Length

A Short List Can Be The Stricter One

Three compulsory items admit one profile in eight. Eight optional items requiring three admit two hundred and nineteen in two hundred and fifty-six.

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Three compulsory items admit one profile in eight — thirty-two in two hundred and fifty-six, to put it on a common denominator.

Eight optional items requiring three admit two hundred and nineteen in two hundred and fifty-six.

For recurring connector work, reviewers can learn more from the official source and test whether the record improves planning rather than adding administration. For an independent technical reference, see Stitch.

The three-line list is about seven times narrower than the eight-line one.

Short against long

filled: a requirement that must be met
open: one of the optional ones
area of the inner square: the share admitted
a stroke instead: too small for this panel to draw

Four shapes drawn.

Three lines against eight, and the three-line list is the narrower filter by a wide margin. At five against eight the gap is wider still.

Computed from the shape of the list. The shape is a stated convention; the count of admitted profiles is arithmetic on subsets.

Why this is not a trick

Nothing unusual has been done to either list. A three-item conjunction is the most ordinary kind of requirement list there is, and three-of-eight is a thoroughly reasonable rule.

The asymmetry comes from the structure. A conjunction has exactly one way to pass. A threshold rule has many — for three of eight there are two hundred and nineteen passing profiles, because there are so many combinations of three or more items out of eight.

Multiplicity of routes is what makes a filter wide, and it has nothing to do with how many lines there are.

List	Lines	Ways to pass	Space	Admits
3 compulsory	3	1	8	1/8
8 optional, 3 required	8	219	256	219/256

Where the crossover lies

Raising the threshold on the eight-item list narrows it until it overtakes.

Five of eight admits ninety-three in two hundred and fifty-six, which is still wider than three compulsory items at thirty-two. Six of eight admits thirty-seven — close. Seven of eight admits nine, and is now considerably narrower.

So a three-line conjunction sits somewhere between six-of-eight and seven-of-eight in strictness. Three lines are doing the work of roughly six and a half optional ones.

A compulsory item buys roughly what two optional ones buy at a middling threshold. That exchange rate decides which of two lists is harder, and nothing on either page displays it.

What this does to a comparison

It means that two lists cannot be compared by eye at all, and that the direction of the error is not even consistent.

Sometimes the long list is the stricter one — eight optional items requiring seven, against three compulsory items. Sometimes the short one is, as above. Nothing about the appearance of the documents indicates which case you are in.

The only method is to compute both, which takes a few seconds each once the rules are known, and is impossible when they are not.

Why short lists feel lenient

Because brevity reads as modesty. A list asking for three things appears to be asking for less than one naming eight.

It is asking for fewer things and demanding them absolutely. The absoluteness is where the strictness lives, and absoluteness does not take up space on the page.

The exchange rate between the two kinds of item

One compulsory item is worth about two optional items at a middling threshold. The figure is worth having because it is the only way to compare two lists built differently.

A compulsory item halves the intake, exactly and always. An optional item at a threshold near the middle multiplies the intake by something between about three quarters and about one and a quarter, depending on which direction the threshold moves with it.

So a three-item conjunction, at one eighth, sits in the same region as six or seven optional items at a threshold around six. That is the comparison the page cannot show: three lines against seven, with the three-line document being the harder one.

Where this shows up in practice

In the gap between a short, old list and a long, new one.

Lists tend to start short and absolute — a handful of things, all required — and grow long and hedged, with more items and softer language. The usual assumption is that the list has become more demanding as it got longer.

Arithmetically it has often become far more generous, because the growth came in the optional part and the threshold either stayed low or was never stated. The document looks harder and admits more, and the only way to know which happened is to compute both versions.

Why the longer list is often the better document

None of this is an argument for short lists.

The eight-item list in the comparison above names eight things the work touches and admits most people who meet three of them. It informs a reader far better than three absolute lines do, and it excludes far fewer of them. On both counts it is the more useful document.

The condition is the one this section keeps returning to: the rule has to be written down. With a stated threshold of three, the long list is generous and legible. Without one, it is a long conjunction in the minds of half its readers and a wish list in the minds of the rest.

The practical use

If a filter needs to be narrow, a short conjunction is the efficient way to build one: three lines buy what six or seven optional lines would.

If a filter needs to be wide while still naming a lot of ground, a long optional list with a low threshold does that, and does it without the deterrent effect of a long conjunction — provided the rule is stated, which is the condition this whole section keeps returning to.

The mistake is a long conjunction, which is simultaneously the most deterring document to read and the narrowest filter to pass, and which is what a list becomes by default when nobody writes a rule.