is sometimes called the Universal Domain assumption.)

It is stupid. What could work is an arbitrary, but sensible, stipulation that 'on average, an adult male needs x number of calories, while a baby needs x amount of milk' and then the implementation of an economic plan to make sure, on average, people get enough nourishment while some great existential threat- e.g. a total war or natural disaster- is being dealt with. Here the only way you can get anywhere is by arbitrarily restricting the domain very much indeed. But this is also how contracts of adhesion work. I buy an ice-cream and eat it. I want my money back because I now prefer to have preferred not to eat it. Also, I now identify as a Lesbian walrus and such creatures don't eat ice-cream. Will a court of law award me my money back? No. They will tell me to fuck the fuck off.  

The liberal paradox states that every social choice function satisfies at most one of the following properties, never both:

No social choice functions exist. They can't satisfy shit.  

Pareto optimality (collective efficiency): whenever all individuals of a society strictly prefer an outcome x over an outcome y, the choice function doesn't pick y.

We don't know if everybody would prefer an outcome where everybody would prefer to prefer that outcome. Thus any y picked by a choice function may be inferior to everybody preferring to prefer y a bit more even if that y was obtained by preferring to prefer its predecessor.  Equally one may prefer to prefer to not prefer the thing you end up preferring anyway. 

Obviously, we could also prefer that x preferred he didn't prefer to prefer whatever it is that we all prefer. 

Formally, a social choice function F is Pareto optimal if whenever p∊Rel(X)N is a configuration of preference relations and there are two outcomes x and y such that x⪲iy for every individual i∊N, then y∉ F(p).

Under unrestricted domain, which permits there to be preferences over preferences, there can be no social choice function. True we may arbitrarily call an arbitrary procedure a mathematical function but then we could also call it a lesbian walrus. 

Intuitively, Pareto optimality captures an aspect of collective efficiency: the social choice is made so that everyone is collectively as well off as possible, to the extent that every available tradeoff would make someone worse off.

In other words, if you don't feel like finishing your glass of milk but think you might like a biscuit, you could do a trade with a guy on the opposite side of the world who is in the reverse position. Moreover, this would be a world without Knightian uncertainty- in other words, all future states of the world will be known at least probabilistically. However, it is easy to show, in such a world there would be no language or education or scientific research or necessity for paper money or Banks or other financial or legal institutions.  

Minimal liberalism (individual freedom): More than one individual in the society is decisive on a pair of social outcomes.

How do we know who is decisive or not? Some other guy may have decided to let this bloke be decisive for some reason of his own. Minimal liberalism is achieved if an absolute ruler lets his court jester decide to wear his underpants on his head.  The jester himself may say 'it wasn't my decision to wear my underpants on my head. Indeed, it was the last thing I wanted to do. That's why I did it. I just didn't fancy being killed today.' 

Intuitively, minimal liberalism captures an aspect of individual freedom: for some issues, if you prefer x over y (or vice versa), then society respects your preference for x over y even if everyone else is against you.

In my society I am permitted to publish this blog. Nobody respects this preference of mine. They merely think the thing is too minor a nuisance to be worth curbing by the strong arm of the law. 

Sen's example is your personal preference for sleeping on your back or your side: on at least one innocuous personal area like this, a liberal society ought to prioritize your individual preference even if everyone else in society would prefer you to sleep another way.

An illiberal society too shouldn't give two farts about this. Sen's example is foolish.  

The formal requirement is that at least two people are decisive in this way, to rule out the possibility of a single person who dictates society's preferences.

This formal requirement is useless. A tyrant can exhibit his jester and thus show 'minimal liberalism' obtains. A territory with no organized government may not be able to show anything at all because Society has no recognized representative. The crazy guy who says he is controlling everybody with his thoughts and the philosopher who says everybody is doing pretty much what they want are on an equal footing.  

In other words, the liberal paradox states that for every social choice function F,

it can be easily shown that it isn't a mathematical function at all 

there is a configuration of preference relations p∊Rel(X)N

which too can't exist in any mathematical shape or form 

for which F violates either Pareto optimality or Minimal liberalism (or both).

but only because it is already violating a Lesbian Walrus. That's what we should be focusing on. Neoliberalism is sodomizing marine animals. Why is Greta Thurnberg not speaking out on this issue? Is it because she is actually a platypus?  

In the examples of Sen and Gibbard noted above, the social choice function satisfies minimal liberalism at the expense of Pareto optimality.

No! It doesn't satisfy shit. Otherwise Lesbian Walruses would be minimally Neo-Liberal, but they aren't. They demand the immediate collectivization of the Solar System so as to increase the supply of nice fish to eat. But no ice-cream. Ice-cream is totes Fascist.