Decision Making Under Uncertainty, with a Special Emphasis on Geosciences and Education

Description

This book describes new techniques for making decisions in situations with uncertainty and new applications of decision-making techniques. The main emphasis is on situations when it is difficult to decrease uncertainty. For example, it is very difficult to accurately predict human economic behavior, so in economics, it is very important to take this uncertainty into account when making decisions. Other areas where it is difficult to decrease uncertainty are geosciences and teaching. The book analyzes the general problem of decision making and shows how its results can be applied to economics, geosciences, and teaching. Since all these applications involve computing, the book also shows how these results can be applied to computing, including deep learning and quantum computing. The book is recommended to researchers, practitioners, and students who want to learn more about decision making under uncertainty―and who want to work on remaining challenges. Contents Part I Introduction 1 General Introduction 2 (Rational) Individual Decision Making: Main Ideas References 3 (Rational) Group Decision Making: General Formulas and a New Simplified Derivation of These Formulas 3.1 (Rational) Group Decision Making: General Formulas 3.2 A New (Simplified) Explanation of Nash's Bargaining Solution 3.3 Taking Empathy into Account References 4 How We Can Control Group Decision Making by Modifying the Proposed Options 4.1 Formulation of the Problem 4.2 Main Idea and the Resulting Explanation 4.3 Proof of the Main Result References Part II How People Actually Make Decisions 5 The Fact That We Can Only Have Approximate Estimates Explains Why Buying and Selling Prices are Different 5.1 People's Actual Decisions Often Differ from What Decision Theory Recommends 5.2 Buying and Selling Prices are Different: A Phenomenon and Its Current Quantitative Explanations 5.3 A New (Hopefully, More Adequate) Quantitative Explanation References 6 The ``No Trade Theorem'' Paradox 6.1 ``No Trade Theorem'' and Why It is a Paradox 6.2 Analysis of the Problem and the Resulting Explanation of the ``No Trade Theorem'' Paradox 6.3 Auxiliary Result: Decision Theory Explains Why Depressed People are More Risk-Averse References 7 People Make Decisions Based on Clusters Containing Actual Values 7.1 Formulation of the Problem 7.2 A Possible Geometric Explanation 7.3 Auxiliary Observation: How all This is Related to Our Understanding of Directions References 8 When Revolutions Succeed 8.1 Formulation of the Problem 8.2 80/20 Rule: Reminder 8.3 How These Two Laws Explain the 3.5% Rule References 9 How People Combine Utility Values 9.1 Common Sense Addition 9.2 Towards Precise Formulation of the Problem 9.3 Hurwicz Optimism-Pessimism Criterion: Reminder 9.4 Analysis of the Problem and the Resulting Explanation of Common Sense Addition References 10 Biased Perception of Time 10.1 Formulation of the Problem 10.2 How Decision Theory Can Explain the Telescoping Effect References 11 Biased Perception of Future Time Leads to Non-Optimal Decisions References 12 People Have Biased Perception of Other People's Utility References 13 People Select Approximately Optimal Alternatives 13.1 People Use Softmax Instead of Optimization 13.2 Problem: Need to Generalize Softmax to the Case of Interval Uncertainty 13.3 How to Generalize: The Proposed Solution References 14 People Make Decisions Using Heuristics. I 14.1 Formulation of the Problem 14.2 Case When We Only Know the Expected Rates of Return … 14.3 Case When We Only Know the Intervals Containing the Actual … References 15 People Make Decisions Using Heuristics. II 15.1 Formulation of the Problem 15.2 Formal Explanation of the Anchoring Formula 15.3 Explaining the Numerical Values of the Anchoring Index References Part III Applications to Geosciences 16 Few-Parametric Spatial Models and How They Explain Bhutan Landscape Anomaly 16.1 Formulation of the Problem 16.2 What Is the Optimal Description of Elevation Profiles 16.3 Why Convexity and Concavity Are Important in Elevation Profiles: An Explanation Based on the Optimality Result 16.4 Bhutan Anomaly Explained 16.5 Auxiliary Question: How to Best Locate an Inflection Point References 17 Few-Parametric Temporal Models and How They Explain Gamma Distribution of Seismic Inter-Event Times 17.1 Formulation of the Problem 17.2 Our Explanation References 18 Scale-Invariance Explains the Empirical Success of Inverse Distance Weighting and of Dual Inverse Distance Weighting in Geosciences 18.1 Formulation of the Problem 18.2 What Is Scale Invariance and How It Explains the Empirical Success of Inverse Distance Weighting 18.3 Scale Invariance and Fuzzy Techniques Explain Dual Inverse Distance Weighting References 19 Dynamic Triggering of Earthquakes 19.1 Formulation of the First Problem 19.2 Symmetry-Based Geometric Explanation 19.3 A Possible Qualitative Physical Explanation 19.4 Formulation of the Second Problem 19.5 Geometric Explanation References Part IV Applications to Teaching 20 How Can We Explain Different Number Systems? 20.1 Formulation of the Problem 20.2 Which Bases Appear If We Consider Divisibility by All Small Numbers from 1 to Some kk 20.3 What If We Can Skip One Number 20.4 What If We Can Skip Two Numbers 20.5 What If We Can Skip Three or More Numbers References 21 Teaching Optimization 21.1 Formulation of the Problem 21.2 Analysis of the Problem 21.3 Resulting Algorithm References 22 Why Immediate Repetition is Good for Short-Time Learning Results But Bad for Long-Time Learning: Explanation Based on Decision Theory 22.1 Formulation of the Problem: How to Explain Recent Observations Comparing Long-Term Results of Immediate and Delayed Repetition 22.2 Main Idea Behind Our Explanation: Using Decision Theory 22.3 So When Do We Learn: Analysis of the Problem and the Resulting Explanation References 23 How to Assign Grades to Tasks so as to Maximize Student Efforts 23.1 Formulation of the Problem 23.2 Solution to the Problem References Part V Applications to Computing 24 Why Geometric Progression in Selecting the LASSO Parameter 24.1 Formulation of the Problem 24.2 Our Result References 25 Applications to Computing: Why Deep Learning is More Efficient Than Support Vector Machines, and How It is Related to Sparsity Techniques in Signal Processing 25.1 Problem Formulation 25.2 Support Vector Machines Versus Neural Networks 25.3 Support Vector Machines Versus Deep Learning 25.4 Sparsity Techniques: An Explanation of Their Efficiency References 26 Applications to Computing: Representing Functions in Quantum and Reversible Computing 26.1 Formulation of the Problem 26.2 Analysis of the Problem and the Resulting Recommendation 26.3 Discussion References Appendix What Is the Optimal Approximating Family References Index