“A feature which distinguishes our approach is the consideration of multi-dimensional models. How can we assess an appropriate dimension for modelling a particular market? At one level, we could list all potentially relevant attributes of the product. But consumers may evaluate products according to only a few attributes, or according to a real-valued function of all the attributes. It is the dimension of the space of utility parameters rather than the number of product characteristics which is of greater economic interest.”
–Caplin, Andrew, and Barry Nalebuff. “Aggregation and imperfect competition: On the existence of equilibrium.” Econometrica: Journal of the Econometric Society (1991): 25-59.
For the precision of language: the approach that they refer to, i.e. characterizing dimension from the latent preference parameters, is not equal to pure characteristics approach. The traditional pure characteristic approach in IO uses observable product attributes as parameters instead of each product as parameters. As such, when the dimension of attribute grows the model still becomes harder to handle.
But a more appealing claim for using the latent attribute dimension is that it allows characterization of substitution and complementarity in a more precise manner (Yufeng’s comment).
A related comment can be found in Sheena S. Iyengar’s TED talk on choice overload. There, they tried to run the same choice experiment across different countries, testing how people choose among seven brands of coke along with water. The experiment participants in Russia stated that they only see 2 choices–coke and water–instead of eight.