Suppose we all agreed that a cat is a four legged animal which purrs and says meow. Speaking technically, we have agreed that the 'intension' of cat involves meowing and running around on all fours. Suppose I now get down on all fours and purr and say meow. Am I a cat? Is this a question whose answer we all have to agree about?
No. This is an example of the 'intensional fallacy' aka 'masked man fallacy. The fact is the necessary and sufficient conditions we give for a particular name or 'intension' to apply are 'epistemic' (knowledge based) in nature. As our knowledge base changes the 'intension' changes. We discover surprising things- e.g. there are adults who crawl around saying meow. But, no great aporia or paradox is created in this manner.
No doubt, if I make enough of a nuisance of myself, everybody may say 'Enough, already! We get it. You're a cat. Happy now?' . But they might be better advised to ignore me and talk of other matters.
One aspect of Liberalism is the Rule of Law such that there are many choices a person can make which Society can have no say in. Thus, I can buy whichever brand of toothpaste I like. No representative of Society has the legal power to force me to reveal or change my preference. It is nobody's business but my own.
Sadly, this is also a feature of every fucking society of every fucking type. There are always things w.r.t which everybody has a 'Hohfeldian immunity' though, no doubt, some may be subject to bullying or other repugnant actions such that they aren't even allowed to fart loudly at their sister's birthday party. I'm not saying that's what happened to me. It's the sort of thing which could happen to any elderly Tambram.
Amartya Sen, in his paper 'Impossibility of a Paretian Liberal' pretends that Liberalism alone grants Hohfeldian immunities re. self-regarding actions with no externalities. This simply isn't true.
More bizarrely, Sen thinks a Liberal Society has a preference, which is the same as my own, when it comes to how I clean my teeth. I would argue that a Liberal Society ought not to have knowledge or reveal a Preference about something wholly private to myself. This is not to say that Society can't prefer to have a citizenry with healthy gums. It just means Society mustn't state a preference with respect to a wholly private decision of my own.
Why? If Society were permitted to express a preference in this matter then there is a slippery slope to the erosion of my freedom. I have an interest in acting tactically so as to exercise a countervailing power.
Sen, like Arrow, insists that Society has a preference over alternatives which everybody in Society agrees it must not and ought not to have. But no such Society has ever existed. Clearly, Society has no preference whatsoever if no Collective body is authorised to express or otherwise reveal any preference in private matters.
Thus, if the current British Prime Minister is asked in Parliament, by the Leader of Her Majesty's Opposition, why she approves of the fact that I use shoe-polish to clean my teeth, she should reply- 'I don't approve or disapprove of it. It is none of my business, or yours- Jezza you great big Lezza'.
Sen may say, 'what's the harm in pretending that Society prefers what you prefer in this context?'
My reply is 'that way madness lies. Any guy who wants to get out of paying child support can claim to be a cat by getting down on all fours and saying meow. Society would have to decide whether it prefers to pretend he really is a cat as opposed to ignoring his unseemly display and punishing him according to the law.'
If you don't use words properly- i.e. the way other people do- you end up talking nonsense. Stuff like this-
This is the opposite of Liberalism. I don't want the May-bot saying that H.M.G prefers my using boot-polish to clean my teeth. The thing is none of her business. Society must not have, within its choice domain, stuff that is private to me and nobody's business but my own.
Why desire a freedom one is merely permitted to have? It is better to want a freedom which does not depend on anyone's permission. Nor do we want Society to say 'In this matter, we prefer what you prefer coz u are such a special little snowflake and we want to validate you and support you in exercising your autonomy coz we respect the shit out of your dignity coz you're not at all a big fat fucking retard. '
Why was Sen being so stupid as to think Society has a preference when it clearly does not? The answer is he wanted to show he was smart- like Ken Arrow. But, Arrow was an idiot. He didn't get that a Collective Social Choice rule which fucked with people's private lives would never be implemented in accordance with any other Rule which met his criteria. In other words, the first rule would drastically prune the Domain of the 'Constitution'. Nobody would ever vote for 'Unrestricted Domain' coz that includes the option of your being paraded around with a radish up your bum- not the radish you'd have chosen yourself but a really shitty radish which had already been up the bum of the person you most loathe.
Since, for prudential reasons, everybody would agree to place the vast majority of decisions outside the Social Choice function, we can say that the 'Pareto principle' requires hugely restricted Domain. Thus Arrow's theorem is worthless.
So is Sen's.
It is perfectly possible that, for any given Society, there could be a Paretian partition of the Decision Space such that only pairwise voting obtains and no intransitivity results. We may not know what that Paretian partition is, but for large enough populations with Rational Expectations, we can't prove it doesn't exist.
Consider what happens if Society takes account of preferences people might have about what is none of their business. People would feel defensive. Since attack is the best form of defense, they would stockpile grievances and moral claims of their own to use against anyone who sticks their nose where it don't belong. Thus if a posh vegan makes some comment about your menu choice in the canteen, you immediately start ranting about the inequity of Private Education. The stupid bint will then reveal she wasn't born with a silver spoon up her nose but overcame adversity and went to Night Skool to better herself. You then get to sneer at her affectations and go around telling everybody her Mum is that smelly homeless woman wot begs outside Waitrose.
Sen understands this sort of mental pathology. He gives the following illustration of his bogus result-
To want something or wish for something does not necessarily mean one prefers that outcome. I might say 'I wish Trump were elected! That would put the cat among the pigeons sho' nuff!' However, I don't actually prefer Trump and certainly wouldn't vote for him or send money to his campaign.
Sen has devised a facetious enough scenario, but it relates to wishful thinking of a certain type, not what economists mean by preferences.
Arrow studied under Tarski who explained
When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be immediately understandable; the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings. At the same time we adopt the principle: not to employ any of the other expressions of the discipline under consideration, unless its meaning has first been determined with the help of primitive terms and of such expressions of the discipline whose meanings have been explained previously. The sentence which determines the meaning of a term in this way is called a DEFINITION.In Sen's example, the undefined term 'preference' has been misapplied. What it means is 'the thing a person habitually chooses for self-interested reasons'. What Sen is referring to is a book nobody prefers to read. They say 'I wish the other guy were forced/forbidden to read it coz that might have such and such effect on them'. This is not a preference. It is a type of schadenfreude, albeit couched in moralistic terms, which may relate to preferences but which does not correspond to the primitive notion of preferences and thus needs to be separately defined.
Arrow went wrong because he didn't understand that Knightian Uncertainty obtains. There is no way of specifying all possible states of the world and ascribing probabilities to them or defining choice functions upon them. His 'primitive terms' could not bottom out in the real world. He was bound to produce more and more specious shite. Indeed, the Arrow-Debreu security was the radioactive core of what Warren Buffet would describe as Weapons of Mass Financial Destruction.
Sen went wrong because he relied on Arrow. By the end of the Seventies, Econ Journals refused to publish any more Social Choice shite. The thing was pure mental masturbation. By contrast, mechanism design was always welcome. Still, the future lay with Junk Social Science. Why? Econ's primitive terms were only understood by non Economists who went ahead and gained utility by doing utile stuff for which they were very well rewarded. Meanwhile a few Economists made a bit of money out of a Credentialized Ponzi scheme. But, it was at the price of turning their students into cretins. That's a good, a salutary, thing. Not everybody was born stupid. Me? I just won the genetic lottery in that respect.
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