#### DMCA

## Utility Representation of an Incomplete Preference Relation (2000)

Citations: | 64 - 6 self |

### Citations

218 | Partially ordered sets - Dushnik, Miller - 1941 |

216 | Topological Spaces - Berge - 1997 |

176 | Interval orders and interval graphs - Fishburn - 1985 |

156 | Representation of a Preference Ordering by a Numerical Function. In Decision Processes. - Debreu - 1954 |

144 | Equilibrium binding agreements
- Ray, Vohra
- 1997
(Show Context)
Citation Context ...ach coalition by using a vector of utility functions (one for each member of the coalition), which forces one to model the preferences of a coalition as an incomplete preorder (cf. Shapley, 1957, and =-=Ray and Vohra, 1997-=-). 6 Given such considerations, it may perhaps be useful at times to take a (possibly incomplete) preorder as the primitive of analysis. Yet the fact that an incomplete preorder does not admit a utili... |

123 | Revealed Preference Theory", - Richter - 1966 |

117 | Topologies on spaces of subsets, - Michael - 1951 |

103 | 1895): “Beiträge zur begrundung der transifiniten mengelehre - Cantor |

84 | Theory of Correspondences, - Klein, Thompson - 1984 |

41 | Rational Choice - Richter - 1971 |

34 |
Utility Theory without
- Aumann
- 1962
(Show Context)
Citation Context ...might be extremely complex, too complex for intuitive “insight,” and our individual might prefer to make no decision at all in these problems. ... Is it “rational” to force decisions in such cases?” (=-=Aumann, 1962-=-, p. 446). The links between the notion of rationality and incomplete preferences are thoroughly elaborated further in Bewley (1986) and Mandler (1999). 3 I owe this particular insight to an anonymous... |

34 | Utility functions for partially ordered topological spaces, - Peleg - 1970 |

30 | Incomplete Preferences and Rational Intransitivity of Choice," - Mandler - 2005 |

21 | A General Extension Theorem for Binary Relations”. - Duggan - 1999 |

20 |
The Existence of a Utility Function to Represent Preferences,”
- Rader
- 1963
(Show Context)
Citation Context ...hen |X| < ∞.) 11sby two utility functions one of which is continuous and the other is upper semicontinuous, need not be continuously representable. Another classical theorem of utility theory (due to =-=Rader, 1963-=-) gives sufficient conditions for the upper (and lower) semicontinuous representation of a complete preference relation. This is quite useful because upper semicontinuity is often adequate for purpose... |

19 |
Equilibrium points in games with vector payoffs,
- Shapley
- 1959
(Show Context)
Citation Context ...he preferences of each coalition by using a vector of utility functions (one for each member of the coalition), which forces one to model the preferences of a coalition as an incomplete preorder (cf. =-=Shapley, 1957-=-, and Ray and Vohra, 1997). 6 Given such considerations, it may perhaps be useful at times to take a (possibly incomplete) preorder as the primitive of analysis. Yet the fact that an incomplete preord... |

18 | Dimension theory for ordered sets - Kelly, Trotter - 1981 |

17 |
A quasiordering is the intersection of orderings,”
- Donaldson, Weymark
- 1998
(Show Context)
Citation Context ...e in concert with this position. After all, the standard social welfare orderings like Pareto dominance and (generalized or ordinary) Lorenz ordering are incomplete preorders (see Fishburn, 1974, and =-=Donaldson and Weymark, 1998-=-, for further discussion.) 6 Before proceeding any further, we should note that the issue of incomplete preferences is only interesting if we impose transitivity (or some other restriction) on prefere... |

13 | Knightian Uncertainty Theory: Part I,” Cowles Foundation Discussion Paper No - Bewley - 1986 |

12 | Semicontinuous extension of a partial order,” - Jaffray - 1975 |

8 | On Dilworth’s theorem in the infinite case - Perles - 1963 |

6 | Utility representation for partial orders - Sondermann - 1980 |

6 | Inequalities in Dimension Theory for Posets - Trotter - 1975 |

5 |
On the Dimension of Partially Ordered Sets
- Komm
- 1948
(Show Context)
Citation Context ...(R n , ≥) =n. 11 If X is finite, we trivially have dim(X, �) < ∞. If, on the other hand, (X, �) is an infinite poset, then dim(X, �) need not be finite; for instance, dim(2A , ⊇) =∞ whenever |A| = ∞ (=-=Komm 1948-=-). However, by a theorem of Hiraguchi (1955), we have w(X, �) ≥ dim(X, �) for any poset (X, �). Thus an infinite poset with finite width must have finite dimension. Many other interesting inequalities... |

1 | A Decomposition for Partially Ordered - Dilworth - 1950 |

1 | A Model of Procedural Decision making - A - 1999 |

1 |
Impossibility Theorems without the
- Fishburn
- 1974
(Show Context)
Citation Context ... seems at large to be in concert with this position. After all, the standard social welfare orderings like Pareto dominance and (generalized or ordinary) Lorenz ordering are incomplete preorders (see =-=Fishburn, 1974-=-, and Donaldson and Weymark, 1998, for further discussion.) 6 Before proceeding any further, we should note that the issue of incomplete preferences is only interesting if we impose transitivity (or s... |

1 | On the Dimension of Ordered Sets - Hiraguchi - 1955 |

1 |
Dilworth’s Decomposition Theorem in the Infinite Case
- Milner
- 1990
(Show Context)
Citation Context ...ection principle. Several alternative proofs have been since then furnished; the most direct proof that I know deduces the result readily from the finite case by applying Gödel’s compactness theorem (=-=Milner, 1990-=-). 11 n In what follows, we adopt the following notation for vector inequalities in R : x ≥ y iff xi ≥ yi for all i; x>y iff x ≥ y and x �= y; x � y iff xi >yi for all i. 7sunder which we can associat... |

1 | Sur l’Extension de l’Orde Partiel,” Fund - Szpilrajn - 1930 |