Same filter

Eight Items And Sixteen, The Same Filter

The extreme case: a list of eight and a list of sixteen that admit identically. What the extra eight lines are doing, and why nobody can tell.

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A list of eight compulsory items admits one profile in two hundred and fifty-six.

A list of eight compulsory items followed by eight optional ones with no threshold admits one profile in two hundred and fifty-six.

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Sixteen lines against eight, and not a hair of difference in the filter.

Three ways to write one filter

Three shapes drawn, running from 8 items to 16. They are not variants of one list; they are different lists that happen to be the same filter.

Three shapes from the same class. The first is eight optional items all required; the second is eight compulsory items; the third is sixteen items of which half do nothing.

Computed separately for each shape shown. They agree because the arithmetic makes them agree, not because they were chosen to.

What the extra eight lines do

As a filter, nothing whatsoever. An optional item with a threshold of none cannot exclude anybody; it has no mechanism to.

As a document they do a great deal. They tell a reader what the work touches. They name skills, tools and areas that the compulsory eight do not cover. Somebody reading the longer list learns more about the job.

They also deter. A reader seeing sixteen lines reads sixteen requirements, counts how many they meet, and concludes accordingly — without any way of knowing that half the list has no teeth.

	Eight-item version	Sixteen-item version
profiles admitted	1 in 256	1 in 256
information given to a reader	less	more
reader's impression of difficulty	lower	higher
people who withdraw before applying	fewer	more

The uncomfortable conclusion

The longer document is a worse instrument despite being identical arithmetically, because the gap between what it does and what it appears to do is larger.

That is not an argument for short lists. It is an argument for saying which lines bite — one sentence, naming the threshold, which converts the extra eight lines from apparent barriers into what they actually are.

A line that cannot exclude anybody still excludes people, by being read as a line that could. The arithmetic does not see it and it happens anyway.

Why the author cannot see it either

Because the author knows which items matter and the document does not record that knowledge.

Writing a list of sixteen in which eight are decisive and eight are context feels, from inside, like writing a thorough description. The distinction is perfectly clear in the writer's head. It is nowhere on the page, and the page is what the reader has.

This is the same failure as the unwritten threshold, in a different costume: information that exists in one place and is needed in another, with no mechanism moving it across.

The repair

State the rule, and state it in a way that identifies which part of the list it governs.

"All eight of the following are required. The eight below them describe the work and none is required." Two sentences. The filter is unchanged, the document now says what it is doing, and the eight decorative lines can do their informative job without doing a deterrent one.

The pair, side by side

The two extremes of the class are the clearest illustration in the record.

The eight-line list	The sixteen-line list
eight items, all optional	eight compulsory items
all eight required	eight further optional items
—	none of those eight required
admits 1/256	admits 1/256

The left-hand document is a page of eight lines under a rule saying every one is needed. The right-hand document is twice as long, and the second half of it does not affect the outcome in any way: a profile meeting all eight optional items and a profile meeting none are treated identically.

The sixteen-line version read as a document

A reader works down it and encounters sixteen things. They have no way of knowing that the filter closed after the eighth.

Worse, the eight inert lines are the ones most likely to deter. They are the extras, the nice-to-haves, the ones that make the list look formidable — and they are precisely the ones with no arithmetical effect at all. A reader meeting all eight compulsory items but none of the preferred ones is through, and may well not come forward.

So the eight lines do the opposite of nothing. They filter, by discouragement, exactly the people the arithmetic admits. The document is wider than it looks and the gap between those two facts falls entirely on the reader.

The same pair with the second half switched on

Put a threshold over those eight inert lines and they stop being inert.

A sixteen-item list with eight compulsory items and a threshold of four over the remaining eight admits one hundred and sixty-three profiles in sixty-five thousand five hundred and thirty-six — about one in four hundred and two, against one in two hundred and fifty-six for the version with no rule.

So the difference between the eight optional lines doing nothing and the same eight lines doing something is a factor of about one and a half, achieved by writing one number. The lines themselves are identical in both documents; the only difference is whether a rule was stated over them.

The general principle this case illustrates

Within a class of equal intake, shapes differ in everything except selectivity: length, tone, information content, deterrent effect, clarity.

Choosing among them is therefore a free choice on every axis the arithmetic does not measure — which is most of the axes that matter to the people reading. The arithmetic's job is to tell you the choice is free; it has no view on how to use the freedom.