Social choice theory analyzes under which conditions the preferences and values of different individuals can (or cannot) be transformed into social preferences and values capable of legitimizing collective choices. With his famous Impossibility Theorem, Nobel economist Kenneth Arrow was the main founder of this field of study (see Kenneth J. Arrow, Social Choice and Individual Values [Yale University Press, 1963; 1951 for the first edition]). Welfare economics was a precursor of social choice and with similar results: there is no way without arbitrary value judgments to aggregate individual preferences and values in a “social welfare function” representative of the preferences of all individuals.
Here is a simple example. Suppose a society composed of two individuals, A and B. If A’s preferred color is blue and B’s is yellow, is their socially preferred color green, to be coercively imposed on everybody? A and B will be forbidden to buy cars of any other color than green, and forced to knit only green sweaters for their grandkids. The Department of Commerce will allow only green stuff to be imported from China. And so forth. Or is the social choice blue because A is a “dictator.” (The reader will recognize non-dictatorship as one Arrow’s conditions for a representative or legitimate social choice.) The conventional wisdom of our times lies in one or the other of these social choices: all green or all blue; that is, either a sort of vague communitarianism, or the dictatorship of the majority.
Preferences and choices in a real society involve a very large number of goods and activities, which cannot generally be mixed like colors, as well as a large number of individuals with different preferences and values. But the color example may be useful to illustrate the basic problem of social choice.
Except arguably in tribes or in an ideal dictatorship of one person, social choices are collective choices with a certain level of formalism. And collective choices are nothing but government decisions.
For most classical liberals, legitimate collective or governmental choices are possible but only within a restricted domain. Mainstream contemporary economic theory characterizes this restricted domain as the production or financing of “public goods” as formally defined by Paul Samuelson (another Nobel economist) in two 1950s articles in the Review of Economics and Statistics (“The Pure Theory of Public Expenditures” and “Diagrammatic Exposition of a Theory of Public Expenditure”). Economists in the classical liberal tradition have entertained different views of where exactly to limit the domain of collective choices.
James Buchanan, also a Nobel economist, argued that public goods are whatever is publicly provided according to basic constitutional rules unanimously agreed to in an implicit social contract. Buchanan certainly saw the role of the state as more restricted than Samuelson, who was not philosophically a classical liberal. (Among my articles on Buchanan’s theory, see my Econlib review of his 1975 book The Limits of Liberty: Between Anarchy and Leviathan.) Nobel economist Friedrich Hayek saw a free society as an auto-regulated order, which still allowed for a quite wide role of government. (See notably the third part of his Law, Legislation, and Liberty, which I reviewed for Econlib; he later became less tolerant of government power.)
Anthony de Jasay, a fascinating economist and political philosopher who defined himself as both a classical liberal and an anarchist, argued that any social choice is dictatorial: a collective choice necessarily favors some individuals to the detriment of other individuals who are forced to obey and to choose what they would not otherwise have chosen if not for threats of fines and jail if not worse. In other words, a truly social choice is impossible. A “social choice” is always coercively imposed on some peaceful individuals. It is an interesting fact that Buchanan is nearly as critical of “social choice” as de Jasay, except for the possibility of an implicit social contract, which would be the only true social choice. If you are up to deep political philosophy solidly anchored in economics, perhaps the best book to read from de Jasay after The State is his Against Politics: On Government, Anarchy, and Order (Routledge, 1997). Expect to be challenged.
READER COMMENTS
David Seltzer
Dec 22 2023 at 7:20pm
Pierre: Kenneth Arrow quote, “there is no way without arbitrary value judgments to aggregate individual preferences and values in a “social welfare function” representative of the preferences of all individuals.” Arrow may have influenced Myron Scholes when the pricing model for derivatives was developed. Full disclosure. Myron visited the CBOE and we spoke on several occasions. I was a market-maker on the CBOE. His brilliant insight was risk-neutral evaluation. Individual preferences cannot be aggregated, neither can risk preferences. Risk-neutral valuation is independent of risk preferences. The Black-Scholes differential equation would not be independent of risk preferences if it included expected returns on a stock.
Pierre Lemieux
Dec 23 2023 at 10:48am
David: Interesting potential application, although it should be noted that the market is not a mechanism of social choice (Buchanan is quite implicit on that). A contrarian can always make another choice.
