Personal Choice is about outcomes determined by your own tastes and values which in turn depend on your own knowledge of yourself and your circumstances.
Social Choice is about outcomes determined by what we as a Society value or consider normative or necessary or advantageous under the circumstances.
Neither are arrived by 'aggregating' anything though, no doubt, totals of some type weigh upon decisions. Thus, I add up my expenditure and check if my income covers it and Society, too, needs to do something similar.
Speaking loosely, we do sometimes say things like 'I can't go to the pub with you tonight coz I'm overdrawn' or 'the Government can't cut taxes because the deficit is too large'. However, other people will point out that you can go to the pub if only you didn't insist on taking taxis everywhere. Get a bus like a normal person. Similarly, the Government could cut taxes if it didn't keep pissing money up the wall on all sorts of boondoggle.
If actual Choices, we as a Society made, could be resolved by 'aggregating' things then we should leave things to stick-up-their butt Accountants who follow rigid rules. The Greek word 'Akrebia' captures this sort of rigid thinking. Its opposite is 'Economia' which means discretionary accommodation of an imaginative, creative, sort.
Sadly, Academic Economics, thanks to the Cowles Commission & the RAND Corporation, got saddled an Arrowvian 'Social Choice theory' which wasn't about Social Choice at all. It was about pretending that markets were a type of voting mechanism and voting mechanisms were a type of auction whereby judgments were given on the basis of which side put together more money to bribe the judge. In other words, this theory took a metaphor- viz. that markets were places where people voted with their money- and treated it as a fact about the world. But, the metaphor was misleading. Markets are based on expectations regarding what is exchangeable and they can operate without money. Similarly, where there is free entry and exit- i.e. no coercion- there would be no need for voting. But, already, the metaphor has stretched too thin. Any type of behavior could be described as voting- my teeth just voted to get brushed because of their preference to be clean- with the exception of actual voting which does not correspond to voting according to the preferences the theory imputes to me because it is perfectly possible for me to misread the ballot paper and tick the wrong box, or else to fall for false propaganda or be constrained by a cognitive bias or mimetic effect. One may say that counting votes ought to be like aggregating preferences but an ought is not an is. Indeed an imperative statement may have no alethic correlative. It may be wholly incompossible with our lived world.
In a 1977 paper, Amartya Sen nicely summarizes why, by focusing on aggregation, this was a Theory that forbade itself any subject matter whatsoever in advance. This is because individual preferences are connected to Social choice in two very different ways, neither of which is additive- in some matters it is advantageous for everyone to want the same thing and it doesn't matter whether the majority's preference is respected- we can call this a coordination game- but there are other situations where this would be catastrophic. It is better that everybody 'does their own thing'- in which case no solution is focal- or, alternatively, there is a 'separating equilibrium' with a 'costly' signal which some must acquire. These situations can be said to involve 'discoordination games'.
Even with 'coordination games'- like having a rule re. which side of the road to drive on, there are situations where the choice is not binding. On a lonely, potholed, country lane everybody drives in the middle. But this 'eusocial' because having lower average speed in such contexts is beneficial for all sorts of idiographic reasons. There are also matters where everybody wants the same thing but prefers to have a leader who is known to prefer that thing even more passionately but won't deliver it at all. The more the leader does not deliver, the more fervently he is adored. Why? Preferences have an alethic component which may conflict with the imperative component for a perfectly rational reason. We participate in coordination games but hedge on discoordination games. There is 'cheap talk' with respect to a pooling equilibrium but there is also a potential separating equilibrium whose 'costly signal' becomes cheaper as a result. The fog of uncertainty is all pervasive. That risk is a priori calculable is a mirage.
Suppose Uncertainty did not exist- we knew every possible configuration of the world and its likelihood- then some aggregation mechanism must yield omniscience. If it is deterministic, then it is just a matter of time and computing power before we could compute the 'right' thing to do for Society. But this would also mean we would know the right theory of Physics and Biology and Chemistry and Mathematics. But our present knowledge of that last prevents us entertaining any such possibility.
If the aggregation mechanism is non deterministic, there is lower likelihood that it could involve 'Common Knowledge'. But, if 'oracles' exist, who is to say some Dictator or Cult leader is not to be unquestionably obeyed? Her claim to know what's best and true may be true. Our claim that she must be a charlatan must itself be irrational There is no known method to rule out the possibility that she possesses the charismatic gifts she claims. Even if she is a fraud, we can't generalize to the class she represents. Just because I am not in fact, as I claim, a Chidambaram look-alike gigolo catering to young Bollywood actresses, this does not mean there are no such gigolos who are doing very well for themselves financially. Why else would I make such a claim? Thus exposing me as a fraud merely means you have to look harder for the real cheez till, in a plot twist nobody didn't see coming, P. Chidambaram is revealed to himself have been that gigolo- thus explaining any disproportionate assets his family may have acquired.
