and the first conclusion is "something that you think will improve relevance probably won't"; the TREC conference went for about five years before making the first real discovery
It's true that Arrow's Theorem doesn't strictly apply, but thinking about it makes it clear that the aggregation problem is ill-defined and tricky. (e.g. note also that a ranking function for full text search might have a range of 0-1 but is not a meaningful number, like a probability estimate that a document is relevant, but it just means that a result with a higher score is likely to be more relevant than one with a lower score.)
Another way to think about it is that for any given feature architecture (say "bag of words") there is an (unknown) ideal ranking function.
You might think that a real ranking function is the ideal ranking function plus an error and that averaging several ranking functions would keep the contribution of the ideal ranking function and the errors would average out, but actually the errors are correlated.
In the case of BM25 for instance, it turns out you have to carefully tune between the biases of "long documents get more hits because they have more words in them" and "short documents rank higher because the document vectors are spiky like the query the vectors". Until BM25 there wasn't a function that could be tuned up properly and just averaging several bad functions doesn't solve the real problem.
https://ccc.inaoep.mx/~villasen/bib/AN%20OVERVIEW%20OF%20EVA...
and the first conclusion is "something that you think will improve relevance probably won't"; the TREC conference went for about five years before making the first real discovery
https://en.wikipedia.org/wiki/Okapi_BM25
It's true that Arrow's Theorem doesn't strictly apply, but thinking about it makes it clear that the aggregation problem is ill-defined and tricky. (e.g. note also that a ranking function for full text search might have a range of 0-1 but is not a meaningful number, like a probability estimate that a document is relevant, but it just means that a result with a higher score is likely to be more relevant than one with a lower score.)
Another way to think about it is that for any given feature architecture (say "bag of words") there is an (unknown) ideal ranking function.
You might think that a real ranking function is the ideal ranking function plus an error and that averaging several ranking functions would keep the contribution of the ideal ranking function and the errors would average out, but actually the errors are correlated.
In the case of BM25 for instance, it turns out you have to carefully tune between the biases of "long documents get more hits because they have more words in them" and "short documents rank higher because the document vectors are spiky like the query the vectors". Until BM25 there wasn't a function that could be tuned up properly and just averaging several bad functions doesn't solve the real problem.