This book highlights mathematical ideas to help explain a number of important aspects of the dynamics of social groups. These ideas are similar to those used to describe the behaviour of Lagrangian mechanical systems, and as such this book appeals to anyone wanting to gain an understanding of the intrinsic unity of natural phenomena.

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Prof. Francesco dell'Isola is co-author of more than 164 papers (indexed in Scopus). He was editor or co-author of 5 technical books published in Springer Nature, also. He supervised or co-supervised more than 20 Ph.D. students and 10 postdoctoral projects. He gave more than 70 invited lectures in several universities and international conferences and has been Visiting Professor in more than 7 universities (France, USA, and Russia). In 2018, he has been Russell Severance Springer Professor at the University of California, Berkeley. His research interests are in several fields of theoretical mechanics and applied mathematics: the common techniques used are variational principles, as a heuristic tool for formulating mathematical models. In particular, he has studied the possible applications of Lagrangian mechanics methods to social sciences and economy and the present book popularises some of the most important results in this field.

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PREFACE

A DICTATOR MUST ALWAYS EXIST

MANY PERSONS BELIEVE THAT MATHEMATICS IS TOO ABSTRACT A SCIENCE TO BE REALLY USEFUL.

DICTATORS OR OPINION LEADERS ?

IS IT POSSIBLE TO FIND A DEMOCRATIC METHOD FOR THE DETERMINATION OF SOCIAL

CHOICES ?

A QUESTION OF RULES OR, MATHEMATICALLY SPEAKING, A QUESTION OF ALGORITHMS

CONSIDERATIONS ON THE PRACTICAL USE OF POSSIBLE SOLUTIONS OF CONDORCET PROBLEM

IN POLITICS

A FIRST INFORMAL FORMULATION OF ARROW THEOREM

THE MATHEMATICAL MODEL FOR A CHOICE: TOTAL ORDER RELATIONS

A SECOND, MORE PRECISE, FORMULATION OF ARROW THEOREM

MONOTONICITY AND INDEPENDENCE OF IRRELEVANT ORDER ARROW'S THEOREM IS A POWERFUL TOOL FOR UNDERSTANDING MANY

SOCIAL PHENOMENA

ARROW'S THEOREM AND THE SELECTION OF SUPER ALPHA INDIVIDUALS

ARROW THEOREM AS A TOOL FOR UNDERSTANDING HISTORY

ARROW THEOREM AS THE FIRST MATHEMATICAL RESULT IN PSICO-HISTORY

A PRIORI IMPOSED SOCIAL CHOICES, ALTERNATIVES WHICH MAY BE RELEVANT, AND

INSTITUTIONAL SYSTEMS INCAPABLE TO DECIDE KING, EMPERORS, (ABSOLUTE) MONARCHS AND DESPOTS

DEMOCRACY AS A POSSIBLE ALTERNATIVE

CATHERINE THE GREAT AND GENGHIS KHAN: POWER HAS NO GENDER

GENGHIS KHAN

CATHERINE THE GREAT, EMPRESS AND AUTOCRAT OF ALL THE RUSSIAS

SOME INITIAL CONCLUSIONS ABOUT THE RELATIONSHIP BETWEEN POWER AND GENDER

SOME OPEN PROBLEMS FOR A GENERAL MATHEMATICAL THEORY OF SOCIAL STRUCTURES

A CASUAL LIST OF PROBLEMS WHICH COULD BE TREATED BY THE THEORY OF SOCIAL

STRUCTURES

PLATO'S REPUBLIC: A PRISTINE TEXTBOOK IN SOCIAL SCIENCES

A QUEST OF PHENOLOGICAL BASIS FOR FUTURE THEORETICAL DEVELOPMENTS

PHENOMENOLOGY OF LEADERSHIP

LEADERSHIPS AND UNIFICATIONS: ANALYSIS OF AN HISTORICAL NECESSITY SOUTHERN VERSUS NORTHERN LEADERS

LEADERS FROM SOUTH AIM AT UNREACHABLE IDEALS?

AN EXEMPLARY IDEALISTIC SOUTHERNER: CARLO FILANGIERI

THE MAIN EVENTS IN THE LIFE OF CARLO FILANGIERI

A REAPPRAISAL OF THE RES GESTAE (i.e. THE DEEDS) OF CARLO FILANGIERI

THE TALENTS NEEDED TO BE A WINNER: POWER IS THE PRIZE FOR MACHIAVELLIAN BEHAVIOUR

CAMILLO BENSO, COUNT OF CAVOUR: THE HETEROGENESIS OF ENDS

A SHORT LIST OF THE ACHIEVEMENTS OF CAVOUR

PHENOMENOLOGY OF DICTATORSHIP

THE WEAKNESSES OF TWO SICILIES AS EXPLOITED BY CAVOUR AND GARIBALDI

THOSE MASTERS OF DUPLICITY WHO SURRENDERED NAPLES 83

DON PASQUALE

THE WIFE OF DON PASQUALE

PATROCLUS PETRONS: THE PUPPET OF THE CRYPTO-DICTATOR

A TENTATIVE EXPLANATION OF SOME OF DESCRIBED PHENOMENA BASED

ON THE CONCEPT OF NASH EQUILIBRIUM

GAME THEORY: A POWERFUL CONCEPTUAL TOOL (STABLE) EQUILIBRIUM CONFIGURATIONS

NON-UNIQUENESS OF EQUILIBRIA

STRATEGIES IN A GAME

NASH EQUILIBRIUM SOME TENTATIVE APPLICATIONS OF NASH THEOREM

MIXED RANDOM STRATEGIES

IS THE PHENOMENOLOGY OF THE DICTATOR AND OF THE LEADER

OBSERVED ONLY IN HUMAN GROUPS ?

MAMA, TESTOSTERONE AND DICTATORS

YEROEN, NIKKIE, LUIT: MALE COMPETITION FOR POWER

UNMASKING HUMAN BEHAVIOUR

KANZI, THE BONOBO: A MESSAGE OF HOPE

PHENOMENOLOGY OF SERVITUDE

PART I. WHY DO PEOPLE OBEY A GOVERNMENT

PART II. LIBERTY IS THE NATURAL CONDITION OF THE PEOPLE PART III. THE FOUNDATION OF TYRANNY

SERVITUDE AS AN INNATE INSTINCT

MONTESQUIEU: THE POSSIBLE DEMOCRACY

TOWARDS A RATIONAL THEORY OF CONSTITUTIONS

THE DIVISION OF POWERS IMAGINED BY MONTESQUIEU

MORE SOPHISTICATED MATHEMATICAL THEORIES ARE NEEDED

APPENDIX 1. THE STORY OF TWO WORDS: DICTATOR/TYRANT APPENDIX 2. MORE DETAILS ABOUT THE MATHEMATICAL STRUCTURE OF THE

THEOREM OF DICTATOR

INDIVIDUAL OR SOCIAL CHOICES AMONG SEVERAL OPTIONS

OPTIONS PREFERRED TO ALL OPTIONS IN A SPECIFIC SET RATIONAL CHOICE,...