Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.

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The Market Model of Interest Rate Dynamics

Recent developments in social choice theory are critically surveyed in the light of a categorization of interpersonal aggregation problems into four distinct types that seem to require varying treatment but typically do not receive it. Informational inadequacy of the usual social choice framework is discussed in this context. A fairly thorough exploration of the correspondences between consistency conditions for choice functions and regularity properties of the binary relation of preference leads to a re-examination of the class of "impossibility" results in social choice theory, necessitating reinterpretations of various theorems (including Arrow's). SOCIAL CHOICE THEORY is "concerned with relationships between individuals' preferences and social choice" (Fishburn (1973, p. 3)). But a great many problems fit this general description and they can be classified into types that are fundamentally different from each other. It can be argued that some of the difficulties in the general theory of social choice arise from a desire to fit essentially different classes of group aggregation problems into one uniform framework and from seeking excessive generality. An alternative is to classify these problems into a number of categories and to investigate the appropriate structure for each category. In a small way, this is what will be done in this paper, and some of the recent developments in the theory of social choice will be examined in that light.

Social Choice Theory: A Re-Examination

The subject of social choice includes within its capacious frame various problems with the common feature of relating social judgments and group decisions to the views and interests of the individuals who make up the society or the group. Some challenges and foundational problems faced by social choice theory as a discipline are discussed. Social choice theory is a subject in which formal and mathematical techniques have been very extensively used. Voting-based procedures are entirely natural for some kinds of social choice problems, such as elections, referendums, or committee decisions. They are, however, altogether unsuitable for many other problems of social choice. Impossibility results in social choice theory - led by the pioneering work of Arrow (1951) - have often been interpreted as being thoroughly destructive of the possibility of reasoned and democratic social choice, including welfare economics. That view is argued against.

The Possibility of Social Choice

The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

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Handbook of Computational Social Choice

Arrow's theorem, many agents, and invisible dictators☆

Economies of scale and equilibria in coalition production economies

Alternative ways of introducing uncertainty to the term structure of interest rates are considered. They correspond to the different expectation hypotheses. The dynamics of the term structure is analysed in a convenient framework of stochastic equations in infinite dimensions.

Different Dynamical Specifications of the Term Structure of Interest Rates and their Implications

We show that if limit orders are required to vary smoothly, then strategic (Nash) equilibria of the double auction mechanism yield competitive (Walras) allocations. It is not necessary to have competitors on any side of any market: smooth trading is a substitute for price wars. In particular, Nash equilibria are Walrasian even in a bilateral monopoly.

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Dieter Sondermann

Papers

Arrow's theorem, many agents, and invisible dictators☆

Economies of scale and equilibria in coalition production economies

Different Dynamical Specifications of the Term Structure of Interest Rates and their Implications

Perfect Competition in a Bilateral Monopoly

Perfect Competition in a Bilateral Monopoly (in Honor of Martin Shubik)