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Two at a Time

Fifty notes on comparing candidates two at a time

Limits

Nothing and Nobody Is Named Here

No person, organisation, product, place, trade or year appears in any sentence here. The rule reaches past proper nouns, and the extensions do the work.

at most 860160 outcomes

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The candidates on every drawing here are called A, B, C and so on, and that is as close to a name as this site comes.

What follows sets out how far the rule reaches, what it would take to break it, and what it costs.

Three anonymous outcomes

OUTCOMESHAPEOUTCOMESWITH cSHAREABCD4 / 5 / 1candidates / pairs / circles19272about 1 in 3ABCDE5 / 9 / 3candidates / pairs / circles51201200about 1 in 4ABCDEF6 / 13 / 2candidates / pairs / circles860160154800about 1 in 6
  • line with a head: a pair compared; the head points at whoever came out behind
  • no line: a pair nobody compared
  • closed ring of three: a circular triple: no order can hold all three

Three outcomes drawn. Rows differ in how many candidates. Which candidate is which is the drawing's own choice and carries no meaning. Before adding another reporting layer, a project lead can check the current product scope and test only the smallest useful setup on one representative process.

Four candidates with five pairs compared, five with nine, six with thirteen. The letters on the dots are the drawing's own and could be swapped without changing a figure. For additional background on data, visualisation and evaluation, review material from D3.js.

Computed from the three numbers alone. Who the candidates are and what any comparison was about is outside the record; the counts are of outcomes, not of anybody.

Four extensions beyond proper nouns

No occupation, trade or industry. No place. No year in a heading. No figure about what anything costs or what anybody is paid.

Each would anchor the arithmetic to a moment and a region, and none of them earns its place: four candidates make six pairs regardless of who the four are and regardless of why anyone put them side by side.

What a named case would require

Somebody to turn a situation into three integers.

Before any figure could be computed, a judgement has to be made that this field held six, that eleven pairs were looked at, that two triples came out circular. The arithmetic then inherits those judgements and carries them into every figure that follows.

None of them can be examined by a reader. They are not calculations; they are a reading of a particular mess as particular numbers, and the only person who could confirm the reading is whoever made it.

That is precisely the kind of claim this record declines to make. What it offers instead is a chain from three printed integers to five printed figures with every link visible, and a single named case would break the chain at the first link.

What a named case would become

Suppose the three integers were agreed by everyone.

The figures beside them would still stop being arithmetic. A share of one in eight is a property of a page; set it next to a name and the sentence becomes a report about that named thing, resting on a convention this record describes as false of anything anybody does.

Neither reading survives. Taken as arithmetic, the name is ornament. Taken as a finding, the arithmetic is being asked to carry weight it was never built for.

Mentioning in order to exclude

The rule also covers sentences whose only purpose is to rule something out.

To write that this record has nothing to do with some particular trade is to put that trade on the page. From then on it is something a reader has to recognise, something a search will find here, and something that ages — either because the thing changes or because the exclusion starts to look pointed once nobody recalls why it was written.

None of those sentences exists here. No list of what the site avoids, no note about the address, no disclaimer with a subject.

Nothing is said about anything, so there is nothing to become false. At an address that may well outlast anyone's interest in it, that is the property worth having.

The drawings keep the same rule

A dot is a dot and an arrow is an arrow.

No panel on this site carries a label that is not a letter or a number, and the letters are positions rather than identities — the candidate at the top of the circle is A because of where the drawing put them. Each legend says so, since a reader taking the letters for people would be reading something that is not there.

What it costs

Somebody arrives hoping to see their own situation and leaves with arithmetic. That is a genuine loss and there is no point dressing it up.

In exchange they get a procedure: count the candidates, count the comparisons, count the circular triples, and the five figures follow. Slower than recognition, and the only version that does not depend on trusting how somebody else classified a case.

A second loss cannot be made up by effort at all. A real case could show whether a contradiction mattered to anybody, and that needs people. This record has integers.

Where the rule is hardest to keep

In the examples.

A note about comparing wants a worked case, and a worked case wants a setting — somebody deciding something about somebody, somewhere, at some time. Any such setting would make the arithmetic easier to follow, and every one of them would bring a trade, a place and an era in through the back door.

So the examples here are letters and integers throughout, and when a passage needs something concrete it reaches for a number rather than a scene. Four candidates, five pairs compared, one triple closed. That is as concrete as the record gets, and it is concrete enough to recompute, which is the only kind of concreteness the figures can support.

The rule applied to this page

A note about naming that names nothing.

It does not say what previously stood at this address, what kind of comparing prompted the record, or what field any of it is adjacent to. Each of those would be a name given by description, which ages exactly as a name does and is harder to spot doing it.

Near this one