How does a Society decide on what it should do? The answer, in a Democracy, is that it chooses particular agents and entrusts those agents to decide on certain matters. Some of those agents may be chosen through elections. Others may have specific skills and may have risen through merit or seniority. There are five main types of decisions and each has different types of agents in charge of decision making.
1) There is an Executive which decides matters of general fiscal, monetary, military and diplomatic policy. The Chief Executive may be directly elected or may be chosen by Parliament or, during periods of Emergency, be appointed because of some special expertise or popular reverence that they enjoy.
2) there is a Legislature which passes laws and approves the budget. Some portion of it may be directly elected and some may be nominated or belong by hereditary right.
3) there is a Judiciary which is, at least notionally, independent. It may be self-selecting. It may strike down decisions of the Executive or the Legislature. On the other hand, it may have a capacious doctrine of political question such that many such decisions are not justiciable.
4) there is an Army and a professional Civil and Diplomatic Service. It may have countervailing power.
5) there may be corporate interests- e.g. Trade Unions, Professional Associations, Business lobbies etc- which too have countervailing power.
It is also possible that a country may have plebiscites or referendums on particular issues. Here the majority of voters get to directly decide particular matters of policy.
What has never happened and can never happen is a mechanism whereby individual preferences over all social states are aggregated so as to give rise to a Social Choice function. The thing is not mathematically feasible because of problems of complexity, concurrency, computability and categoricity. Moreover, preferences are epistemic and impredicative and thus have no well defined mathematical expression.
Sadly, over the last 75 years, some stupid Mathematical Economists have ignored this obvious truth and written nonsense about a mathematical impossibility.
The Stanford Encyclopaedia of Philosophy's article on Social Choice Theory gives us a flavour of the Alice in Wonderland world which Social Choice theorists live in.
Social choice theory is the study of collective decision procedures and mechanisms.
This is what political analysts do. It is an ideographic matter. Forecasters try to figure out what issue most matters to particular types of voters and thus they try to predict the outcome of elections or else they advise candidates on 'messaging'- i.e. what to emphasize when appealing for votes.
It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs (e.g., votes, preferences, judgments, welfare) into collective outputs (e.g., collective decisions, preferences, judgments, welfare).
Political analysts do look at votes and preferences. They conduct opinion polls and compare the actual behaviour of voters with what what they said they would do or what they said was important to them. Sometimes, it is the personality of the candidate which garners votes, not the policies they advocate. At other times, the reverse is the case.
Central questions are: How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options?
The answer is that they form expectations on the basis of available information or, more commonly, on the bases of their own prejudices and cognitive biases.
What are the properties of different voting systems?
This is a matter for political scientists or commentators.
When is a voting system democratic?
When it gives us the outcome we want. Otherwise it is nothing but Fascism.
How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members’ individual preferences or judgments?
It can say it spent some time trying to do this by canvassing opinions and consulting with interested parties. However, the outcome is arbitrary because at some point, the trigger must be pulled.
How can we rank different social alternatives in an order of social welfare?
We can do so arbitrarily and then seek to justify our ranking.
Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems.
Sadly, what they are doing is eating their own shit.
Pioneered in the 18th century by Nicolas de Condorcet and Jean-Charles de Borda and in the 19th century by Charles Dodgson (also known as Lewis Carroll), social choice theory took off in the 20th century with the works of Kenneth Arrow, Amartya Sen, and Duncan Black.
None of whom were ever consulted by actual politicians. If their theories weren't utterly stupid, they would have had predictive power and thus they would have been much sought after by political parties.
Its influence extends across economics, political science, philosophy, mathematics, and recently computer science and biology.
It has been a waste of time wherever it has been taken up. The thing is nothing but a cascade of intensional fallacies.
Apart from contributing to our understanding of collective decision procedures, social choice theory has applications in the areas of institutional design, welfare economics, and social epistemology
But those 'applications' were mischievous or useless.
The law of large numbers states that as the size of the sample increases the sample mean converges to the true mean. Restated, this is the Condorcet Jury theorem. But it is not something peculiar to Social choice. Indeed, in a given society it is likely that some agents know more than other agents and a better choice is made if only the knowledgeable agents are consulted. Thus the Judge decides matter of law- of which he has expertise- but the jury decides such matters of fact where they are equally competent. However, the Judge may stipulate that they must heed the testimony of a particular expert witness, while disregarding that of another witness who, it is likely, has been bribed to give a particular testimony.
Condorcet’s second insight, often called Condorcet’s paradox, is the observation that majority preferences can be ‘irrational’ (specifically, intransitive) even when individual preferences are ‘rational’ (specifically, transitive).
If such is the case, a representative or other body with authority can recognize this fact. They may use some arbitrary method to break the tie or otherwise prevent cyclicity. Alternatively, there may be some 'horse trading' or bribery. In econ, this is called 'transferable utility'- i.e. money changing hands. What is important to note is that preferences may be 'strategic'- i.e. people deliberately create a tie in the hope of a pay off.
