Random Utility interpretation Can someone explain intuitively, the Block-Marschack Polynomials that completely characterize random utility.
Given a universe of choices $X$, subsets of alternatives $A \subseteq X$, and choice probabilities $\Pi_{A}(x)$ for item $x \in A \subseteq X$, the Block-Marschak polynomials can be defined recursively as (see McFadden, Revealed stochastic preference:
a synthesis, 2005) as

$K_{x, \emptyset} = \Pi_{X}(x) \,, \quad K_{x, A} = \Pi_{X\setminus A}(x) - \sum_{C \subset A} K_{x, C}$

When the choice probabilities are the result of utility maximization, Barbara and Pattanaik (Falmagne and the rationalizability of stochastic choices in terms of random orderings, 1986) provide a useful and intuitive interpretation of $K_{x,A}$ as the probability of the event that $x$ is ranked behind the elements of $A$ and ahead of all the remaining elements in $X \setminus A$.