# choix¶

choix is a Python library that provides inference algorithms for models based on Luce’s choice axiom. These probabilistic models can be used to explain and predict outcomes of comparisons between items.

• Pairwise comparisons: when the data consists of comparisons between two items, the model variant is usually referred to as the Bradley-Terry model. It is closely related to the Elo rating system used to rank chess players.
• Partial rankings: when the data consists of rankings over (a subset of) the items, the model variant is usually referred to as the Plackett-Luce model.
• Top-1 lists: another variation of the model arises when the data consists of discrete choices, i.e., we observe the selection of one item out of a subset of items.
• Choices in a network: when the data consists of counts of the number of visits to each node in a network, the model is known as the Network Choice Model.

choix makes it easy to infer model parameters from these different types of data, using a variety of algorithms:

• Luce Spectral Ranking
• Minorization-Maximization
• Rank Centrality
• Approximate Bayesian inference with expectation propagation

An easy way to get started is by exploring the notebooks!