Chapter

Musical Chairs and Inescapable Mathematics

ROBERT V. DODGE

in Schelling's Game Theory

Published in print February 2012 | ISBN: 9780199857203
Published online May 2012 | e-ISBN: 9780199932597 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199857203.003.0011
Musical Chairs and Inescapable Mathematics

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The metaphor “musical chairs” encompasses a broad range of observations and behaviors in which the same patterns emerge in the aggregate regardless of how the individuals who comprise the aggregate behave. This happens as a result of inescapable mathematical relationships. This chapter is divided into sections. First, it looks at paired phenomena, which refers to things that occur together. It includes a population problem, with an explanation, plus a counter-intuitive puzzle from Schelling. The idea of “either, or” is another of the observations in this section. There may be only one of two equal options for certain outcomes, and to think otherwise can lead to difficulties. The concept of positions in a distribution describes statements that hold true regardless of changes in the individuals who comprise the populations being discussed. The Acceleration Principle is the final topic in the chapter. This describes the relationship between independent activities when one is the source of the other's growth. The chapter analyzes the rate of increase of the rate of production, rather than just the increase in the rate of production alone. Supplementing the chapter is “Politicians, Liars and Mathematical Puzzles,” by John Allen Paulos.

Keywords: national income accounting; gambler's fallacy; mathematical certainty in society; either or paired phenomena; Acceleration Principle; positions in a distribution

Chapter.  5562 words. 

Subjects: Economics

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