One edit
Moving The Threshold Instead
Raising the threshold by one multiplies the intake by eleven twenty-firsts; lowering it, by nineteen fourteenths. Both are reversible; the others are not.
From a starting shape of three compulsory and six optional requiring three, raising the threshold to four multiplies the intake by eleven twenty-firsts — a reduction of about half.
Lowering it to two multiplies by nineteen fourteenths — an increase of about a third.
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Neither is the largest edit available. Both have a property the larger edits lack.
Six optional items, the three treads in play
Three thresholds drawn. The tread is flat because the threshold is a whole number: there is nothing between one item and the next.
The middle tread is the starting rule. One step down widens by about a third; one step up narrows by nearly half.
Computed from the threshold. Each item is counted as a separate coin: this is the unit of measurement, not an estimate of any population.
What they have that the others do not
Reversibility, in practice rather than in principle.
Every edit in this record can be undone arithmetically. Only the threshold can be undone socially, because changing it requires nobody to say that an item is or is not essential.
Moving a threshold from three to four is a statement about how much slack the work tolerates. Moving it back is a revision of the same judgement. Neither move implies that anybody was wrong about any particular item, so neither leaves a residue.
Promotion and demotion do leave a residue. Having argued that an item is essential, moving it back down means conceding the earlier argument, and that is a conversation most groups will have once and then avoid.
The threshold is the only parameter that can be tuned. Everything else can only be changed, and a change that costs somebody an argument is not a tuning.
The sizes, for comparison
| Edit | Multiplier | Reversible without an argument |
|---|---|---|
| demote an item | 33/14 | no |
| lower the threshold | 19/14 | yes |
| raise the threshold | 11/21 | yes |
| promote an item | 8/21 | no |
The threshold moves are the inner pair — smaller than the promotions in both directions, and the only two that can be made twice.
Where the threshold move is unexpectedly large
At the strict end of the staircase, as the section on thresholds sets out. The multipliers above are from a middling rule; from a strict one the same single step is worth far more.
A list requiring seven of eight moves to six of eight for a multiplier of about four. From eight of eight to seven, the multiplier is nine. Those dwarf anything promotion or demotion can do, and they are available at exactly the point where a list is most likely to be admitting nobody.
So the rule is not "the threshold is a small lever". It is "the threshold is a small lever in the middle of the staircase and a very large one at the ends", and knowing where you are standing comes first.
The practical order
For a list that needs adjusting, try the threshold first — not because it is the biggest move but because it is the cheapest to try and the easiest to undo.
If one step does not do enough, look at the placements, where the factors of six live. If those are all correct, the list has the wrong items on it, which is the only remaining possibility and the one that should be reached last rather than first.
Where the two figures come from
Six optional items give sixty-four profiles. The running sums from the top are one, seven, twenty-two, forty-two, fifty-seven, sixty-three and sixty-four, for thresholds of six down to none.
The starting shape sits at a threshold of three, with forty-two. Raise it to four and the numerator becomes twenty-two; twenty-two over forty-two reduces to eleven twenty-firsts. Lower it to two and the numerator becomes fifty-seven; fifty-seven over forty-two reduces to nineteen fourteenths.
The compulsory part never enters the calculation, because it is unchanged. That is why a threshold move is the one edit that can be computed without knowing the rest of the list.
The same move at other thresholds
The multiplier is not a property of the edit. It is a property of where on the staircase the edit happens.
| Threshold move on six optional items | Multiplier |
|---|---|
| 1 → 2 | 19/21 |
| 2 → 3 | 14/19 |
| 3 → 4 | 11/21 |
| 4 → 5 | 7/22 |
| 5 → 6 | 1/7 |
A single step therefore multiplies the intake by anything from about nine tenths to about one seventh, depending entirely on where it starts. Quoting eleven twenty-firsts as "the cost of raising a threshold" is therefore wrong in general and right only for the shape it was computed on, which is the discipline this whole section depends on.
The one trap
A threshold move is cheap to make and therefore easy to make repeatedly without noticing the cumulative effect. Three successive one-step tightenings, each defended on its own, can take a list from two hundred and nineteen profiles in two hundred and fifty-six to thirty-seven — a factor of six accumulated in three uncontroversial meetings.
Compounding is taken up on its own page, because it applies to every edit here and it is the thing that makes a sequence of reasonable changes unreasonable.
Near this one
- Adding An Optional Item Makes The List Wider
Adding an optional item without moving the threshold multiplies the intake by thirty-three twenty-eighths. The - The Cheapest Useful Change
Ranking the eight edits not by size but by what they cost the document and the people arguing about it. The be - 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 - Eight Edits, One Starting List
Every single change that can be made to a list, measured against the same starting shape. The multipliers run