reminded me that the AIMR-PPS(R)'s view of composite return is that it's "a single value that reflects the overall performance (the 'central tendency') of the set. The objective in reporting the returns of composites is to use a method for reporting the composite return that will give the same value achieved if the composite were treated as one master portfolio. That is, the value being calculated is the same value that would result if all of the assets and transactions of the individual portfolios/classes were combined and the return were computed using the procedures discussed earlier." [page 27 of the '93 version] Actually, I hadn't so much forgotten this, but rather was unable to locate a definition in the '93 or '97 editions of the AIMR-PPS (neither of their indexes provide easy passage to what Brian located, and I wasn't as diligent as he in trying to locate it).
When I taught classes for the CFA Institute (and prior to that, AIMR) on the standards (AIMR-PPS and GIPS(R)) the explanations regarding the math more often than not fell to me, and I would explain that asset weighting is used so that the return looks like it's coming from a single portfolio. I guess I hadn't really given this explanation a whole lot of thought: I had first heard it in 1992, when a debate was occurring on this subject, with the ICAA and IMCA challenging the approach that AIMR was implementing. The arguments against asset weighting were that it would cause larger accounts to overly influence the results; however, with the aggregate method we don't actually see this, since we end up with a mix of all accounts' holdings tossed together, with no reference or link to their source.
Further research is in order to understand "why" AIMR (and then the CFA Institute, and arguably now the GIPS Executive Committee, by default) would favor this approach. Is the blending of assets from a variety of accounts truly what we want?
It's somewhat ironic, I think, that the only method that AIMR came up with in their '93 edition fails at achieving the definition they laid out, as it provides an asset weighted average of returns (what IMCA and the ICAA objected to), not a result which truly represents the composite as if it was a single portfolio (though some would argue that it is an approximation of this).
If by now you're growing tired of this topic, I apologize. But I happen to find this somewhat fascinating.