The Information Theory of Comparisons

This book finds a broad domain of relevance in statistics and the social sciences. Its conceptual development is supported by applications to economics and income distribution, finance, education, demographics and actuarial science, political studies, psychology, and general statistics.

Fresh perspectives on directional complexity have generated an informational theory of ‘more versus less’, with representative polar outcomes as good or bad, or rich or poor. New duality metrics for spread and asymmetry have resulted, motivated by internal perspectives on the part of subjects, such as attitudes to their comparative (dis)advantage. This book is a readable review of these developments. Concepts and applications are described in tandem with each other. They consolidate recent contributions to the research literature, augmented with fresh insights and applications. Dynamic extensions include modeling shifting social attitudes, while the broader agenda encompasses topical areas such as subjectivist probability, investment decision making, and income distribution.

• Partition Entropy
• Differential Entropy
• Spread and Asymmetry
• Double Smoothing
• Shannon Differential Entropy
• Dispersion
• D-Metric
• Distribution Shifting
• Entropic Shifts
• Entropy Bandwidth
• Entropic Centre
• Entropy Divergence
• Friedman–Savage
• Gini Coefficient
• Income Inequality
• Log Odds
• Gini Mean Absolute Difference
• Mutual Information
• Social Welfare Function
• V-Metric

• Kiwicap Research Ltd., Kelburn, New Zealand

  Roger Bowden

Roger Bowden has extensive international experience in academia and research institutions, with permanent or visiting professorships and research fellowships spanning eight countries. His research has resulted in many journal articles, as well as research monographs, spanning economics, econometrics, statistics, finance, psychometrics, management science and law. A New Zealander by birth, Roger is a fellow of the Royal Society of New Zealand. He is currently Director, Kiwicap Research Ltd in Wellington, New Zealand.

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