It is foolish to give a mathematical treatment to a situation where 'preference revelation' is a fundamental problem- i.e. where there is no 'Momus window' into the soul such that we can establish what a person's true motivations are. Still, for the purpose of pragmatic mechanism design, we can assume a 'Revelation Principle' such that for a large enough sample, people have no incentive to act strategically.
Arrow introduced a general approach to the study of preference aggregation,
sadly, since preferences are epistemic and impredicative there is no well defined 'extension' (set) corresponding the intension 'Preferences'. Thus no mathematical or logical work can be done in this area. There are no sets and no functions. Still, for some rough and ready purpose we can arbitrarily assume the thing exists so as to make a prediction. But, that's what political analysts, not economists, do.
partly inspired by his teacher of logic, Alfred Tarski (1901–1983), from whom he had learnt relation theory as an undergraduate at the City College of New York (Suppes 2005).
A relation denotes some kind of relationship between two objects in a set. Sadly, if there is 'impredicativity'- e.g. one object depends on the value of another object which in turn depends on its value (which is often the case for epistemic objects) - then there is no set. The thing is not 'well defined'. Arbitrarily, for some purpose we can assume they are independent but though that may be useful, it is not mathematically sound.
Arrow considered a class of possible aggregation methods, which he called social welfare functions,
If there is a function then there must be a graph of the function. But with epistemic objects there is no such graph because of impredicativity. This is nonsense piled on nonsense.
and asked which of them satisfy certain axioms or desiderata.
The answer is obvious. Social Choice is delegated to some authoritative body. It may be elected or it may be (like the Judiciary) staffed by people with expertise in a particular field. There is no 'pure democracy' under the Sun. I suppose some small city state thousands of years ago could have periodic meetings of the entire adult population but the result- as the example of ancient Athens teaches us- was seldom good. Such states were absorbed by big Empires staffed by 'logothete' bureaucrats or Military pro-consuls.
He proved that, surprisingly, there exists no method for aggregating the preferences of two or more individuals over three or more alternatives into collective preferences,
there is also no method of aggregating the preferences of one individual over one alternative- e.g. whether to fart. Sometimes you fart when you don't want to and sometimes you can't fart though the situation calls for nothing less.
where this method satisfies five seemingly plausible axioms, discussed below.
Those 'axioms' were crazy shit.
William Riker (1920–1993), who inspired the Rochester school in political science, interpreted it as a mathematical proof of the impossibility of populist democracy (e.g., Riker 1982).
Yet populist democracies exist. The fact that their behaviour violates 'transitivity'- e.g. guys who voted against Trump four years ago decided to vote for him this time- is explained by the fact that everybody violates it all the time.
Others, most prominently Amartya Sen (born 1933), who won the 1998 Nobel Memorial Prize, took it to show that ordinal preferences are insufficient for making satisfactory social choices and that social decisions require a richer informational basis.
Which isn't available. People act strategically- i.e. they tell lies. There is no 'Momus window' into the soul.
Commentators also questioned whether Arrow’s desiderata on an aggregation method are as innocuous as claimed or whether they should be relaxed
They were nonsense. Why was this not obvious? The answer is that mathsy guys can be as stupid as fuck. Arrow's theorem looks like magic. That is because it is nonsense.
The lessons from Arrow’s theorem depend,
on not understanding that epistemic objects- e.g. Preferences- are impredicative and have no well defined extension. There are no sets or functions in this realm. Social Choice theory is just an availability cascade of 'masked man fallacies' first described in the fourth century BC.
in part, on how we interpret an Arrovian social welfare function. The use of ordinal preferences as the ‘aggreganda’ may be easier to justify if we interpret the aggregation rule as a voting method than if we interpret it as a social evaluation method.
This is mere semantics. You vote based on your evaluation. However, you may do so strategically- e.g. voting for Trump to punish Kamala for not supporting the Palestinians though you know that Trump doesn't give a fart for them.
Sen argued that when a social planner seeks to rank different social alternatives in an order of social desirability (thereby employing some aggregation rule as a social evaluation method), it may be justifiable and even necessary to use additional information over and above ordinal preferences, such as interpersonally comparable welfare measurements (e.g., Sen 1982) or information about people’s capabilities to achieve valuable functionings (e.g., Sen 1992).
Sen is Bengali. There is a strong Fascist streak in the Bengali. They want a strong leader who does whatever he wants. Alternatively, maybe the Bench could usurp all power and do whatever stupid shit Bengali economists want to see done.
Arrow himself held the view
‘that interpersonal comparison of utilities has no meaning
Because a guy who says 'I really really want to fuck my best friend's wife. I would get more utility from fucking her than he would' is making an interpersonal comparison of utility. Sen did in fact run off with his best friend's wife. Arrow didn't want the same thing happening to him.
and … that there is no meaning relevant to welfare comparisons in the measurability of individual utility.’ (1951/1963: 9)
You can always give such a meaning to 'preference intensity'. Sen was prepared to wreck his career in India by running off with his best friend's wife. Fortunately, he landed on his feet at the LSE. Still, there was a time when other Bengali economists made fun of him because he had to iron his own shirts and didn't even have a chauffeur. Then he married a Rothschild.
