1 Ranking Models with Item Covariates -- 1.1 Introduction -- 1.2 Basic Ranking Models and Their Parameters -- 1.3 Ranking Models with Covariates -- 1.4 Estimation -- 1.5 Example -- 1.6 Discussion -- 1.7 Appendix -- 1.8 References -- 2 Nonparametric Methods of Ranking from Paired Comparisons -- 2.1 Introduction and Literature Review -- 2.2 The Proposed Method of Scoring -- 2.3 Distribution Theory and Tests of Significance for ??ij = pij -- 2.4 Ranking Methods -- 2.5 Numerical Example -- 2.6 References -- 3 On the Babington Smith Class of Models for Rankings -- 3.1 Introduction -- 3.2 Alternative Parametrizations and Related Models -- 3.3 Stochastic Transitivity and Item Preference -- 3.4 Examples and Data Analysis -- 3.5 References -- 4 Latent Structure Models for Ranking Data -- 4.1 Introduction -- 4.2 Latent Class Analyses Based on the Bradley-Terry-Luce Model -- 4.3 Latent Class Analyses Based on a Quasi-independence Model -- 4.4 Models that Allow for Association Between Choices within the Classes -- 4.5 References -- 5 Modelling and Analysing Paired Ranking Data -- 5.1 Introduction -- 5.2 Two Models -- 5.3 Estimation and Hypothesis Testing -- 5.4 Analysis of Simulated Data Sets -- 5.5 Analysis of Rogers Data -- 5.6 References -- 6 Maximum Likelihood Estimation in Mallows's Model Using Partially Ranked Data -- 6.1 Introduction -- 6.2 Notation -- 6.3 Maximum Likelihood Estimation Using the EM Algorithm -- 6.4 Example -- 6.5 Discussion -- 6.6 References -- 7 Extensions of Mallows' ? Model -- 7.1 Introduction -- 7.2 The General Model -- 7.3 Ties, Partial Rankings -- 7.4 Example: Word Association -- 7.5 Example: APA Voting -- 7.6 Example: ANOVA -- 7.7 Discussion of Contrasts -- 7.8 Appendix -- 7.9 References -- 8 Rank Correlations and the Analysis of Rank-Based Experimental Designs -- 8.1 Introduction -- 8.2 Distance Based Measures of Correlation -- 8.3 The Problem of m Rankings -- 8.4 The Two Sample Problem -- 8.5 The Problem of m Rankings for a Balanced Incomplete Block Design -- 8.6 The Problem of m Rankings for Cyclic Designs -- 8.7 Measuring Correlation Between Incomplete Rankings -- 8.8 References -- 9 Applications of Thurstonian Models to Ranking Data -- 9.1 Introduction -- 9.2 The Ranking Model -- 9.3 Modeling ? -- 9.4 Subpopulations -- 9.5 Model Estimation and Tests -- 9.6 Applications -- 9.7 Discussion -- 9.8 References -- 10 Probability Models on Rankings and the Electoral Process -- 10.1 Introduction -- 10.2 Electoral Systems -- 10.3 Models for Permutations -- 10.4 The American Psychological Association Election -- 10.5 Simulation Results -- 10.6 Conclusions and Summary -- 10.7 Acknowledgements -- 10.8 References -- 11 Permutations and Regression Models -- 11.1 Introduction -- 11.2 Models for Random Permutations -- 11.3 Sufficient Statistics and Log-linear Models -- 11.4 Conclusions -- 11.5 References -- 12 Aggregation Theorems and the Combination of Probabilistic Rank Orders -- 12.1 Introduction -- 12.2 Notation and Basic Aggregation Theorems -- 12.3 Specific Multidimensional Ranking and Subset Selection Models and Their Properties -- 12.4 Multidimensional Random Variable Models -- 12.5 Conclusion -- 12.6 References -- 13 A Nonparametric Distance Model for Unidimensional Unfolding -- 13.1 Introduction -- 13.2 Social Choice Theory -- 13.3 Distance Measures for Rankings -- 13.4 Strongly Unimodal Distance Models for Rankings -- 13.5 Generalization of Coombs' and Goodman's Conditions -- 13.6 Equal Results for ML or MNI Criterion -- 13.7 Unfolding and Social Choice Theory: Illustrations -- 13.8 Discussion -- 13.9 References -- Miscellanea -- Models on Spheres and Models for Permutations -- Complete Consensus and Order Independence: Relating Ranking and Choice -- Ranking From Paired Comparisons by Minimizing Inconsistency -- Graphical Techniques for Ranked Data -- Matched Pairs and Ranked Data.