It states that if x, y, and z are incomparable elements of a finite poset, then
where P(*) is the probability that a linear order < extending the partial order has the property *.
In other words the probability that x < z strictly increases if one adds the condition that x < y. In the language of conditional probability,
The proof uses the Ahlswede–Daykin inequality.
- Fishburn, Peter C. (1984), "A correlational inequality for linear extensions of a poset", Order 1 (2): 127–137, doi:10.1007/BF00565648, ISSN 0167-8094, MR 764320
- Fishburn, P.C.; Shepp, L.A. (2001), "f/f110080", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Shepp, L. A. (1982), "The XYZ conjecture and the FKG inequality", The Annals of Probability (Institute of Mathematical Statistics) 10 (3): 824–827, doi:10.1214/aop/1176993791, ISSN 0091-1798, JSTOR 2243391, MR 659563