Nowadays most social choice theorists have moved beyond the negative interpretations of Arrow’s theorem and are interested in the trade-offs involved in finding satisfactory decision procedures and the possibilities opened up by relaxing certain restrictive assumptions.
This is cool if you are a UN bureaucrat or enjoy attending Conferences where everybody can virtue signal while claiming fat per diems.
Sen has promoted this ‘possibilist’ interpretation of social choice theory (e.g., in his 1998 Nobel lecture).
In other words, wasting money for high minded reasons. Consider the plight of starving people. Many of them may not know that eating nice food will be beneficial to them. Moreover, some of them may be Lesbian. Just sending food to these starving people would be a grave injustice. We must consider the Capabilities and Functionings of starving Lesbians. Consider their ability to jump up and down. Just giving them food may distract them from developing this valuable functioning or Capability.
Moreover, as Fabienne Peter has argued, by moving beyond the narrow informational basis leading to the classic impossibility results, social choice theory can become a more promising framework for policy evaluation and offer resources for taking into account the situated nature of people’s agency, inequalities between them, and issues of gender (Peter 2003).
In other words, you can virtue signal like crazy while criticizing the FAO and the Gates Foundation for wanting to 'help' starving Lesbians by giving them food and medicines while completely neglecting their 'agency' and capability to jump up and down.
In contemporary social choice theory, it is perhaps fair to say, Arrow’s axiomatic method is more influential than his impossibility theorem itself (on the axiomatic method, see Thomson 2000).
Arrow neglected Knightian Uncertainty. That's why Arrow Debreu securities are 'weapons of mass financial destruction'. As for Social Choice theory, it is neither concerned with Society nor with Choice. It is merely pseudo-mathsy masturbation.
In mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it. The problem here is that epistemic objects have no mathematical characterization. They can't be logically equivalent to anything, even themselves, because Leibniz's laws have no purchase on them.The paradigmatic kind of result in formal work is now the ‘characterization theorem’.
Here the aim is to identify a set of plausible
plausible to fucking morons
necessary and sufficient conditions that uniquely characterize a particular solution (or class of solutions) to a given type of collective decision problem.
One can give an arbitrary extension to relevant intensions for some particular purpose. But there are no necessary of sufficient conditions for what is merely arbitrary. Either the thing is useful enough or it can't 'pay for itself' and must be discarded.
Two points about the concept of an aggregation rule are worth noting. First, under the standard definition, an aggregation rule is defined extensionally, not intensionally:
the problem is that epistemic objects don't have well defined extensions. You can arbitrarily assign such an extension for some practical purpose and this may be useful in a rough and ready fashion. But as our knowledge base changes, that 'extension' becomes less and less useful. Back in 2007, it seemed obvious to me that a black man named Barak Hussein Obama was unelectable. In 2015, it seemed obvious that a fat pussy-grabbing Billionaire was unelected. Women would vote overwhelmingly for Hilary as would African Americans and Hispanics. I was wrong.
it is a mapping (functional relationship) between individual inputs and collective outputs, not a set of explicit instructions (a rule in the ordinary-language sense).
Sadly, it isn't a mapping because there is no well defined 'graph of the function'. We can pretend otherwise for some practical purpose, but this is pretence. It isn't mathematics.
Different sets of instructions could in principle give rise to the same mapping from inputs to outputs. Secondly, an aggregation rule is defined for a fixed set of individuals N and a fixed decision problem, so that majority rule in a group of two individuals is a different mathematical object from majority rule in a group of three.
There is no 'mathematical object'. There may be an arbitrary mathematical assignation for some particular purpose.
One potential disadvantage of this way of defining an aggregation rule is that it makes it harder to determine how a given aggregation rule is to be extended to inputs outside the function’s formal domain.
Or inside it. Our preferences are epistemic and impredicative. Moreover, there is regret minimizing behaviour which militates for 'discovery' and 'FOMO' (fear of missing out). We don't have a model for individual choice much less preference formation where there are 'Tardean' effects and other sorts of 'crowd psychological' effects.
By contrast, if we were given an explicit set of instructions, it might be easier to infer, for instance, how these are to be extended from the case of n +1
The principle of induction falls down in the one person, one alternative, case. Should I have a decision rule or not? No. It is a waste of time. Suppose someone else joins me. Should we have a decision rule? No. It is silly. A third person arrives. Now there is a 'tie breaker'. Should we have a decision rule? No. The other two may gang up on me. The result is we have no decision rule for all social states. We may cobble together some mechanism for specific 'collective action problems'. But there will be 'transferable utility' more particularly to solve 'hold out' problems. With bigger numbers, you may have elections to decide fiscal questions (Taxation can rise if you have Representation), but you would also have 'Checks and Balances' and a pretty opaque sort of politics conducted in smoke filled rooms. There will be 'log rolling' and 'pork barrel' politics and a continuous attempt to make the policy space more and more multi-dimensional so that, by the McKelvey chaos theorem, 'agenda control' becomes more and more important. In other words, you would get the pig's breakfast we see in democratic countries around the world today. Still, the alternative would be worse. King Trump would be worse than President Trump.
