Multistage Ranking Models

Abstract Suppose that a sample of people independently examines a fixed set of k items and then ranks these items according to personal judgment. The process of ranking the items is decomposed into k −1 stages. In the forward model, the most preferred item is selected at the first stage, the best of the remaining items is selected at the second stage, and so on until the least preferred item is selected by default. Various probability models are adopted at each stage, and properties of the resulting models for randomly sampled rankings are investigated. Luce (1959) first proposed such a modeling scheme, where each item i was thought to have an intrinsic value θi , and the probability of choosing a particular item i at any stage, conditional on the set S of items not previously chosen, was given by I{i ∈ S}θ i /Σ j∈S θ j , where I{} is an indicator function. Plackett (1975) began with the same model but added interaction terms that would theoretically extend the usefulness of this approach when the basic m...