One more facet

Adding A Choice

One more option inside a filter multiplies the cells by k plus one over k. The cheap edit, and nearly always the one that gets done.

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

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Adding a value to a filter that already offers k choices multiplies the resolution by k plus one over k.

Taking a facet from four choices to five multiplies the cells by five quarters. From five to six, by six fifths. The edit gets less valuable the larger the facet already is.

Teams comparing a planned schema with day-to-day work may test remote team activity insights beside completed tasks, review notes and direct employee explanations. For a separate technical reference, see Typesense.

The rates

Facet goes from	Cells	Questions
2 to 3	×3/2	×4/3
3 to 4	×4/3	×5/4
4 to 5	×5/4	×6/5
5 to 6	×6/5	×7/6

The best case is a two-choice toggle becoming a three-way choice, which multiplies the resolution by half again. The worst is a five-value facet becoming six, which adds a fifth.

Against a new facet, which multiplies by at least two, none of these is close.

Why it gets done anyway

Because it is the edit the work naturally produces.

A board notices that one of its categories is too broad: listings of two quite different kinds are both being filed under it. Splitting that category in two is an obvious, small, well-understood change. It requires reclassifying only the listings currently in that one category, and only into two options that are already familiar.

Nobody has to ask the field a new question, nobody has to revisit old listings outside the affected category, and the sidebar looks almost identical afterwards.

The cheap edit is the one that arrives as a complaint about a specific category. The expensive edit is the one nobody complains about, because readers cannot see the dimension that is missing.

The asymmetry in what gets noticed

This is the part worth sitting with.

A category that is too broad produces a visible symptom: results that mix two kinds. Readers notice, somebody says so, the category gets split.

A dimension the board does not carry at all produces no symptom. Readers get results that mix two kinds, cannot say which dimension would have separated them, and generally conclude the board is fine and their search was imprecise.

So the feedback a board receives points almost entirely at the cheap edit, and the expensive edit — the one that buys a multiple rather than a fraction — has nobody advocating for it.

What a sequence of cheap edits adds up to

Less than one expensive one, usually.

Take a board of four and six choices, twenty-four cells. Push the four up to five, then six: the resolution goes to thirty, then thirty-six. Two rounds of reclassification for an increase of a half.

A single new facet of three would have taken it to seventy-two.

Path	Edits	Cells
4 to 5 to 6	two	36
add a facet of three	one	72

The second column is work and the third is what it bought. The cheap path did more work for a quarter of the result.

The sequence that reaches the bound

A facet cannot grow past six in this record, so the cheap edit runs out.

A facet of two can be widened four times, to three, four, five and six. Each step buys less than the last: half again, then a third again, then a quarter, then a fifth. The four steps together multiply the resolution by three.

A single new facet of three does the same in one edit, and a new facet of six does twice as much.

So a board that only ever makes the cheap edit has a ceiling: it can multiply its resolution by at most three per facet it already has, and then there is nothing left to widen.

When the cheap edit is right

When the category genuinely is too broad.

None of this is an argument against splitting a category that needs splitting. If two kinds of listing are being merged by a single option, the split separates them, and that is exactly the problem worth solving.

The argument is against mistaking the cheap edit for progress on the other problem. Refining existing filters never reaches the listings merged because a dimension is absent, and the two cases look identical from a reader's chair: a result containing things that should have been apart.

Telling them apart requires knowing which dimension is missing, and that is not something the arithmetic can supply. What it supplies is the price of each remedy, so that the conversation is at least about the right-sized move.