One edit

Two Edits Are Not The Sum Of Two Edits

Edits multiply rather than add. Three uncontroversial tightenings, each defended on its own merits, can narrow a list by a factor of a hundred and sixty-eight.

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Edits to a list compound. Two changes that each halve the intake do not take away half of it twice — they take it to a quarter.

That is obvious stated baldly and it is reliably lost in practice, because the changes arrive one at a time, in separate conversations, each judged on its own.

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One list, tightened three times

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; two of them admit too little for the square to be drawn, and carry a stroke instead.

The starting shape, then three successive tightenings. Each step was a single reasonable change; the four rows span a factor of a hundred and sixty-eight.

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

A worked sequence

Start at three compulsory and six optional requiring three: twenty-one profiles in two hundred and fifty-six.

Raise the threshold by one. Eleven in two hundred and fifty-six. Somebody argued that three of six was too lenient, and they may have been right.

Add a compulsory item and raise the threshold again. Seven in one thousand and twenty-four. A new absolute requirement emerged, and the rule tightened with it.

One more of each. One profile in two thousand and forty-eight.

Step	Shape	Admits
start	3, 6, 3	21/256
after one	3, 6, 4	11/256
after two	4, 6, 5	7/1024
after three	5, 6, 6	1/2048

Three changes, a factor of a hundred and sixty-eight, and no single step was unreasonable.

Why nobody sees it coming

Because each step is compared with the step before it, not with the start.

Going from twenty-one in two hundred and fifty-six to eleven is halving — noticeable but not alarming. Going from eleven in two hundred and fifty-six to seven in one thousand and twenty-four is a little worse again. At no point is anybody looking at a change large enough to stop a meeting.

The aggregate is a filter a hundred and sixty-eight times narrower than the one everybody agreed to at the beginning, and no meeting ever discussed it, because the comparison with the beginning was never made.

A sequence of defensible changes is not a defensible sequence. The only way to find out is to compare the end with the start, and nothing in the process prompts anybody to.

The same thing in the other direction

Loosening compounds too, and this is the useful half.

A list stuck at one profile in two thousand and forty-eight can be moved back with the same three steps reversed, and the gain is the same factor of a hundred and sixty-eight. Two or three cheap, reversible changes — a threshold step, a demotion, another threshold step — recover an enormous amount.

That is worth knowing because the instinct for a list admitting nobody is to make one dramatic change. Three small ones do more, cost less, and are easier to agree.

The one practice that prevents it

Record the figure at the top of the list and update it whenever the list changes.

A document carrying its own intake makes compounding visible at the moment it happens. Somebody proposing the third tightening is looking at a figure that has already fallen by a factor of twelve, and the conversation that would never otherwise occur occurs.

It costs one line in the document and it is the only mechanism in this record that works against the ratchet described in the first section.

The three multipliers, separately

Each step in the sequence is defensible on its own and the three are nothing like equal in size.

Step	Shape after it	Admits	Multiplier
start	3 compulsory, 6 optional, 3 needed	42/512	—
add a compulsory item	4, 6, 3	42/1024	1/2
raise the threshold to five	4, 6, 5	7/1024	1/6
add another and raise to six	5, 6, 6	1/2048	1/14

One half, one sixth, one fourteenth. Multiplied together they give one hundred and sixty-eighth, and the middle step — two notches on a threshold — did more than either of the two new lines.

What a hundred and sixty-eight looks like from outside

It looks like a slightly longer list.

The document gained two lines and its threshold wording changed twice. Anybody comparing the first version with the last would describe the difference as modest: eleven items instead of nine, and a rule that now says most of them rather than some of them.

The filter went from admitting about one profile in twelve to about one in two thousand. Nothing in the appearance of the document carries that, nobody along the way made a decision they would describe as drastic, and the only way the change would ever be noticed is if somebody had computed the intake at the start and wrote the figure down.

What generalises

Multipliers multiply. Anybody holding the eight edits from the start of this section can combine them freely: promote and raise the threshold is eight twenty-firsts times eleven twenty-firsts, and so on.

The arithmetic is trivial. The discipline of doing it before rather than after is the whole content of this page.