Fullranking

Fullranking is a term used in ranking theory and data analysis to denote a framework or approach for generating a complete, strict order of items based on comparative judgments or scored criteria. In a full ranking, every item is assigned a unique position, resulting in a total order; this contrasts with partial rankings, where some items may be unranked or tied. Fullranking can be achieved through score-based methods, pairwise comparison, or rank aggregation across multiple criteria or sources.

Common methods include score-based aggregation, where items receive numerical scores from one or more criteria, and a final ranking is obtained by sorting items by total or weighted score; pairwise comparison methods, where preferences between each pair of items are recorded and a ranking is inferred through an optimization rule (e.g., Kemeny-Young, Copeland). Rank aggregation combines several input rankings into a single full ranking, increasingly used to fuse multiple signals.

Applications span information retrieval, recommender systems, competitive sports standings, and evaluation of algorithms or products. In practice, full ranking raises challenges such as computational complexity for exact solutions in some methods, susceptibility to paradoxes like the Condorcet paradox, and handling ties and missing data. Uncertainty in judgments can be modeled probabilistically to produce probabilistic rankings or distributions over possible full rankings.

Terminology varies: some sources describe “full ranking” as a general term for complete orderings, while others use it in specific methodological contexts. See also ranking, aggregation, Borda count, Condorcet method, Copeland, Kemeny-Young.