Why is it so hard to sort by price?

A common use case for online shopping is searching for products — say, coffee makers — and then sorting the results by price, from low to high, in order to find a cheap one. Surprisingly, this use case fails on most ecommerce sites.

You’d think that ecommerce sites would have solved this problem years ago. But sorting by price isn’t as simple as it sounds. Why is it so hard?

Sorting exposes the difference between “relevance” and “ranking”.

Most shopping sites allow searchers to sort results by price, but the results often aren’t what you’d expect. For example, the cheapest results for “coffee maker” usually aren’t coffee makers. Instead, they’re accessories like coffee filters and single-use capsules. These irrelevant results match the keywords “coffee” and “maker”, and they cost less than the cheapest coffee maker.

The problem is that most search engines conflate relevance with ranking. In theory, a search engine should only return results that are relevant to the query. In practice, search engine developers focus primarily — or even exclusively — on the relevance of results that searchers are likely to see. Indeed, search evaluation metrics like discounted cumulative gain (DCG) are position-biased, mostly measuring the relevance of top-ranked results.

Position bias isn’t a problem when results are sorted by their relevance scores — indeed, it’s the whole point of such a sort. But when searchers sort results by price — or by any attribute other than relevance score — then the irrelevant results that had been buried suddenly show up front and center.

So it’s just a relevance problem?

Yes, it’s just a relevance problem. But it’s a problem that isn’t easy to solve.

Search engines face a trade-off between precision (aka relevance) and recall. No search engine is perfect. Increasing precision causes recall to suffer: attempts to remove irrelevant results lead to removing some of the relevant results. Conversely, increasing recall causes precision to suffer: attempts to include more of the relevant results increase the number of irrelevant results.

When searchers sort by relevance score, the search engine can afford to err on the side of recall, since searchers won’t see most of the irrelevant results. But when searchers sort by price, poor precision has very negative impact on the search experience.

In fact, sorting by price tends to amplify precision issues. Consider the coffee makers example: irrelevant results like accessories tend to be outliers on price, so they dominate the lowest-priced results.

Allowing searchers to sort requires separating relevance from ranking.

A search engine that allows searchers to sort by price — or other attributes that don’t correlate with the relevance score — needs to separate relevance from ranking. Rather that optimizing for a position-biased relevance metric like DCG, it needs to consider precision for the entire result set.

In other words, search engines can’t keep relying on relevance ranking as a crutch that allows them to err aggressively on the side of recall. Instead, they have to face a real trade-off between precision and recall.

In practice, that means establishing a relevance threshold and filtering out results whose relevance score is below that threshold.

It’s important to provide transparency and control to searchers.

Filtering results using a relevance threshold inevitably filter out some results that are relevant. As discussed above, it’s a trade-off. But, in a sort by price, searchers may think that the search engine is deliberately — and deviously — filtering out less expensive results.

In order to earn searchers’ trust, it’s important for the search engine to provide transparency and control. A best practice for implementing a relevance threshold is to show a prominent message at the top of the results, e.g., “We removed some results to show you the most relevant listings. Click here to view all results.”

Offering searchers transparency and control helps assure them that the search engine is making a good-faith effort to satisfy their intent. It’s also useful as a quality check: if many searchers click the link to view all results, it probably means that the relevance threshold is too aggressive.

Maybe the searcher doesn’t really want to sort by price.

Given the challenges of implementing sorting by price, it’s a good idea to offer searchers alternative ways to refine or organize the results.

One alternative to sorting by price is filtering by price, e.g, allowing searchers to only see results that cost less than $20. Filters don’t change the sort, i.e., results that satisfy the price filter are still sorted by relevance score. But it is important to provide price filters that are appropriate to the search query, e.g., different ranges for coffee makers than for diamond rings.

Another alternative is to organize results using facets or clusters. In the case of coffee makers, that could mean organizing results by the different kinds of coffee makers: automatic drip, French press, super automatic espresso, etc. Indeed, sorting results by price isn’t very useful for heterogenous result sets, but it can be quite useful once the searcher has narrowed down the result set.

Many searchers use sorting by price as a proxy for some other intent. If the search engine can directly address that intent, everybody wins.

Summary

Sorting by price is surprisingly difficult — and we haven’t even considered issues like unit pricing and product variations. Allowing users to sort results requires the search engine to separate relevance from ranking, which requires them to face the trade-off between precision and recall. If a search engine implements a relevance threshold, it’s important that it provides transparency and control to earn searchers’ trust. Finally, sorting by price may be a proxy for some other intent that the search engine can address directly.