.. _library_thurstone_mosteller_ranker:

thurstone_mosteller_ranker

Thurstone-Mosteller Case V pairwise preference ranker. It aggregates pairwise outcomes into matchup probabilities, applies a fixed continuity correction to avoid infinite probit values, transforms them with the inverse standard normal CDF, and fits Case V latent utilities using a deterministic weighted least-squares linear solve.

The library implements the ranker_protocol defined in the ranking_protocols library. It provides predicates for learning a ranker from pairwise preferences, using it to order candidate items, and exporting it as a list of predicate clauses or to a file.

Datasets are represented as objects implementing the pairwise_ranking_dataset_protocol protocol from the ranking_protocols library. See the test_datasets directory for examples. The current implementation requires a well-formed connected pairwise dataset so that all learned utilities remain comparable across the ranked items.

API documentation

Open the `../../apis/library_index.html#thurstone_mosteller_ranker <../../apis/library_index.html#thurstone_mosteller_ranker>`__ link in a web browser.

Loading

To load this library, load the loader.lgt file:

::

| ?- logtalk_load(thurstone_mosteller_ranker(loader)).

Testing

To test this library predicates, load the tester.lgt file:

::

| ?- logtalk_load(thurstone_mosteller_ranker(tester)).

Features

• Pairwise Preference Learning: Learns one deterministic latent utility per item from aggregated pairwise outcomes.
• Case V Thurstone-Mosteller Fit: Uses continuity-corrected matchup win probabilities transformed by the inverse standard normal CDF and fitted with a deterministic weighted least-squares solve.
• Centered Utility Scale: Learned scores are centered so that only utility differences encode preference strength while the absolute location remains arbitrary.
• Deterministic Ranking: Orders candidate items by learned utility with deterministic tie-breaking.
• Strict Dataset Validation: Rejects duplicate items, undeclared items, self-preferences, non-positive weights, and disconnected comparison graphs.
• Training Diagnostics: Learned rankers include metadata describing the fitting method, continuity correction, and validated dataset summary.
• Ranker Export: Learned rankers can be exported as self-contained terms.

Scoring semantics

This implementation aggregates pairwise preferences into matchup totals and then estimates latent utilities under the Thurstone-Mosteller Case V model. For each observed unordered pair, it computes a continuity-corrected empirical win probability

::

(wins + 0.5) / (total + 1.0)

maps that probability through the inverse standard normal CDF, and fits utility differences using weighted least squares with matchup totals as the weights.

The resulting utilities are centered, real-valued scores on an arbitrary additive scale. Only differences between utilities are meaningful when interpreting implied paired-comparison probabilities and ranking order.

Options

The current learn/3 implementation does not define any user options beyond the default empty list. Non-empty options lists are rejected.

Diagnostics syntax

The diagnostics/2 predicate returns a list of metadata terms with the form:

::

[ model(thurstone_mosteller_ranker), options(Options), fitting(weighted_least_squares_case_v), continuity_correction(0.5), dataset_summary(DatasetSummary) ]

Ranker representation

The learned ranker is represented by a compound term of the form:

::

thurstone_mosteller_ranker(Items, Scores, Diagnostics)

Where:

• Items: List of ranked items.
• Scores: List of Item-Score pairs.
• Diagnostics: List of metadata terms, including the fitting method, continuity correction, and dataset summary.