One other point. Social alternatives are infinite. Consider a single period economy where my alternatives are 'fart' or 'don't fart'. I can add the alternative 'fart if Mochizuki's proof of the abc theorem is valid' or 'Don't fart if Jennifer Aniston is a fat Australian man' and so forth. In practice, voting is seldom just about the candidates. You may vote to register a protest against things in general or abstain from voting because you think things in general are perfectly fine. My own concern is that Jennifer Aniston may actually be a fat Australian man. Australians are very good actors. What if I have been beating my meat while imagining an Ozzie dude? OMG! What if I'm Gay!
May (1952) introduced four requirements:
Universal domain: The domain of admissible inputs of the aggregation rule consists of all logically possible profiles of votes , where each .
Presumably voting is compulsory. Even so, these 'profiles' are post hoc. We may assume they correspond to 'preferences' but can't be sure.
Anonymity: For any admissible profiles and that are permutations of each other (i.e., one can be obtained from the other by reordering the entries), the social decision is the same, i.e., .
So, this does not apply to a representative democracy where voters in 'swing states' may have more influence on the outcome. Also, though elections may change who the legislators are, it may not change the social decision. Finally, 'anonymity' scarcely exists where people 'vote their caste' rather than just cast their vote.
Neutrality: For any admissible profile , if the votes for the two alternatives are reversed, the social decision is reversed too, i.e., .
Elections have magical properties. Thus when FDR was elected as the man who kept and would keep the US out of the war, the US stayed out of the War.
Positive responsiveness: For any admissible profile , if some voters change their votes in favour of one alternative (say the first) and all other votes remain the same, the social decision does not change in the opposite direction;
That's why the US did not enter the Second World War. Tojo and Hilter won.
if the social decision was a tie prior to the change, the tie is broken in the direction of the change, i.e., if [ for some and for all other ] and or 1, then .
Sadly, the direction of the change may be opposite to that which was voted for.
Universal domain requires the aggregation rule to cope with any level of ‘pluralism’ in its inputs;
Suppose we vote for a guy thinking he will do x. He then does the opposite perhaps because of exogenous pressure. We may still rebel and kill him. Elections don't have magic powers.
anonymity requires it to treat all voters equally;
Though some voters have more power to select candidates or set the agenda
neutrality requires it to treat all alternatives equally; and positive responsiveness requires the social decision to be a positive function of the way people vote. May proved the following:
Theorem (May 1952): An aggregation rule satisfies universal domain, anonymity, neutrality, and positive responsiveness if and only if it is majority rule.
Sadly, 'majority rule' may involve the collapse of the state. Aggregation rules have no magical powers. If a country does stupid shit, it may cease to be a country. That is why successful Democracies have 'checks and balances'. In any case, what voters may really want is that sensible things are done. They may not want 'majority rule' because this would mean the collapse of the country.
Apart from providing an argument for majority rule based on four plausible procedural desiderata,
there is no 'argument' here. May merely described the way he thought universal suffrage works. He was wrong.
the theorem helps us characterize other aggregation rules in terms of which desiderata they violate.
No. It is obviously shite.
Dictatorships
May be wildly popular.
and weighted majority rules with unequal individual weights
e.g. the system the US and the UK have
violate anonymity.
people who live in 'swing states' or constituencies know that they will be courted by all political parties. They will seek to translate this into economic benefits.
Asymmetrical supermajority rules (under which a supermajority of the votes, such as two thirds or three quarters, is required for a decision in favour of one of the alternatives, while the other alternative is the default choice) violate neutrality.
But may be necessary to prevent the country going up in flames.
This may sometimes be justifiable,
Anything at all may be justifiable under some circumstance. Most countries have a 'State of Exception' whereby the Executive can wield emergency powers.
for instance when there is a presumption in favour of one alternative, such as a presumption of innocence in a jury decision.
I suppose one might say that the doctrine of political question presumes the Executive acts in the public interest.
Symmetrical supermajority rules (under which neither alternative is chosen unless it is supported by a sufficiently large supermajority) violate positive responsiveness.
So does the fact that wishes aren't horses which beggars are welcome to ride.
Some societies can only survive with 'majority rule'. But this may be done democratically or dictatorially or by some other traditional type of social mechanism. Other societies can't survive with 'majority rule'. The experiment of democracy is soon given up and you have the rule of a strong-man though this may be disguised by fraudulent elections.
In practice, 'preference intensity' can express itself in various ways- e.g. by raising funds for lobbying or political activism or else by establishing a 'threat point' such that the Executive fears a confrontation with a particular interest group.
Economists may not be aware that all Societies have some sort of legal system which holds certain activities to be repugnant. Legislatures may be able to change this but may lack the incentive to do so. Sometimes the Courts step in to move matters along or else the letter of the law ceases to be enforced.
Although the weak Pareto principle is arguably one of the least contentious ones of Arrow’s conditions,
it is meaningless. Nobody knows if it applies. Some will falsely claim they are adversely affected and demand compensation. Others may fear the thing is 'the thin end of the wedge' or invoke 'Chesterton's fence'- i.e. the notion that there must be a good thing our ancestors didn't permit the thing.
