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This paper initiates the reverse mathematics of social choice theory, studying Arrow’s impossibility theorem and related results including Fishburn’s possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics. We formalise fundamental notions of social choice theory in second-order arithmetic, yielding a definition of countable society which is tractable in ${\mathsf {RCA}}_0$. We then show that the Kirman–Sondermann analysis of social welfare functions can be carried out in ${\mathsf {RCA}}_0$. This approach yields a proof of Arrow’s theorem in ${\mathsf {RCA}}_0$, and thus in $\mathrm {PRA}$, since Arrow’s theorem can be formalised as a $\Pi ^0_1$ sentence. Finally we show that Fishburn’s possibility theorem for countable societies is equivalent to ${\mathsf {ACA}}_0$ over ${\mathsf {RCA}}_0$.
In the literature on philosophical progress it is often assumed that agreement is a necessary condition for progress. This assumption is sensible only if agreement is a reliable sign of the truth, since agreement on false answers to philosophical questions would not constitute progress. This paper asks whether agreement among philosophers is (or would be) likely to be a reliable sign of truth. Insights from social choice theory are used to identify the conditions under which agreement among philosophers would be a reliable indicator of the truth, and it is argued that we lack good reason to think that philosophical inquiry meets these conditions. The upshot is that philosophical agreement is epistemically uninformative: agreement on the answer to a philosophical question does not supply even a prima facie reason to think that the agreed-upon view is true. However, the epistemic uninformativeness of philosophical agreement is not an indictment of philosophy's progress, because philosophy is valuable independent of its ability to generate agreement on the correct answers to philosophical questions.
In Chapter 7, I discuss the latest crisis of capitalism and Amartya Sen’s journey to rescue capitalism from the capitalists. I begin by discussing the increasing vulnerability of capitalist societies at the end of the twentieth century due to the deregulatory environment encouraged by the Chicago School. I use Karl Polanyi’s double-movement theory to explain the rise of the Chicago School and its assault on the “relationship capitalism” that had evolved in the postwar period. While the new “investor capitalism” was successful at unleashing the power of the market, it also increased the vulnerability of capitalist societies to opportunistic self-interest. This increased vulnerability was fully realized in the 2007–08 mortgage-backed security crisis that nearly collapsed the global financial system. After describing the near collapse of the global financial system, I discuss the implications of the collapse for the neoclassical theory out of Chicago. This leads to a discussion of Amartya Sen’s journey from India to the West to rescue capitalism from the capitalists. This discussion introduces the role of the East in the development of capitalism and its future promise. I conclude by discussing Sen’s critique of capitalism based on Adam Smith’s original moral foundation.
Chapter 6 shows how false Stories help to perpetuate the economic imbalance described in Chapter 4. These Stories include those of economic growth, comparative advantage, creative destruction, and ceaseless innovation. Most of them originate in mainstream economics, including praise for shareholder interests and insistence on social choice theory. Karl Polanyi claimed that such Stories, which endorse a society roiled by constant change, ignore what he called community welfare.
Chapter 4 sketches the contemporary theory of economic welfare. It argues that welfare economics is a theoretically driven discipline, whose questions are determined more by equilibrium theory than by practical problems of economic welfare. Section 1 begins with the fundamental question: what is welfare or, synonymously, well-being? Section 2 explains why the answer that economists give has led them to eschew utilitarianism, and it links this chapter to the previous three, presenting the fundamental theorems of welfare economics, the grounds for the admiration economists have for the operation of perfectly competitive markets, the problems of markets that are not perfectly competitive, and further theorems concerning social choice and welfare. Section 3 turns to practical work in welfare economics and the foundations of cost-benefit analysis. Section 4 ends with an overview, including some remarks about alternatives to mainstream normative economics.
This chapter critically examines the argument that Arrow’s theorem supports giving the corporate vote to shareholders alone. We begin by laying out the argument and distinguish it from two, related arguments: the argument from politics and the argument for absolute delegation. We then show that the Arrow’s theorem argument is flawed on many fronts. Shareholder preferences are not, as supposed, homogeneous. Even if they were homogeneous, they would not translate into the kind of agreement on board candidates necessary to avoid intransitive corporate election results. Finally, restricting voting rights to shareholders gives up a fundamental condition of democracy in a situation where the likelihood and impact of intransitive results are already negligible.
We present a model of collective decision making in which aggregation and deliberation are treated simultaneously. Individuals debate in a public forum and potentially revise their judgements in light of deliberation. Once this process is exhausted, a rule is applied to aggregate post-deliberation judgements in order to make a social choice. Restricting attention to three alternatives, we identify conditions under which a democracy is ‘truth-revealing’. This condition says that the deliberation path and the aggregation rule always lead to the correct social choice being made, irrespective of both the original profile of judgements and the size of the electorate.
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