Preference Modeling

The following scheme summarizes the different families introduced in this chapter and the connections between them. Family of interval orders f Row-homogeneous Column-homogeneous Family of family of interval semi orders family of interval orders orders Homogeneous family of i nterva 1 orders Homogeneous family of semi orders Family of weak orders 85 5.13. EXAMPLES We let to the reader the verification of the following assertions. Example 1 is a family of interval orders which is neither row-homogeneous nor column-homogeneous. Example 2 is a column-homogeneous family of interval orders which is not row-homogeneous but where each interval order is a semiorder. Example 3 is an homogeneous family of interval orders which are not semiorders. Example 4 is an homogeneous family of semi orders . . 8 __ --, b ---i>---_ C a .2 d c Example Example 2 .8 .6 c .5 a 0 a d Example 3 Example 4 5.14. REFERENCES DOIGNON. J.-P Generalizations of interval orders. in E. Degreef and J. Van Buggenhaut (eds). T ndS in MathematiaaZ PsyahoZogy. Elsevier Science Publishers B.V. (North-Holland), Amsterdam, 1984. FISHBURN. P.C., Intransitive indifference with unequal indifference intervals. J. Math. Psyaho. 7 (1970) 144-149. FISHBURN. P.C., Binary choice on the varieties of stochastic transitivity. J. Math. Psyaho. 10 (1973) 327-352."