Thresholds

Choosing A Threshold On Purpose

The threshold is the one parameter worth setting deliberately, and setting it takes under a minute. What the minute consists of.

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A threshold is a whole number between none and however many optional items there are. For a list of eight that is nine possibilities, and the record gives the intake of all nine.

Choosing one deliberately is therefore a small, finite task: look at nine numbers and pick a row. The reason it so rarely happens is not difficulty.

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The minute, in four steps

Count the optional items. Everything on the list that is not an absolute barrier belongs here. If an item would not, on its own, disqualify somebody, it is optional whatever the heading above it says.

Read the staircase for that count. On eight items the treads run 1, 255/256, 247/256, 219/256, 163/256, 93/256, 37/256, 9/256, 1/256. Those are the only nine filters available from those eight lines.

Ask what the work needs. Not what sounds right — what the work needs. Can somebody missing half of these do it? If yes, the threshold is at or below four. If missing one is already fatal, the item was never optional.

Pick the tread and write the number down. In words, next to the list, where a reader will see it.

What usually goes wrong at step three

The question gets answered about an imagined ideal candidate rather than about the work.

Asked "can somebody missing three of these do the job", the honest answer is often yes, and the uncomfortable answer is that the three were on the list because they would be nice, not because they are needed. Admitting that moves the threshold down and widens the filter considerably — from, say, six-of-eight at thirty-seven in two hundred and fifty-six to three-of-eight at two hundred and nineteen, a factor of nearly six.

The discomfort is real and it is not an argument. The filter either reflects the work or it does not, and the arithmetic does not care which.

A threshold set against an imagined candidate is a threshold set against nobody, because the imagined candidate is always available and never applies.

A useful default, stated as a default

Where the work genuinely tolerates gaps — which is most work — a threshold around a third of the optional items gives a wide filter that still means something. On eight items that is three, admitting two hundred and nineteen profiles in two hundred and fifty-six.

That is offered as a starting point to argue with, not as a recommendation about anybody's situation. The record knows nothing about any particular job and would be overstepping to say more.

What setting it buys

Three things that an unstated rule cannot provide.

One filter instead of several. Every reader applies the same rule, so the same candidate gets the same answer regardless of who looks.

A number to disagree with. Somebody who thinks three is too lenient can propose four, and the two positions differ by a stateable amount — two hundred and nineteen against one hundred and sixty-three.

A record of the decision. In six months, when the list is revisited, the threshold is on the page rather than in somebody's memory of what they meant.

The minute, worked through on a real shape

Take a list of eleven items: three compulsory and eight optional. The denominator is two thousand and forty-eight.

The compulsory part contributes a factor of one eighth and is not up for discussion — those three items are required and the arithmetic is settled. The whole decision is which of nine thresholds to put over the eight optional items.

Threshold	Admits	Roughly
3 of 8	219/2048	one in 9
5 of 8	93/2048	one in 22
6 of 8	37/2048	one in 55

Three plausible rules, and a sixfold spread between the outer two. The minute consists of reading those three figures and choosing one, which is a different activity from picking an adjective and hoping.

The objection that this is over-engineering

The objection is that nobody needs a fraction to write a list of requirements, and it is worth taking seriously rather than brushing aside.

What survives it is the spread. Nobody needs a fraction to choose between two rules that differ by five per cent. The rules here differ by a factor of six, and the person writing the list has no other instrument that would reveal that.

The arithmetic is also not laborious: one halving per compulsory item, one running sum of binomial coefficients for the optional part, and the two multiplied. That is the whole method, it takes under a minute by hand, and the alternative is not a cheaper method but no method.

The last check

Having set it, compute the whole filter: the halving from the compulsory items multiplied by the tread from the optional ones. Say the result out loud.

If a list of three compulsory and six optional requiring three comes out at twenty-one profiles in two hundred and fifty-six, that is the sentence to test against the work. It is a narrow filter. Whether it is the right one is not something this record can judge — but it is now a thing that somebody chose, which is the entire difference this section is about.