Sen (1970a) offered a critique of it that applies when the aggregation rule is interpreted not as a voting method, but as a social evaluation method
it is not a method. We merely say 'if people voted for this, they must want it and consider it superior to what went before.'
which a social planner can use to rank social alternatives in an order of social desirability. Here, the alternatives are understood not as coarse-grained electoral options but as more richly specified states of society.
Sadly, only a dude who knows a lot about a particular society can make this specification. Mathematical economists don't know shit about shit.
Sen showed that, in this setting, the Pareto principle conflicts with a ‘liberal’ principle, which—he suggested—a social planner ought to respect.
It doesn't. This is because nobody knows what it requires.
The liberal principle requires that each individual be given some basic rights, to the effect that his or her preferences are sometimes socially decisive (i.e., cannot be overridden by others’ preferences).
No. Liberalism upholds the rule of law such that people have defeasible Hohfeldian immunities in certain matters.
Intuitively, each individual has a personal sphere in which this individual alone should be able to decide what happens.
This is not the case. All Hohfeldian incidents are defeasible. In other words, under certain circumstances a particular immunity is cancelled by some superior entitlement enjoyed by some other party.
To give a trivial example, I alone should be able to decide whether I sleep on my right side or on my left side, and the same should be true for everyone else.
No. There may be some sick person who must only sleep on his right side and this rule may be enforced by the hospital staff. Suppose he finds this unreasonable and approaches the court. The judge may rule that he is not competent to decide what is best for himself. It permits the hospital staff to continue to restrain him from sleeping on his left side.
So, if two social alternatives, xx and yy, differ only with respect to the side on which individual ii sleeps, then individual ii’s preference between xx and yy should determine the social preference between xx and yy.
We don't know how any two social alternatives differ. A court may accept expert testimony. But that testimony may be wrong.
(Recall that alternatives are here understood as richly specified states of society.)
Which are unknown and unknowable to us.
Sen’s ‘minimal liberal’ requirement says that at least two individuals in society should have such a decisiveness right between two alternatives each.
There is no such requirement in any liberal society under the rule of law. All Hohfeldian incidents are defeasible.
To illustrate the conflict between minimal liberalism and the weak Pareto principle, Sen asked us to imagine a society that consists of two individuals, Lewd and Prude, faced with the decision of who among them (if any) should read a controversial book, Lady Chatterley’s Lover.
This is a question about 'repugnancy' markets. At one time, material which might cause people to masturbate was considered repugnant. This was because masturbation was considered very harmful. We no longer think that way.
In Sen’s story, Lewd most prefers that Prude read the book (alternative x)x),
just as Prude most prefers that Lewd enter a Convent and take Holy Orders. It isn't an actual preference. It is like my saying 'I wish pigs could fly. I bet that would fly over Trump's head and shit on him'.
second-most prefers that he (Lewd) read the book himself (alternative y)y), and least prefers that neither of the two read the book (z)(z). Prude most prefers that neither read the book (z)(z), second-most prefers that he (Prude) read the book himself (x)(x), and least prefers that Lewd read the book (y)(y). Assuming Lewd is decisive over the pair yy and zz, society should prefer yy to zz.
This is nonsense. The matter is justiciable. The Court may ban the book if approached by Prude. It may reverse the ban if Lewd assembles experts to testify to the book's literary value. Neither Prude no Lewd are decisive. The Court is.
Sen generalized this problem—now known as the ‘liberal paradox’—as follows.
Theorem (Sen 1970a): There exists no preference aggregation rule satisfying universal domain, acyclicity of social preferences, the weak Pareto principle, and minimal liberalism.
We don't and can't know that because there may, after our species has died out, be a way of 'factorizing' everything in our social or psychological sphere such that all epistemic 'intension's have well defined 'extensions' (in other words, nothing would be impredicative because we have found independent elements for all epistemic sets. At that point, there may be a non-arbitrary aggregation rule. But it would not be known to us. It would be known to some advanced species which has the technology to uncover all relevant facts about our species.
This result suggests that if we wish to respect individual rights, we may sometimes have to sacrifice Paretian efficiency.
Nobody knows what is or isn't a Pareto improvement. The thing is epistemic and changes as our knowledge base changes.
Hence, Sen’s spoke of the ‘impossibility of a Paretian liberal’.
Though plenty of such people existed and were personally known to Sen. I suppose, as a Bengali, he preferred Fascism or Communism to Liberal Democracy though he had to pretend otherwise so as to get the Nobel Prize.
An alternative conclusion is that the weak Pareto principle can be rendered compatible with minimal liberalism only if the domain of admissible preference profiles is suitably restricted, for instance to preferences that are ‘tolerant’ or not ‘meddlesome’ (Blau 1975; Craven 1982; Gigliotti 1986; Sen 1983).
In which case Liberalism would be banned. It is rather intolerant of intolerant despots.
Lewd’s and Prude’s preferences in Sen’s example are ‘meddlesome’.
