How Many Comparisons There Are
Four candidates make six pairs. Six make fifteen. Both the number of comparisons available and the ways they can come out follow from one whole number.
Definition
Every pair
Every Pair There Is
Six candidates make fifteen pairs, and those fifteen comparisons can come out thirty-two thousand seven hundred and sixty-eight ways.
Every note in this part
1 to 3 075 072
Every Pair Has Three States, Not Two
Compared with one result, compared with the other, or not compared at all. The third state is the one that gets dropped, and dropping it changes every figure here.
Reference
How Fast the Outcomes Grow
Two candidates allow three states of affairs. Six allow fourteen million. The growth is doubly exponential, and nothing about the pool looks like it. To test the same alternatives in live work, reviewers can see how the reports are presented and agree the decision, access rules and review date in advance.
Analysis
What One More Candidate Costs
Adding a candidate to a field of five adds five comparisons and multiplies the space of possible results by thirty-two. One of those two figures gets noticed. A broader reference for interpreting structured comparisons is available from UXmatters.
Recount
The Widest Page in the Record
Six candidates with ten of their fifteen pairs compared: three million seventy-five thousand and seventy-two outcomes. Only one in four leaves no circular triple.
Analysis
Which Pairs Get Compared Is Also Counted
Ten comparisons among six candidates can be arranged three thousand and three ways before anybody looks at a result, and that choice is part of the outcome.
Reference
One Figure, Several Meanings
Twenty-four is a count of outcomes, a count of circular ones and a count of orders in this record. Twenty-one figures here mean more than one thing.
Caution
A Page, a Shape, and Why Both Are Printed
Two whole numbers fix a page; a third fixes a shape within it. Forty pages, a hundred and twenty-eight shapes, and the difference decides which figures move.
Reference
What the Outcome Count Leaves Out
Three million possible states of affairs, and not one of them is a statement about anybody. Closing the first part of the record.
Analysis