Lest we suffer the indignities of Claudine Gay, we should note that the quote you reproduce is my interpretation of the results of welfare economics and not a quote from Arrow. The latter would say he was more nuanced.
David Seltzer
Dec 23 2023 at 11:44am
Pierre: I think Myron, Fischer and Bob Merton developed the model as an applied understanding of the subjective nature of utility. Apologies about the quote gaffe. Good stuff. I have a better understanding of this topic.
Knut P. Heen
Dec 23 2023 at 10:52am
Risk-neutral valuation is not independent of risk preferences. The risk preferences are baked into the state prices. The state prices are treated as “risk-neutral probabilities”, but are really the market valuations of one dollar paid out in these future states (the Arrow-Debreu model). The Black-Scholes model takes the present stock price as an input. The risk preferences are baked into the present stock price.
David Seltzer
Dec 23 2023 at 11:36am
Knut, risk-neutral valuation arises from the Black-Scholes differential equation. The equation does not involve any variables affected by risk preferences of traders. Stock price, volatility, and risk-free rate are in the equation and are independent of risk preferences. Expected returns on securities drop out of the equation because the value of the expected return does depend on risk preferences. This was their dramatic insight as each individual investor has a subjective assessment of risk and, hence, utility. A look at the binomial pricing model will yield a risk-neutral probability distribution. Applied: Standard conversion, Long stock, long put, short call, same strike, same expiry is a risk-neutral hedge. A no arb condition. the deltas of the puts and calls are in fact risk-neutral probabilities. Thanks for your comment. I had to think through this.
Mactoul
Dec 22 2023 at 8:28pm
Jasay is both right and irrelevant. Some are born to rule and others are born to be ruled. This is what a society is and has to be.
Mosca had got it down more than a century ago. Society, or a political community strictly speaking, is formed out of the complementarity of the ruling element and the ruled element.
Jon Murphy
Dec 22 2023 at 10:47pm
Good stuff, Pierre.
It occurs to me there is another problem of social choice: communication.
In the theory of bureaucracy, there is a well-known problem of authority leakage (I believe it was Anthony Downs who first coined this term). Authority leakage is when there is a natural distortion of orders passing from a superior to his subordinates, like in a game of telephone. By the time the orders reach those who have to carry them out, they may be distored so much that the superior’s wishes are not carried out, at least in any manner he would desire.
It occurs to me there is likely a symmetrical problem in social choice: through the communication process, the desires of the collective (however defined) will likely get distorted. Consequently, those tasked with carrying out “the general will” may not be able to do so effectively because the collective cannot effectively communicate its “will” to the ones who have to carry it out. Social choice, then, becomes ambigious. It’s not much more than random guessing. Can it be said to be “choice” in any reasonable sense of the term?
Pierre Lemieux
Dec 23 2023 at 10:39am
Jon: Gordon Tullock notes that the order of the general in the City of Command (to use Jouvenel’s term for the general headquarters in the capital) is not the same when it reaches the soldier in the trenches after hopping through the chain of command. As you note, the problem is multiplied for a more general “social choice” coming from our very collective mouth.
Walt
Dec 22 2023 at 11:59pm
Aren’t we already living under Dictator A? Removing our choices of gasoline-powered cars as well as stoves, lightbulbs and other consumer goods? Dictator A has already removed the choice of smoking a cigarette in a bar and is about to eliminate the choice of menthol-flavoring (and soon the amount of nicotine) in all cigarettes.
Then, too, coming from a different (economically rational) direction, manufacturers also limit our choices to reflect which of their products get the greatest volume in sales. So those who prefer previously available niche flavors or odd sizes become suddenly out of luck. .
Pierre Lemieux
Dec 23 2023 at 10:22am
Walt: Your first paragraph is very relevant to the problem of social choice. The second one, less so (except to the extent that “social choice” limits market competition and entrepreneurship). If I want a pink tie with a pattern of green peas and brown unicorns, it is likely that I won’t be willing to pay the real resource cost of catering to this very minority preference. A large number of other consumers bid up the price of the resources used to manufacture ties of different patterns as well as other goods. Note however that one seldom sees two identical cars on the road, or two identical neckties for that matter. And competition among manufacturers, including those from China or India, if not constrained by dirigisme from one consumer’s own government, virtually insures that I will get the good I want if I am willing to pay its economic (opportunity) cost. This is much less sure if I am a consumer in China, Russia, or North Korea.
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