Ranking: an ordering from most to least important

A ranking is an ordering of items from most to least important or most to least preferred. A ranking is ordinal: it shows order, not distance, so ranking housing first and transport second does not say how much more important housing is. When many people’s rankings are combined into one, the method chosen shapes the result, and social choice theory shows that no method satisfies every reasonable fairness condition at once.

Definition

A ranking assigns positions (first, second, third) to a set of items. In measurement terms it is ordinal data: it supports statements about order (“A above B”) but not about size (“A is twice as important as B”). The Stanford Encyclopedia of Philosophy notes that Kenneth Arrow’s framework for collective choice uses only ordinal information, rankings without measures of strength, and treats preferences as interpersonally incomparable.⁠¹ That is the standard sense of ranking on this site. A resource allocation, by contrast, records relative size.

Origin and history

Formal thinking about combining rankings is older than modern democracy. The Stanford Encyclopedia of Philosophy describes the “paradox of voting” discovered by the Marquis de Condorcet in 1785: with three voters ranking three alternatives, pairwise majority voting can produce a cycle in which A beats B, B beats C, and C beats A, so there is no overall winner even though each individual ranking is consistent.⁠¹ A different approach is scoring. The Borda count gives each alternative points by its position in each ranking; the encyclopedia’s social choice entry notes that it “avoids Condorcet’s paradox but violates one of Arrow’s conditions”.⁠²

In 1951 Kenneth Arrow proved the result now called Arrow’s impossibility theorem: with more than two alternatives, no method of turning individual rankings into a social ranking satisfies unrestricted domain, weak Pareto, independence of irrelevant alternatives, non-dictatorship, and a consistent social ordering all at once.⁠¹ For two alternatives, the picture is cleaner: May’s theorem (1952) shows that majority rule is the only rule satisfying a short list of fairness conditions.⁠²

How rankings are measured and used

Rankings appear in three main places in civic life.

• Elections. Ranked-choice voting asks voters to rank candidates and counts in rounds. Maine’s statute, for example, counts each continuing ballot “as one vote for its highest-ranked continuing candidate” in each round.⁠³
• Surveys of priorities. Respondents order a list of subjects. The list, its length, and its order all affect results, so the full list must be disclosed. See Question design.
• Aggregation. Researchers combine rankings by average rank, Borda scores, pairwise comparisons, or share ranked first. Each answers a different question: “most often first” is not the same as “highest on average.”

Common confusions and neighboring terms

• Ranking vs. resource allocation. A ranking cannot express that two items are nearly tied or far apart; an allocation can.
• Ranking vs. priority. A priority is the judgment; a ranking is one way to record it.
• Ranking vs. rating. A rating scores each item independently (for example, 1 to 5), so ties are allowed and items are not forced against each other.
• Ranking vs. approval voting. Approval voting asks only which options are acceptable, with no order among them.
• Average rank vs. majority preference. An item can have the best average rank and still lose a head-to-head majority comparison against another item.

How My Vote Forward uses the term

My Vote Forward uses rankings to record priorities among subjects. Because rankings are ordinal, the framework does not present a ranked result as a measure of how much more one subject matters, and it reports the aggregation method alongside any combined ranking. The reasoning, including why Arrow’s theorem is a reason for transparency rather than despair, is in Collective priorities. Measurement choices are covered in Measurement.

Unresolved questions

• Which aggregation method should be the headline, and should the choice be fixed in advance to prevent picking the most convenient result?
• How many items can people rank reliably before the bottom of the list becomes noise?
• Should ties be allowed, and if so, how should they be counted?