Are Preference Relations Robust to Aggregation
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.