Some Social Science Applications of Ordered Sets

Ordered sets arise in artifact dating in archaeology, in preference measurement in psychology, in hierarchies in sociology, in decision problems in economics and political science. In this lecture, we discuss the nature of the ordered sets that arise in each of these disciplines and the nature of the problems in ordered sets that arise. Finally we shall consider the order-theoretic aspects of two problems that arise throughout these fields: the problem of determining a consensus from a group of orderings and the problem of making statistically significant statements about orderings.

[1]  Issie Rabinovitch,et al.  The Scott-Suppes theorem on semiorders , 1977 .

[2]  P. Gilmore,et al.  A Characterization of Comparability Graphs and of Interval Graphs , 1964, Canadian Journal of Mathematics.

[3]  F. Roberts.  Measurement Theory with Applications to Decisionmaking, Utility, and the Social Sciences: Measurement Theory , 1984 .

[4]  Howard Raiffa,et al.  Games And Decisions , 1958 .

[5]  K. Arrow.  Social Choice and Individual Values , 1951 .

[6]  John G. Kemeny,et al.  Mathematical models in the social sciences , 1964 .

[7]  Fred S. Roberts,et al.  INDIFFERENCE AND SERIATION , 1979 .

[8]  I. Rabinovitch,et al.  The Dimension of Semiorders , 1978, J. Comb. Theory, Ser. A.

[9]  K. Bogart.  Preference structures I: Distances between transitive preference relations† , 1973 .

[10]  J. Kemeny.  Generalized random variables , 1959 .

[11]  J. Decani,et al.  Maximum likelihood paired comparison ranking by linear programming , 1969 .

[12]  D. Kendall.  Incidence matrices, interval graphs and seriation in archeology. , 1969 .

[13]  L. A. Goodman,et al.  Social Welfare Functions Based on Individual Rankings , 1952, American Journal of Sociology.

[14]  P. Fishburn.  Intransitive indifference with unequal indifference intervals , 1970 .

[15]  R. Luce.  Semiorders and a Theory of Utility Discrimination , 1956 .

[16]  J. Barthélemy,et al.  Caractérisations axiomatiques de la distance de la différence symétrique entre des relations binaires , 1979 .

[17]  G. Kolata.  Overlapping genes: more than anomalies? , 1977, Science.

[18]  Kenneth P. Bogart,et al.  Consensus Signed Digraphs , 1979 .

[19]  D. Black.  The theory of committees and elections , 1959 .

[20]  Clyde H. Coombs,et al.  On the detection of structure in attitudes and developmental processes. , 1973 .

[21]  K. Bogart.  Preference Structures. II: Distances Between Asymmetric Relations , 1975 .

[22]  Andy B. Anderson.  The Bogart preference structures: Applications , 1973 .

[23]  Dean T. Jamison,et al.  Semiorders and the Theory of Choice , 1973 .

[24]  Bernard Monjardet,et al.  The median procedure in cluster analysis and social choice theory , 1981, Math. Soc. Sci..

[25]  A Committee Ranking Problem Using Ordinal Utilities. , 1977 .

[26]  Pierre Michaud,et al.  Modèles d'optimisation en analyse des données relationnelles , 1979 .

[27]  William T. Trotter,et al.  A Bound on the Dimension of Interval Orders , 1976, J. Comb. Theory, Ser. A.

[28]  E. Szpilrajn.  Sur l'extension de l'ordre partiel , 1930 .

[29]  Fred S. Roberts,et al.  ON THE MOBILE RADIO FREQUENCY ASSIGNMENT PROBLEM AND THE TRAFFIC LIGHT PHASING PROBLEM , 1979 .

[30]  Peter C. Fishburn,et al.  PARTIAL ORDERS OF DIMENSION 2, INTERVAL ORDERS AND INTERVAL GRAPHS, , 1970 .

[31]  C. S. Colantoni,et al.  Majority Rule Under Transitivity Constraints , 1973 .

[32]  T. MARGUSH,et al.  Distances between trees , 1982, Discret. Appl. Math..

[33]  W. Hoeffding,et al.  Rank Correlation Methods , 1949 .

[34]  Patrick Suppes,et al.  Foundational aspects of theories of measurement , 1958, Journal of Symbolic Logic.

[35]  Bernard Monjardet,et al.  Ordered Sets and Social Sciences , 1982 .

[36]  Fred R. McMorris,et al.  Consensusn-trees , 1981 .

[37]  William T. Trotter,et al.  Dimension Theory for Ordered Sets , 1982 .

[38]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .