This is more a question of putting the theory into practice, or at least clarifying the theory in practice. The question has to do with the application of preference relation axioms and aggregation. Take the transitivity relation for example;
$\forall (x,y,z) \in X,$ if $ x \succ y \wedge y \succ z \iff x \succ z $
Suppose I have a set of data on the preferences of $n$ consumers $C_1,C_2,...,C_n$ over products $a, b,$ and $c$ such that;
$C_1$ prefers $a \succ b \succ c$
$C_2$ prefers $a \succ c \succ b$
$C_3$ prefers $c \succ b \succ a$
and so on until consumer $n$, each with a respective WTP for each product.
So the question is, if the data were aggregated over $n$ consumers we would achieve an aggregate WTP for whichever preference dominates. Lets say that the aggregate data reveals $a \succsim b \succsim c $. Does this result violate transitivity and completeness since the individual consumer $C_3$ prefers $c \succ b \succ a$. Do individual and aggregate preferences have to be consistent.