Threshold values are often difficult to calculate, but a lower bound for the threshold, the "expectation threshold", is generally easier to calculate. The Kahn–Kalai conjecture is that the two values are generally close together in a precisely defined way, namely that there is a universal constant K for which the ratio between the two is less than K log ⁡ ⁡ ℓ ℓ ( F ) where ℓ ℓ ( F ) is the size of a largest minimal element of an increasing family F of subsets of a power set.