Checkable

One Checkable Statement and the Missed Share

With one verifiable statement published, the blind share is exactly the fraction of the set a reader missed. No combinatorics survive.

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Publish one statement a reader can verify. Everything else is unverifiable. The reader meets some part of the set.

The share of possible contents that hold nothing checkable is, in that case, exactly the fraction of the set the reader did not reach.

Six published with three met: three of six missed, so half the contents are blind — ten of twenty. Eight with four met: thirty-five of seventy. Ten with five met: one hundred and twenty-six of two hundred and fifty-two. One half in all three. Before a wider rollout, decision-makers should check the current setup details and record who will have access to each type of information.

One checkable statement, half the set met

the whole bar: every content a reader might come away with
the dashed part: contents holding nothing checkable

Three shapes drawn.

Three pages, each publishing exactly one checkable statement, each read half-way. The blind share is exactly one half in all three.

Computed from the three numbers. A blind content is one holding no checkable statement: that is a property of the page, not a prediction about any reader.

Why the combinatorics drop out

A blind content is one that misses the single checkable statement. The chance of missing a particular statement, when drawing r from n, is the proportion of statements left out: (n − r) over n. Another useful point of reference for the wider question is European Data Protection Board.

Written as counts, C(n − 1, r) over C(n, r) reduces to (n − r) over n, and every binomial coefficient cancels. It is the only quantity in this record that simplifies that far.

That makes it a useful anchor. Anybody wanting to sanity-check the record's blind figures can start here, where the answer is obvious without any counting, and work outward to the cases where it is not.

What the simple case shows

The figure depends only on how much of the set the reader missed. Not on the page size, not on the contents figure, not on anything about the checkable statement itself.

Six published with three met and ten published with five met are different pages in every other respect — twenty contents against two hundred and fifty-two, one hundred and twenty arrangements against thirty thousand two hundred and forty. Their blind shares are identical, because in both cases the reader missed half.

A reader who met one statement of ten, having missed nine tenths of the set, has a blind share of nine tenths. A reader who met six of ten has a blind share of four tenths. The figure tracks the miss and nothing else.

With one verifiable statement, the question "can this reader check anything?" has become the question "how much did they skip?" Those are the same question, and only in this case.

The position this describes

One checkable statement in a set is a common position and not an accidental one. A single externally documented fact, with description around it, lands there.

The record's figure for that position is unforgiving. Unless readers reach most of the set, most of them cannot check anything — and the proportion is not a guess, it is the proportion they missed.

A set of ten statements with one checkable, read five at a time, leaves half its possible contents without anything to confirm. A second checkable statement brings that to two in nine — a shade over twenty percent. A third brings it to one in twelve.

Each added statement helps more than the last, which was shown in the previous note, and the first one helps least of all.

Reading it the other way round

The result can be stated as a rule about what a publisher needs from readers rather than as a figure.

With one verifiable statement, the share of blind contents equals the share of the set a reader missed. So for that share to fall below one in ten, readers have to reach nine tenths of the set. Below one in four, three quarters of it.

Those are demands on reader behaviour, not on the publisher, and they are the sort of demand nobody meets. A set of pages relying on a single verifiable statement is relying on near-complete readership to make it reachable, and near-complete readership is the one thing this record's first part showed cannot be assumed.

The figure in the drawing's third row

Ten published, five met, one verifiable: one hundred and twenty-six blind contents out of two hundred and fifty-two.

One hundred and twenty-six is a large number and the share is a simple one half, and the two together are what makes this row worth printing. A reader who sees a blind count of one hundred and twenty-six might assume something has gone badly wrong with the set. Nothing has: ten statements, one of them verifiable, a reader who got through half. It is an ordinary position and the figure for it is a coin flip.

The record's drawings print the count and the contents figure side by side for exactly this reason. Either number alone misleads, in opposite directions.

Where this breaks down

The simplification holds only at exactly one checkable statement. With two, the blind share is C(n − 2, r) over C(n, r), which does not reduce to anything a person can state in words, and from three onward it becomes less tractable with each step.

So the clean case is the clean case and nothing more. It is a good place to check the arithmetic and a bad place to generalise from, because the simplicity is a property of the number one rather than of the record.

The record carries the general formula everywhere and computes it per shape. The one-checkable case is drawn here because a reader who wants to verify that the machinery is doing something sensible can do it in this note without any tools, and then trust the arithmetic elsewhere for the reason that it is the same arithmetic.