For social choice this is often used as an introductory book:
Wulf Gaertner: A Primer in Social Choice Theory. Oxford UP 2009.
However, I personally found his proof of Arrow's Theorem cumbersome and not so accessible, and prefer the following books:
Christoph Börgers: Mathematics of Social Choice. Siam Publications 2010.
Alan D. Taylor: Social Choice and the Mathematics of Manipulation. Cambridge UP 2005.
They are both concise and easy to follow if you're familiar with this kind of mathematics (for example, if you have a CS background). As for "popular science" books on social choice, I don't know of any good one and unfortunately have heard a few colleagues in philosophy misinterpret Arrow's Theorem. In that respect it's quite similar to Gödel's Theorems.
Edit: A really good book - once I finished listening to the audiobook version I went right back to the start and listened to it again and I'm going to order a paper version.
Economics is an imperfect field, but a major source of criticism of it is that many people fundamentally object to the idea that you can ask "is" questions about the economy. The only proper questions are "ought" questions, and since economics is mostly about "is" questions, it's automatically suspect.
There really were a group of economists that fit the "license to be bad" stereotype, such as Milton Friedman. But Arrow was not one of them.
One of the themes of the book is that a lot of results from people like Arrow, Coase etc. are misrepresented by those belong to that group. From what I remember it is actually pretty complimentary about Arrow and his work - the criticisms being aimed at those who take such things out of context to further ideological arguments.
Edit: I wish I had a paper copy so I could refer to it more easily!
One of the main criticisms of classical political economy (including Quesnay...) and indeed of modern neoclassical economics is that they pretend not to have any normative content despite, for instance in the case of modern economists, a theory of value whose historical evolution was a direct response to the normative power of labour theories. It is a specific set of ideas in response to a social formation, and it's one reason so many economists are allergic to talking about medieval or ancient economies.
Modern economics doesn't really have a theory of value, which is a 19th century concern. (Arguably, Quesnay was the first person to have a theory of value.) Or, if you prefer, economics have a subjective theory of value. This has some normative content -- if you think the purpose of human existence is the greater glory of God you will find economics pretty disappointing -- but economists no longer try to explain what things are "really" worth.
Your argument is an example of what I mean, though. The labor theory of value lost out on "is" grounds -- there are too many things it can't explain. Now some of the people who made this argument were right-wingers, so if you think that only "ought" questions matter, the fact that people with the wrong notion of "ought" made a contribution proves that the whole thing is morally bankrupt.
There are economic historians, but economists don't talk about medieval or ancient economies just because they don't have much to say. Historians are better equipped to understand them. Though a recent paper applied a trade model (the gravity equation) to predict the locations of Assyrian ruins, so maybe there's more to be done.
A "subjective" theory of value grounded on concepts such as "utility" is still a theory of value, just as a theory of subjective morality is still a theory of morality.
> Now some of the people who made this argument were right-wingers, so if you think that only "ought" questions matter, the fact that people with the wrong notion of "ought" made a contribution proves that the whole thing is morally bankrupt.
I don't think that's the case; there is a distinct break in value theory after Marx, which totally pulls him out of the classical tradition, because he has a "truly social" (as Patrick Murray puts it) theory of value - it is the recognition of its historical specificity. And while it's true that not only neoclassicals objected to the labour theory of value, the current status quo was create through ideological objections veiled as a "revolution". Nevertheless, it is a mistake to view Marx and post-Marx value theory (and here I must emphasize not only value theory but the theory of the value-form) as merely a way to explain prices rather than to explain social dynamics. The subjective theory of value stops before that point, and by limiting its scope to analysis of capital's shadow forms it relies either on ahistorical thought experiments (Robinson Crusoe?) or atomistic views of society. By limiting its scope the theory becomes almost tautological and contentless. The Sraffian objection to the labour theory of value, which is that values are redundant, not only fetishises its claimed ability to explain price, but misses the whole point of the theory. As such, some philosophers who hold to the theory even go as far as to say that it does not hold on the level of the individual commodity, but only on aliquots representative of the lot. It is as if these commentators stopped reading Capital on section 2 of chapter 1.
My point about history is this: economics, in claiming to be scientific, should therefore be held to the same standards as any other science, to explain not only the what but also the why, and for its explanation to be full and complete regardless of time. Its object is intrinsically historical in nature, but either by the "limiting of scope" I talked about before or even projecting the laws of specific social formations on all of history, the task is relegated to economic historians.
The subjective theory of value is just that if people think something has value, then it has value. For a Marxist, telling people they are wrong about their subjective judgements is irresistable, so I can see why they strongly reject it.
Value theory was entombed by Marx' followers. Marx offered a theory that was a) a positive theory on how the economy functioned, b) a normative theory on why capitalism was immoral, and c) a mechanical explanation on why capitalism was doomed. In terms of a and c it has failed. I don't even think this is a damning criticism of Marx -- Smith and Ricardo were wrong about plenty as well. The neoclassicals moved on from Ricardo, but Marxists have refused to move on and instead of enveloped "the theory of value" in a cloud of words to insulate Marx from criticism. Mysteriously, while Smith and Ricardo can be criticized, critics of Marx are always "missing the whole point of the theory".
Economics is not all of social science. The core of economics is the study of markets, though it touches on history, or psychology, or sociology. Markets were pretty peripheral for most of human history, and historical, or psychological, or sociological explanations are more important. Maybe you can explain everything that has ever happened for all of human history, but I sure can't.
The fact that expected utility theory isn't nearly as scrutinized as the labor theory of value, whilst being at least as flawed, tells you something about the "value free" nature of modern econ.
Expected utility theory, if anything, is more scrutinized than the labor theory of value. They gave Kahneman the econ Nobel for (among other things) documenting empirical failings of expected utility.
It... is? The difference is that the labor theory has been thrown out as unsalvageable, whereas expected utility theory is useful enough in some theoretical applications to stick around.
Wulf Gaertner: A Primer in Social Choice Theory. Oxford UP 2009.
However, I personally found his proof of Arrow's Theorem cumbersome and not so accessible, and prefer the following books:
Christoph Börgers: Mathematics of Social Choice. Siam Publications 2010.
Alan D. Taylor: Social Choice and the Mathematics of Manipulation. Cambridge UP 2005.
They are both concise and easy to follow if you're familiar with this kind of mathematics (for example, if you have a CS background). As for "popular science" books on social choice, I don't know of any good one and unfortunately have heard a few colleagues in philosophy misinterpret Arrow's Theorem. In that respect it's quite similar to Gödel's Theorems.