On the other hand, if you don't believe Chidu really engaged in prostitution because he could earn more as a very senior lawyer, you do have good reason not to bother with this line of inquiry. This is because we judge a knowledge claim by looking at its plausibility with respect to its underlying structural causal model. This is closely linked to seeing whether it can do something useful for us. In this case, you can actually hire Chidu for legal advice in a difficult case. You probably can't book him for a hen party or get him to shoot a porn movie.
Most people have quite a good implicit 'Social Choice theory' because Man is a Social Animal. We constantly made decisions on the basis not of personal but collective considerations. Moreover, we can update our information set and change our tactics very efficiently and quickly. We can't say how we do this with any great precision of language, but as Aristotle pointed out, it would be a mistake to seek for 'Akrebia' in a context where precision is neither possible nor advisable. Instead, 'economia'- a pragmatics of gesture and reciprocity- is called for. This can be very useful but it may not provide much grist for an academic mill.
This is where Amartya Sen and his ilk fell down.
Under certainty, a Social welfare judgement is aggregation, true enough if everything is common knowledge. But if certainty exists, there is no need for any one actually doing so to feel they were themselves actually judging anything. Anyway, the thing itself would be 'Common Knowledge.
Only if they were using a cardinal measure of utility and doing 'interpersonal' comparisons could this be said to occur. But how is one to prove what one is doing 'Social' rather than idiosyncratic? Who, being aggrieved at your finding, will believe what you did was sufficiently informed and objective to qualify as a judgment?
This is not to say a metric might not be useful if it corresponds to the reduced form of a Structural Causal Model- e.g. National Income statistics based on how much people earn or measures of Homelessness based on how many people are carrying their belongings around in plastic bags and sleeping on park benches. Why are such metrics useful? It's because when you do something designed to boost earnings or put roofs over peoples' heads, then you can see whether you are on the right track. Suppose what you did spend all your money on setting up committees, then, chances are, you didn't really achieve anything at all. This is also true of spending money on the 'theory' of something you don't understand, but everybody else does.
Consider the following-
Let us now consider Sen's 4 'categories'. If Interests are independent of Judgments then interested judgments exist. Equally, self-interest may be modified by the faculty of judgment. How is one to 'factorize' interests and judgments which may be intermingled at a very deep level in one's psyche? Indeed, if we evolved by natural selection, why would we have independent interests and judgments? Kin-selection? But that is a bias. Indeed, there must be something we are doing which is in our interest even at the moment we make a judgment. Even our species most extreme examples of self-sacrifice are self-interested with respect to maintaining the kind of environment in which beings of our kind can thrive.
Turning to the other type of distinction Sen introduces, we must ask what is the difference between a 'decision' and a 'judgment'? Can there be an intention to judge something without that judgment becoming a ratio for a decision? How can we tell if this is a genuine intention and not hypocrisy simply? Indeed, might it not be something worse? Suppose you contact me and ask to talk to me about the difficulties I face as a Chidambaram look-alike gigolo. You mention that you are concerned with gender inequality in the sex trade. I pour my heart out to you describing my fruitless attempts to find a pimp. Having heard my tale of rejection and hearbreak, you pronounce me the wretchedest wannabe sex-worker you have encountered. I then ask what affirmative action this entitles me to? Your reply is that you don't know and don't care. Decisions of that sort are made- if they are made at all- by somebody else. Your only interest is in judging people. I then beat the shit out of you and get arrested but, coz I represent myself, pretending to be Chidu, the Supreme Court gives me interim protection.
Sen's conclusion is that the classic approach pioneered by Arrow is inadequate to show any 'impossibility result' for interest aggregation but okay for judgement aggregation though less so for judgment decisions. However, if people were genuinely interested in judgment then the impossibility result reappears for interest aggregation. Thus, either Sen is talking worthless shite, or else he has proved that it is impossible to be rational and also interested in justice. This is the opposite of his fundamental assumption in his 'A theory of Justice'.
Did Sen & his ilk have to be such utter fuckwits? Look at Taiwan. In '58, their mathematical economists- people like Sho-Chieh Tsiang & Ta-Chung Liu- convinced Li Kwoh-ting to go for export led growth while India, which had economists of comparable- or greater- stature was doubling down on import substitution and capital-intensive 'turnpike' strategies. South Korea, a little later, took the advise of Irma Adelman and began its spectacular rise. Why did India embrace an obviously stupid course of action? The answer, I think, is that Taiwan & South Korea and even Singapore faced an external threat. They had conscription. The National interest was also the individual's interest because if the enemy prevailed everybody would be worse off. India, on the other hand- long protected by the British and a starving shithole subsequently was coveted by nobody. In vain had Niradh Chaudri pleaded, in his 'autobiography of an unknown Indian', with the White Man to come back. Smart people- and the Bengali buddhijivi has a great belief in his own brilliance- thought they'd be better off as compradors to some new Imperial Master. But there were no takers for the White Man's burden. Nationalism had been a bad bet. Henceforth, the smart Bengali would be anti-national, not in the old fashioned Niradh Babu manner but by pretending to battle Fascism or Nazism or the Spanish Inquisition or, if that failed, Poverty, or Hunger or some other such abstraction best combated on an Ivy League campus.
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