One more facet

Taking A Filter Away

Removing a filter divides the resolution by its size. It is the only edit that makes separable listings inseparable, and readers cannot see it.

One more facetReference×k against ×(k+1)/k

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The two edits that add have two mirrors that remove.

Removing a filter of k choices divides the resolution by k and the question count by k plus one.

Removing a value from a facet of k choices divides the resolution by k over k minus one — a small change, matching the small change that adding one made.

Before a wider rollout, decision-makers should see how this works in practice and document who can access each type of information. For a separate technical reference, see Algolia.

The figures

Starting from three, five and six choices: ninety cells, one hundred and sixty-eight questions.

Edit	Schema	Cells	Questions
none	3·5·6	90	168
remove the three	5·6	30	42
remove the five	3·6	18	28
remove the six	3·5	15	24
take the five to four	3·4·6	72	140

Removing the six cuts the resolution to a sixth. Removing one value from the five cuts it by a fifth.

Why removing is not symmetric with adding

In arithmetic it is: the factors are reciprocal.

In consequence it is not, and the asymmetry is the whole of this page. Adding a filter makes previously merged listings separable. Removing one makes previously separable listings merge — and those two events are not equally visible.

When a filter is added, nothing that worked before stops working. The old queries still exist, still return what they returned, and the new ones are extra.

When a filter is removed, queries that used to be expressible are gone. Readers who relied on that distinction get results containing both kinds, with nothing to tell them what changed.

Adding a filter is additive and nobody is worse off. Removing one silently withdraws distinctions, and the people who lose them cannot see what they lost.

Why filters get removed

Usually to simplify, and usually with evidence.

A board looks at which filters readers actually set, finds one getting very little use, and removes it. The reasoning is sound in its own terms: a control nobody touches is clutter, and clutter costs every reader attention.

What the usage figures do not show is the readers who would have wanted it and did not find it, or who used it rarely and indispensably. A filter set by two per cent of readers may be the only way those readers get anything useful at all.

What a reader experiences afterwards

A board that worked and now does not, with no explanation.

Somebody who used a particular filter every visit arrives to find it gone. Their established way of getting to what they want has been withdrawn, and the results they now get mix in a kind of listing they had learnt to exclude.

Nothing on the page says a filter was removed. From the reader's side it is indistinguishable from the board having got worse at searching, which is roughly what happened.

The figure to weigh against usage

Resolution, and it is the one the usage data cannot supply.

Removing a filter of six divides what the board can tell apart by six. That is a large structural change justified by a usage figure, and the two are not denominated in the same units — one is a fact about this quarter's readers, the other about what the board is capable of permanently.

What the data says	What the arithmetic says
two per cent set this filter	removing it divides resolution by six

Both are true. Neither settles it, and a decision made on the first alone has not looked at the second.

The reverse of the usual advice

Everywhere else this record points towards fewer, larger facets: better share, better resolution per control, gentler cost in precision.

Removal is where that direction stops. Removing a large facet divides the resolution by a large number, so the very facets that earn their place most are the most expensive to take away.

A board simplifying its sidebar by removing its largest dropdown is making the biggest possible cut to what it can tell apart, and the sidebar looks barely different for it.

The one case where removal is clean

A facet whose values nobody differs on.

If every listing takes the same value in a filter, the filter multiplies the achieved resolution by one, whatever its nominal size. Removing it divides the nominal figure by its size and the real figure by nothing.

That is the only removal with no cost in distinction, and it is checkable: look at how the listings are distributed across the filter's values. If they are all in one, the filter is inert and the arithmetic in this record overstates what the board does.

Everywhere else, removal divides by the size, and the reader who needed that distinction has no way of telling anybody.