Detect a cycle before treating group preferences as a ranking

Three individually consistent rankings can produce a group preference that cannot be arranged as one simple order. Examine the pairwise comparisons before printing a winner. This is an invented manual exercise about preference aggregation. It uses an ordinary comparison record and makes no claim about actual team votes, consensus, or a Kiguri ranking feature.

Fix the alternatives and complete rankings

Use three fictional workshop formats labeled A, B, and C. Three invented reviewers supply these complete orders: the first prefers A over B over C; the second prefers B over C over A; the third prefers C over A over B. In this fixture there are no ties, missing responses, or changing alternatives.

Keep each order intact. It describes relative preference, not a score measuring how strongly someone prefers an option. Do not assign arbitrary numbers to the positions and add them without defining a different decision method. The present exercise uses only which option appears earlier in each list.

Count the A-versus-B comparison

For A against B, inspect all three orders. Reviewer one places A above B. Reviewer two places B above A. Reviewer three places A above B. A therefore wins this pair by two to one under the stated majority comparison.

Record the supporting reviewer identities as well as the tally. This lets another reader reconstruct the result. Avoid stopping here and calling A the group's winner: winning one pair says nothing yet about its relation to the remaining option.

Count the other pairs and trace the cycle

For B against C, reviewers one and two prefer B, while reviewer three prefers C. B wins two to one. For C against A, reviewers two and three prefer C, while reviewer one prefers A. C also wins two to one.

The resulting relation is A over B, B over C, and C over A. Following it returns to the starting option. No option wins against both others. Writing A above B above C would discard the C-over-A result even though every comparison used the same voters and rules.

Separate a cycle from an incomplete comparison

Check that each unordered pair was counted once and that every tally came from the original rankings. A missing pair can make a partial result look sortable; this fixture instead contains all three pairs and a genuine cycle. Changing a reviewer's order midway would create a different problem.

The cycle does not mean any individual list was inconsistent. Each person's order is complete and ordered. It is the majority relation across people that lacks a single top option. Keep that distinction visible rather than attributing confusion or unreasonable behavior to a reviewer.

Return the decision to an explicit method

Keep the original orders, three tallies, and cycle witness together. Ask another reader to identify which comparison prevents a complete group ranking. If they select a winner by beginning the comparison at a different option, explain that traversal order is not an agreed decision rule.

The actual decision still needs an established method and authorized owner. This exercise does not choose that method or promise that another voting system solves every tradeoff. Its finish condition is an accurate account of the cyclic preference, without presenting a synthetic example as evidence of real consensus or a customer outcome.