No they differ as to what is or isn't a repugnancy market. There is an issue of public policy at the bottom if their disagreement. Sen invented a fantastic detail, viz Lewd wants Prude to read the book while fisting herself vigorously, in order to pretend that there is some 'meddlesome' aspect to their preferences.
Each of them ‘meddles’ with the other’s private sphere.
No. It is obvious that when I say 'I wish you'd grown a pair of titties and spend all your time playing with them', that I am not expressing a preference relevant for Social Choice.
However, several authors have challenged the relevance of Sen’s result, by arguing that his ‘minimal liberalism’ condition uses an inadequate formalization of the notion of individual rights (e.g., Gaertner, Pattanaik, and Suzumura 1992; Dowding and van Hees 2003).
Those nutters don't understand that 'rights' are merely a bundle of defeasible Hohfeldian incidents. What matters if there is an obligation holder for whom providing remedies is incentive compatible.
The Gibbard Satterthwaite theorem, anticipated by Dummett & Farquharson, merely states what everybody has always known, everything political involves lying- i.e. 'strategic behaviour'.
Universal domain: The domain of ff is the set of all logically possible profiles of complete and transitive individual preference orderings.
It is unknowable which is why it can't be a domain or range or set of any type.
Non-dictatorship: There does not exist an individual i∈Ni∈N such that, for all ⟨R1,R2,…,Rn⟩⟨R1,R2,…,Rn⟩ in the domain of ff and all xx in the range of ff, yRixyRix where y∈f(R1,R2,…,Rn)y∈f(R1,R2,…,Rn).[7]
Nothing wrong with their being a dude who always happens to vote the right way. A Dictator is a guy who can kill his rivals. The question is whether it is known that such an individual exists. If so, his saying he will vote a particular way may alter outcomes. He functions like an Oracle or the millionaire in Newcombe's problem.
The range constraint: The range of ff contains at least three distinct alternatives (and ideally all alternatives in X)X).
We don't know if they are distinct. We vote for Smith rather than Jones or Brown but later realize that Smith will do exactly what Brown would have done. As for Brown, he was only put up to split the vote for Jones.
When supplemented with an appropriate tie-breaking criterion, the plurality and Borda rules can further be made ‘resolute’:
Resoluteness: The social choice rule ff always produces a unique winning alternative (a singleton choice set).
Why should it? If voting uncovers new information, maybe it would be better to run the thing again. Moreover, we don't know if unicity obtains. Any political outcome may in fact be multiply realizable.
Surprisingly, this list of conditions conflicts with the following further requirement.
Every linguistic or social practice conflicts with it. People tell lies. Sad.
Strategy-proofness: There does not exist a profile ⟨R1,R2,…,Rn⟩⟨R1,R2,…,Rn⟩ in the domain of ff at which ff is manipulable by some individual i∈Ni∈N, where manipulability means the following: if ii submits a false preference ordering R′iRi′ (≠Ri)(≠Ri), the winner is an alternative y′y′ that ii strictly prefers (according to Ri)Ri) to the alternative yy that would win if ii submitted the true preference ordering RiRi.[8]
Anybody can be fooled by anybody or may be unable to do anything about the other's blatant lies.
Theorem (Gibbard 1973; Satterthwaite 1975): There exists no social choice rule satisfying universal domain, non-dictatorship, the range constraint, resoluteness, and strategy-proofness.
Sadly, this can't be proved mathematically because we have no access to well defined sets. The problem with the 'intensional fallacy' is that nothing whatsoever can be said about epistemic objects. They change as the knowledge base changes or as bigotry spreads.
I suppose Gibbard Satterthwaite was useful because it changed the focus to 'mechanism design' and incomplete contract theory. But, at the end of the day this is ideographic and has always been done by those with relevant skill and expertise even if they don't talk about it honestly. What was comic was that the post Gibbard literature mentioned computational problems. But such problems also kills off Arrow-Debreu. The time class for the solution to General Equilibrium is exponential. The Capabilities approach is founded in Arrow-Debreu. Thus, it it too is ab ovo useless.
Welfare Economics is part and parcel of the theory of Public Finance. If money raised by taxation is used to solve collective action problems, Income rises and thus Tax revenue rises. There is a virtuous circle. A.O Hume, setting up the Indian National Congress, tried to explain this to Indians. Sadly, they were only interested in virtue signalling and pretending the Viceroy had a magical money tree and was refusing to use it to buy starving Indians some nice food to eat. Consider
Sen’s extension of Arrow’s framework
An assumption built into Arrow’s framework is that preferences are ordinal and not interpersonally comparable:
in any objective sense. But I can look around and find someone doing better than me and try to imitate him.
preference orderings contain no information about each individual’s strength of preference or about how to compare different individuals’ preferences with one another.
You could look at how much people will pay or how many buses they will burn down to get what they want. That's a measure of preference intensity.
Statements such as ‘Individual 1 prefers alternative xx more than Individual 2 prefers alternative yy’
us if the second dude give up yy so that the first gets xx. Money may change hands to facilitate this.
or ‘Individual l prefers a switch from xx to yy more than Individual 2 prefers a switch from x∗x∗ to y∗y∗’ are considered meaningless.
