Investigating Human Interaction through Mathematical Analysis

Cover
Half Title
Title
Copyright
Dedication
Contents
List of Figures
Preface
Acknowledgments
Introduction
1 Social Psychology and Psychophysics: Laying the Foundation
	1.1 Proposing an Objective for Social Psychology
	1.2 Cognitive-Dissonance-Based Definitions and Social Axioms
	1.3 Bibb Latane’s Social Impact Theory
	1.4 Weber’s Law and Fechner’s Law
	1.5 Weber’s Law Revisited
	1.6 Fechner’s Law Revisited
2 Milgram’s Drawing Power of Crowds and Social Impact Theory
	2.1 Sensation Magnitude Probability Mass Function
		2.1.1 Mental Encoding and the Discrete Uniform Probability Mass Function
		2.1.2 Tone Perception – Two-Alternative Forced Choice Experiment (No Feedback)
		2.1.3 Mass Perception – Three-Alternative Forced Choice Experiment (No Feedback)
	2.2 Deriving the Unit Sensation Magnitude Probability Density Function
	2.3 Psychophysical Solution to Milgram’s 1969 Drawing Power of Crowds Experiment
		2.3.1 Encoding: Uniform Distribution as the Basis
		2.3.2 Encoding: Exponential Distribution
	2.4 Fechner’s Law and the Power Law
	2.5 Summary
3 Revisiting Milgram’s 1978 “Response to Intrusion into Waiting Lines” Experiment
	3.1 Establishing an Analytic Model of Intragroup Social Impact
	3.2 Milgram’s “Response to Intrusion Into Waiting Lines”: Reaction Summary and Associated Social Situations
	3.3 Milgram’s “Response to Intrusion Into Waiting Lines”: Analysis and Model Development
		3.3.1 Condition 1: (+1)-Q(1|0|M) Probability of Reaction Calculation
		3.3.2 Condition 4 – Probability of Reaction Calculation for Q(2|0|M)
		3.3.3 Impact of Nonreacting (NR) Confederate Buffers: Deriving z(|UI|) Using Conditions 2: (+2), 5: (+3) and 6: (+3)
		3.3.4 Impact of Reacting Members: Deriving y(|UI|) Using Condition 4: (+2)
		3.3.5 Estimating esH ,1,0 and esH,2,0
	3.4 Summary
		3.4.1 Observations
4 Applying the Queue Transform
	4.1 Variations of the Obedience Study
	4.2 Lady and a Flat Tire
	4.3 Smoke From a Vent
	4.4 Lady Needing Help
	4.5 Accident Victim
	4.6 Theft of Beer and Money (Design of Experiment Lessons Learned)
	4.7 Cumulative Summary of Queue Transform Results
5 From the Queue to the Commons
	5.1 The Common-Pool Resource
	5.2 The Queue as an Open-Access Common-Pool Resource
		5.2.1 Design Principle 1 – Clearly Defined Resource System Boundaries
		5.2.2 Design Principle 2 – Proportional Appropriation and Provision
		5.2.3 Design Principle 3 – Modify Rules Through Consensus
		5.2.4 Design Principles 4 and 5 – Monitoring Access to the Resource and Effective Sanctions Against Violators
		5.2.5 Design Principle 6 – Conflict Resolution Mechanisms
		5.2.6 Design Principle 7 – Right to Modify Resource System Structure
		5.2.7 Design Principle 8 – Effective Coordination Between Interconnected Resource Systems
	5.3 Mapping Complex Social Commons to the Western Queue Social Commons
6 An Algebraic Group in Social Space
	6.1 Dissonance Reduction as a Function of Time
		6.1.1 First-Order Derivation of Dissonance Reduction as a Function of Time
	6.2 The Queue Transform as an Algebraic Abelian Group
	6.3 Potential Implications of Ambiguity Reduction, Cumulative Dissonance, and/or Reevaluation of the Social Situation
7 History as Data
	7.1 The German Confederation and Social Events Leading to Its 1848 Revolution
		7.1.1 Defining Revolution as a Tragedy of the Commons
		7.1.2 Establishing and Legitimizing Representation as a Group Social Norm
		7.1.3 Amplification of Social Dissonance
		7.1.4 The Amplifying Event and Group Member Reaction
	7.2 Response to Intrusion Into Waiting Lines and the German Confederation’s Nobility
	7.3 The Obedience Experiment and the German Confederation’s Revolution of 1848
	7.4 Final Remarks
Appendix A: Deriving Minimum Queue Length Based on Milgram et al. (1986) Data
Glossary of Variables and Notation
Index