A large, but shrinking, proportion of models in macroeconomics assume the existence of a representative agent. While there is clear evidence that households are heterogeneous, under some conditions aggregation may still hold. But even if it does not, what matters is whether it makes a quantitative difference.
Christos Koulovatianos, Carsten Schröder and Ulrich Schmidt address the question from a different angle. They ask whether differences in household size matter. They show it does not, theoretically, if the utility functions exhibit household-size economies (beyond subsistence consumption) that are invariant with income. I think that what the authors want to say here is that household size does not matter as long as preferences are such that consumption demand is linear in household size, which in fact does not imply that preferences are heterogeneous. Household size is just an argument in the household utility function. Or: household utility can be aggregated for individual utilities if the decisions rules can be aggregated, which is the case when they are linear.
Anyway, beyond these semantic issues, Koulovatianos, Schröder and Schmidt then provide survey evidence documenting that preferences have indeed the required property, namely that households perceived that the income necessary to maintain a given standard of living is linear in the number of its members. What is interesting here is that the survey covers many countries, possibly preempting the criticism I mentioned the other day.
On a separate note, this paper is particularly painful to read. It runs for 89 pages, and it is very confusing (even more than my post) because the authors do not use the right terminology. Also, they need to learn the virtues of conciseness and precision. I hope they did not send it to a journal in such bad shape. And of course they assume that all households have the same time preference, against which there is ample evidence and which matters much more as it has strong implications for savings.