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When the Universe is Too Big: Bounding Consideration Probabilities for Plackett-Luce Rankings

Ben Aoki-Sherwood, Catherine Bregou, David Liben-Nowell, Kiran Tomlinson, Thomas Zeng

arXiv 19 Jan 2024 · Machine Learning

arXiv:2401.11016 · PDF · DOI · OpenAlex · Extracted main text

Abstract

The widely used Plackett-Luce ranking model assumes that individuals rank items by making repeated choices from a universe of items. But in many cases the universe is too big for people to plausibly consider all options. In the choice literature, this issue has been addressed by supposing that individuals first sample a small consideration set and then choose among the considered items. However, inferring unobserved consideration sets (or item consideration probabilities) in this "consider then choose" setting poses significant challenges, because even simple models of consideration with strong independence assumptions are not identifiable, even if item utilities are known. We apply the consider-then-choose framework to top-$k$ rankings, where we assume rankings are constructed according to a Plackett-Luce model after sampling a consideration set. While item consideration probabilities remain non-identified in this setting, we prove that we can infer bounds on the relative values of consideration probabilities. Additionally, given a condition on the expected consideration set size and known item utilities, we derive absolute upper and lower bounds on item consideration probabilities. We also provide algorithms to tighten those bounds on consideration probabilities by propagating inferred constraints. Thus, we show that we can learn useful information about consideration probabilities despite not being able to identify them precisely. We demonstrate our methods on a ranking dataset from a psychology experiment with two different ranking tasks (one with fixed consideration sets and one with unknown consideration sets). This combination of data allows us to estimate utilities and then learn about unknown consideration probabilities using our bounds.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
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4Basar, G. and Bhat, C (2004) A parameterized consideration set model for airport choice: an application to the San Francisco Bay area0.73732100%
5Jagabathula, S., Mitrofanov, D., and Vulcano, G (2023) Demand estimation under uncertain consideration sets0.73732100%
6van Nierop, E., Bronnenberg, B., Paap, R., Wedel, M., and Franses, P… (2010) Retrieving unobserved consideration sets from household panel data0.73732100%
7Hauser, J. R. and Wernerfelt, B (1990) An evaluation cost model of consideration sets0.64422100%
8Luce, R. D (1959) Individual Choice Behavior: A Theoretical Analysis0.64422100%
9Plackett, R. L (1975) The analysis of permutations0.64422100%
10Seshadri, A., Ragain, S., and Ugander, J (2020) Learning rich rankings0.64422100%

Showing the top 10 of 46 scored citations.