Arrow-Debreu was meaningless. In any case, it was 'anything goes'.
In voting contexts, this assumption may be plausible, as we often may not be able to elicit more information from voters than their ordinal rankings of the options.
Fuck off! Pollsters spend a lot of money getting such information.
But in welfare-evaluation contexts—when a social planner seeks to rank different social alternatives in an order of social welfare—
there has never been any such Benthamite planner. There may be a bit of money for 'project appraisal' or 'Cost Benefit analysis' but this was just window dressing. He who paid the piper called the tune. He might also pay for some dude to say it was a very nice tune. Sen and his best friend wrote a paper hinting at this before Sen ran off with his best friend's wife to London.
the use of richer information may be justified.
Bureaucrats and 'activists' are welcome to gas on about this. But nothing gets done unless some oligarch pays the fucking piper and goes ahead with the project.
Sen (1970b) generalized Arrow’s framework to incorporate such richer information.
As before, consider a set N={1,2,…,n}N={1,2,…,n} of individuals (n≥2)(n≥2) and a set X={x,y,z,…}X={x,y,z,…} of social alternatives.
Those alternatives are unknown.
Now each individual i∈Ni∈N has a welfare function WiWi over these alternatives, which assigns a real number Wi(x)Wi(x) to each alternative x∈Xx∈X, interpreted as a measure of ii’s welfare under alternative xx.
Sen noticed that starving Indian villagers where too busy assigning such numbers to grow food to eat.
Any welfare function on XX induces an ordering on XX, but the converse is not true: welfare functions encode more information.
They don't exist. Unicorns encode a lot of information. If they shove their horn up your bum you will become very enlightened.
A combination of welfare functions across the individuals, ⟨W1,W2,…,Wn⟩⟨W1,W2,…,Wn⟩, is called a profile.
A social welfare functional (SWFL), also denoted FF, is a function that assigns to each profile ⟨W1,W2,…,Wn⟩⟨W1,W2,…,Wn⟩ (in some domain of admissible profiles) a social preference relation R=F(W1,W2,…,Wn)R=F(W1,W2,…,Wn) on XX, with the familiar interpretation. Again, when FF is clear from the context, we write RR for the social preference relation corresponding to ⟨W1,W2,…,Wn⟩⟨W1,W2,…,Wn⟩. The output of a SWFL is similar to that of a preference aggregation rule (again, we do not build the completeness or transitivity of RR into the definition[9]), but its input is richer.
There is a feasible social state which we would all prefer. It is one where there is virtually free energy and everybody has a 3-D printers which make us anything we want. Sadly, our Scientists haven't yet discovered how to build such things. I suppose they will at some point in the future. The problem with Sen-tentious shite is that it pretends there are no epistemic problems. We already have all possible knowledge.
What we gain from this
is nothing. It is a fairy story.
depends on how much of the enriched informational input
which is wholly inaccessible to us
we allow ourselves to use in determining society’s preferences:
Society told Social Choice theorists to fuck the fuck off. That was their preference. Sen had and has no power. Manmohan was a two term PM. Even Yunus is now running Sen's ancestral East Bengal. Stuff like Trade theory or Micro-credit is real. Social Choice theory is shitting higher than your arsehole.
technically, it depends on our assumption about measurability and interpersonal comparability of welfare.
Just as gaining enlightenment when a unicorn shoves its horn up our rectum depends on our assuming such unicorns exist.
By assigning real numbers to alternatives,
magical powers are gained.
welfare profiles contain a lot of information
Sadly, if I assign you the number 2476563 no information is gained.
over and above the profiles of orderings on XX they induce.
For example, it is discovered that not only are you inferior to me (because I am number one on this list of lovely peeps) but also you are odd. Why don't you just top yourself, you loser?
Many different assignments of numbers to alternatives can give rise to the same orderings.
So the thing has no unicity. It is wholly arbitrary.
But we may not consider all this information meaningful. Some of it could be an artifact of the numerical representation. For example, the difference between the profile ⟨W1,W2,…,Wn⟩⟨W1,W2,…,Wn⟩ and its scaled-up version ⟨10⋅W1,10⋅W2,…,10⋅Wn⟩⟨10⋅W1,10⋅W2,…,10⋅Wn⟩, where everything is the same in proportional terms, could be like the difference between length measurements in centimeters and in inches. The two profiles might be seen as alternative representations of the exact same information, just on different scales.
Also, if you multiply everything by 69, then fellatio and cunnilingus will increase exponentially.
To express different assumptions about which information is truly encoded by a profile of welfare functions and which information is not (and should thus be seen, at best, as an artifact of the numerical representation), it is helpful to introduce the notion of meaningful statements.
No statement by Sen has been meaningful though all have been mischievous in some way.
Some examples of statements about individual welfare that are candidates for meaningful statements are the following
A level comparison: Individual i’s welfare under alternative xx is at least as great as individual jj’s welfare under alternative yy, formally Wi(x)≥Wj(y)Wi(x)≥Wj(y). (The comparison is intrapersonal if i=ji=j, and interpersonal if i≠ji≠j.)
