Incompleteness, Independence, and Negative Dominance

This paper introduces the axiom of Negative Dominance, stating that if a lottery $f$ is strictly preferred to a lottery $g$, then some outcome in the support of $f$ is strictly preferred to some outcome in the support of $g$. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent

Preference structures and their numerical representations

AbstractThis paper presents a selective survey of numerical representations of preference structures from the perspective of the representational theory of measurement. It reviews historical contributions to ordinal, additive, and expected utility theories, then describes recent contributions in these areas

Utilitarianism with and without expected utility

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity

Conflicting Objectives in Decisions

This book deals with quantitative approaches in making decisions when conflicting objectives are present. This problem is central to many applications of decision analysis, policy analysis, operational research, etc. in a wide range of fields, for example, business, economics, engineering, psychology, and planning. The book surveys different approaches to the same problem area and each approach is discussed in considerable detail so that the coverage of the book is both broad and deep. The problem of conflicting objectives is of paramount importance, both in planned and market economies, and this book represents a cross-cultural mixture of approaches from many countries to the same class of problem

Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (hybrid meeting)

The workshop analyzes the constitution, recovery, and role of the classical texts in mathematical practice throughout history. It aims at problematizing the notion of "classic", to make it a historical category and to study the rhetorical, pedagogical, and institutional mechanisms that contribute to secure the status of classic to specific texts. So far, the focus of the historiography has dealt mostly with Greek classics and their impact on Western European societies. We aim to expand the focus of our enquiry culturally and chronologically in two ways. We want to address the reception and transformation of these "classics" outside Europe in different historical periods. We are particularly interested in the roles played by this classical tradition within Islamicate societies, South-East and East Asia. Secondly, we are interested in the ancient mathematical writings in Arabic, Chinese, Sanskrit and other languages that, at certain time periods in these other parts of the world and elsewhere, were perceived as classics. Widening the focus should allow us to inquire into questions such as: what did classical texts mean for various types of actors? How were they available to them? How did they read them? In the contexts of which institutions and with which expectations? The important role classical works have played in mathematical history pose deep methodological questions with far-reaching implications for the history and philosophy of mathematics. In mathematics conceptual and methodological innovations are thought to be legitimized only by appeal to mathematical arguments and consistency. Yet, legitimation has involved in many crucial episodes giving a prominent role to classical works. The mathematical classics have repeatedly been the source and grounds for new ideas and techniques. There is therefore a deep, complex tension between innovation and tradition. We are interested in how innovation has often been legitimized by re-reading old texts, concepts, and methods-old texts whose principles and methods were utterly different from the ones they contributed to sustain. What can this teach us about the nature of mathematical argument, and mathematical practice

Interpersonal comparisons of utility: The epistemological problem.

My doctorate thesis investigates a particularly controversial issue in both philosophy of economics and philosophy of mind, namely, the problem of interpersonal utility comparisons (IUCs henceforth). As I take utility to be a numerical representation of the intensity of individual preferences, IUCs are judgments about how different people's preferences compare in terms of strength. As factual judgments, IUCs appear to be either underdetermined by the empirical evidence or indeterminate. This casts doubt on whether or not we can have (scientific) knowledge of, or, at least, (scientifically) justified beliefs about, how different people's preferences compare in terms of strength. In general, IUCs can be justified if the assumption of interpersonal similarity, in one of its forms, can be vindicated. I consider two strategies, which attempt to vindicate this assumption by means of, respectively, an inference to the best explanation type of argument and a nativist argument. I argue that both strategies fail. These results suggest that preferences may be interpersonally incomparable with respect to the dimension of strength. I consider four 'possibility' arguments addressing this challenge. I argue that, although some of them may solve the conceptual problem concerning the interpersonal comparability of preference strengths, they all fail to solve the epistemological problem of IUCs. Nevertheless, I argue that a 'modest' transcendental argument shows that IUCs can, at least, be justified, provided that we embrace a coherentist view about the structure of epistemic justification

Utilitarianism with and without expected utility

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal comparisons are encoded in a single `individual preorder'. The individual preorder then uniquely determines the social preorder. The theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. If in addition the individual preorder satisfies expected utility, the social preorder must be represented by expected total utility. In the constant population case, this is the conclusion of the social aggregation theorem of Harsanyi (1955) under anonymity, but contra Harsanyi, it is derived without assuming expected utility at the social level. However, the theorems are also consistent with the rejection of all of the expected utility axioms, at both the individual and social levels. Thus expected utility is inessential to Harsanyi's approach under anonymity. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We therefore give further results related to additional constraints on the individual preorder. First, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to the main expected utility axiom of strong independence. Second, the individual preorder satisfies strong independence if and only if the social preorder has a mixture-preserving total utility representation; here the utility values can be taken as vectors in a preordered vector space, or more concretely as lexicographically ordered matrices of real numbers. Third, if the individual preorder satisfies a `local expected utility' condition popular in nonexpected utility theory, then the social preorder is `locally utilitarian'

A Logical Theory of Confirmation

This dissertation concerns the interpretation and structure of two intuitive notions: rational credence and confirmation. Probabilistic accounts of rational credence currently enjoy a position of considerable prestige, underwriting significant work not only in philosophy but also in economics and statistics. Confirmation, in contrast, is widely regarded as ill-formed, a misleading misconception akin to phlogiston, witches, or cosmic ether (de Finetti x). The primary project of this dissertation is to undercut the contemporary consensus on both notions by first demonstrating a systemic weakness in probabilistic accounts of rational credence (part I) and then providing a non-probabilistic account of confirmation (part II). Since any adequate account of confirmation is prima facie an adequate account of rational credence, the negative work of part one dovetails with the positive account offered in part two. Confirmation is no misleading misconception, and rational credences are not probability functions

The Low-Carbon City Pilot Policy and Urban Land Use Efficiency:A Policy Assessment from China

Against the backdrop of severe global warming, the low-carbon city pilot policy, with carbon emission reduction as its main objective, is an important initiative for China to fulfil its international commitment to carbon emission reduction and promote a green and low-carbon development strategy. However, none of the literature has yet evaluated whether the pilot low-carbon city policy promotes urban land use efficiency as a policy effect. In view of this, this paper measures urban land use efficiency from a low-carbon perspective using a global reference super-efficiency SBM model based on data from 186 prefecture-level cities in China from 2005–2017, and subsequently constructs a difference-in-differences method to test the true impact of low-carbon city pilot policies on urban land use efficiency and carbon emissions, and uses a propensity score matching method to test its robustness. It is found that: (1) the average level of urban land use efficiency in China is low and on a downward trend; (2) overall, cities are predominantly low-efficiency cities, with only the high-efficiency cities in Guangdong Province showing spatial agglomeration; and (3) the low-carbon city pilot policy reduces carbon emissions while also negatively affecting urban land use efficiency. Accordingly, this paper puts forward corresponding policy recommendations

Incompleteness, Independence, and Negative Dominance

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent