Intransitive indifference with unequal indifference intervals

@article{Fishburn1970IntransitiveIW,
  title={Intransitive indifference with unequal indifference intervals},
  author={P. Fishburn},
  journal={Journal of Mathematical Psychology},
  year={1970},
  volume={7},
  pages={144-149}
}
  • P. Fishburn
  • Published 1970
  • Mathematics
  • Journal of Mathematical Psychology
Abstract An interval order is a binary relation ≺ on a set X that is irreflexive and satisfies the condition: if x ≺ y and z ≺ w then x ≺ w or z ≺ y . An interval order is a special kind of strict partial order (transitive, irreflexive) and a generalization of the semiorder concept. If X is countable then there are real-valued functions u and p on X such that p is positive and [ x ≺ y if and only if u ( x ) + p ( x ) u ( y )], if and only if ≺ is an interval order. 

References

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