This is an arbitrary assertion. We don't know our own level of welfare. That's why we get a rude shock after visiting our Accountant or our Doctor. Still, if the horn of the omniscient unicorn simultaneously enters all our rectums, then Sen-tentious Social Choice theory might not be an utter wank. I omit the other comparisons mentioned in the article. The fact is such things have never existed because they are too costly and yield no benefit whatsoever. What can be done is estimating how much tax a factor will pay before it decides to fuck off. Public Finance matters. Welfare Econ does not.
Arrow’s view, as noted, is that only intrapersonal level comparisons are meaningful, while all other kinds of comparisons are not.
They are highly meaningful. They drive mimetic effects and change Society. If you can spot such effects 'at the margin' you can make good predictions. You will be well paid and won't have to teach nonsense to credential craving imbeciles.
Still, it is worth pointing out that the Szpilrajn extension theorem shows that any ordinal ranking can give rise to a cardinal measure. So what? We neither have the one nor the other. The plain fact is utility either means 'money' or it is bullshit. Money talks. Bullshit walks.
I suppose a Dictator could hire a bunch of guys to do 'interpersonal comparisons' and calculate Cardinal Utility for everybody. They may show that what Jews really really want is to hand over all their property to Gestapo officers before hopping on a cattle truck to the gas chamber while whistling a merry tune. What would be pricelessly funny would be if some guy working for that dictator published a theorem showing that there could be a SWF which was non-dictatorial and fulfilled all Arrow's other conditions.
I suppose, Social Choice theory is inherently dictatorial because it assumes people won't tell it to fuck the fuck off. Rawlsian Social Contract theory is similarly flawed. No Contract is valid without the passing of consideration. Don't agree to anything unless you get paid.
An important conclusion, therefore, is that Rawls’s difference principle, the classical utilitarian principle, and even the head-count method of poverty measurement can all be seen as solutions to Arrow’s aggregation problem
just like the establishment of a Caliphate after the slaughter of all kaffirs, munafiqs and women who talk too loud.
that become possible once we go beyond Arrow’s framework of ordinal, interpersonally non-comparable preferences.
Caliphate will go beyond Rawls and Sen. Did you know that what kaffirs really really want is to have their throats slit? True, some- like Sen's parents- may run away from East Bengal before this can happen but that is only because kaffirs are 'jahil'- i.e. ignorant.
I suppose Social Choice theorists and Moral Philosophers were beginning to realize that they had chosen a wholly useless profession. Smart people had gained money or wealth or great political influence. Moreover the working class had rebelled against 'equity' and 'redistribution'. They wanted higher living standards and admired self-made billionaires.
...minimal equity, requires (in the words of Sen 1977: 1548) ‘that a person who is going to be best off anyway does not always strictly have his way’,
Unless people think he is smart and should have his way because society will benefit thereby. Meanwhile useless academics should be told to fuck the fuck off.
and another, separability, requires that two welfare profiles that coincide for some subset M⊆NM⊆N while everyone in N∖MN∖M is indifferent between all alternatives in XX lead to the same social ordering.
Or not. Nobody cares because social orderings don't exist. I suppose Social Choice theorists- more particularly after mainstream Journals started to refuse to publish their shite towards the end of the Seventies- realized that they were pretty much at the bottom of the pecking order. Sen had to iron his own shirts in London while Manmohan lived in a mansion with lots of servants as head of the RBI. Then the fucker became Finance Minister and a great hero to India's middle class. Sen's cup of bitter waters overflowed.
‘prioritarian’ SWFLs sum up concavely transformed welfare, giving greater marginal weight to lower levels of welfare.
like the lower welfare of Sen relative to Manmohan or the billionaire Purnendu Chatterjee. The Swedes gave this brown monkey a Nobel for having bravely resisted the temptation to starve to death.
What is the future of Social Choice theory? I think the answer is that it will converge to Ethology. It is likely that the true determinants of responses to collective action problems is a biologically deeper level than epistemic notions like 'preferences' and 'expectations'. Societies have to compete for scarce resources. Some will use 'costly signals' and gravitate to better 'separating equilibria' while others indulge in 'cheap talk' and lose control of resources.
Future historians might consider the vogue which Social Choice enjoyed between about 1950 and 1970 to have to do with the lingering memory of war-time planning and the belief that the Command Economies were catching up, or even surpassing, the Democracies. Equally, the rise of a mathematical Marxian theory seemed to require the RAND corporation and that portion of the Social Science establishment which required State funds to expand to come up with a 'mathsy' alterative. But it set its sights too low. It was merely saying, 'whatever a Command economy can do, we too can do by getting the incentive structure right'. What was missing was a Hayekian vision of the difficulties of information aggregation. Also, neglect of Knightian Uncertainty fatally vitiated the whole program. Then came the mathematical problems of computability, complexity, concurrency and the fact that category theoretical 'naturality' or unicity are far to seek. However, it was the 'intensional fallacy'- this business of pretending an epistemic object can be a set- which permitted this gawdy availability cascade to fascinate a generation of mathsy shitheads.
No comments:
Post a Comment