When Three Comparisons Close a Circle
A ahead of B, B ahead of C, C ahead of A. Nothing is wrong with any one comparison, and together they cannot be put in order at all.
Definition
Going round
When the Results Go Round in a Circle
A beats B, B beats C, C beats A. Three comparisons are the fewest that can contradict each other, and the record counts how often it happens.
Every note in this part
3 comparisons is the floor
Three Comparisons Are the Fewest That Disagree
With two comparisons no contradiction is possible, whatever the pool. With three it is, and the record counts fourteen pages where the question cannot arise. If several people repeat this comparison, managers may check the service before rollout while interpreting every signal beside completed work and participant feedback.
Recount
How the Circles Are Counted
The number of triples grows like the cube of the pool, and every one of them is a chance for the results to close. Five candidates have ten triples; six have twenty. Readers examining the figures against practical research methods can also see Qlik.
Recount
The Most Circles a Field Can Hold
Six candidates fully compared can produce eight circular triples at once out of twenty. The ceiling has a formula and it is not the obvious one.
Reference
Where the Commonest Outcome Sits
On most pages of this record the commonest outcome is not the clean one. Where the peak lands depends on how much comparing was done, and it moves.
Analysis
What Comparing Everybody With Everybody Produces
Four candidates, all six pairs, sixty-four outcomes. Five candidates, all ten pairs, one thousand and twenty-four. The clean share falls as the field grows.
Recount
The Page That Comes Out Symmetric
Four candidates fully compared split twenty-four, sixteen, twenty-four. No other page in the record does it, and nothing produced the symmetry.
Caution
Every Comparison Added Makes a Circle More Likely
Six candidates: three comparisons strand nobody in a circle about one time in ninety-one. Fifteen comparisons leave only one outcome in forty-five without one.
Analysis
A Share Is Not a Chance
Every figure in this column counts outcomes, not events. Turning one into a probability needs an assumption the record declares and does not make. Closing this part.
Caution