Are Preference Relations Robust to Aggregation 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.
I presume you mean to take the total (or average) willingness to pay for each alternative to be the social willingness to pay. $WTP_{soc}(a)=WTP_{1}(a)+WTP_{2}(a)+WTP_{3}(a)$ Then $WTP_{soc}$ is a representation of a social preference relation $a\succsim b \Leftrightarrow WTP_{soc}(a)\geq WTP_{soc}(b)$. This preference is transitive and complete. Individual and aggregate preferences are consistent in the sense that they satisfy the Pareto criterion and the independence axiom of Arrow's impossibility theorem. The way we have tricked the impossibility theorem is that we have taken an ordinal preference relation and turned it into a cardinal concept (WTP).

The question is whether the mean willingness to pay is a meaningful concept in any way. For example, a poor person's willingness to pay for a good may be relatively low, but the marginal utility very high. For a discussion of interpersonal comparisons of utility, see the following article:

Harsanyi, John C. Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Springer Netherlands, 1976.