2 
Contents 
List of Figures 
List of Tables 
Acknowledgements 
Abstract 
1 Introduction 
1.1 
Rationality and Probability of Choice 
Deterministic Models. 
1.2 
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1.2.1 Order Structures 
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1.2.2 Expected Utility Models 
1.2.3 Non-Expected Utility Models 
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1.2.4 Miscellaneous Models 
Probabilistic Models 
1.3 
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1.3.1 Constant Utility Models 
* * * * * 
1.3.2 Random Utility Models 
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Multiattribute Models 
1.4 
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. . 
. . 
1.4.1 Deterministic Multiattribute Models 
1.4.2 Probabilistic Multiattribute Models 
1.5 
Algebraic Decomposition 
. . 
1.6 Summary 
Theory 
2.1 
Directed Cycles and Tournaments 
2.2 Decomposition into Strong Components 
2.2.1 Polynomials 
2.2.2 Critical Arcs in Tournaments 
2.2.3 Examples of Tournaments 
Ear Decomposition 
2.3 
2.3.1 Cycle Space and Dicycle Basis 
2.3.2 Ear Decomposition by Sequence 
2.3.3 Example of Ear Decomposition by Sequence. 
2.4 
Completion by Cuts 
2.4.1 Families of Intransitive Subchains 
2.4.2 Closure and Lattice .. 
* * * * * * * * * * * * 
* * * * 
2.4.3 Example of Completion by Cuts 
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