Abstract
Rank Centrality (RC; Negahban, Oh, & Shah 2017) is a rank-aggregation algorithm that computes a total ranking of elements from noisy pairwise ranking information. I test RC as an alternative to incremental error-driven learning algorithms such as GLA-MaxEnt (Boersma & Hayes 2001; Jäger 2007) for modeling a constraint hierarchy on the basis of two-alternative forced-choice experiment results. For the case study examined here, RC agrees well with GLA-MaxEnt on the ordering of the constraints, but differs somewhat on the distance between constraints; in particular, RC assigns more extreme (low) positions to constraints at the bottom of the hierarchy than GLA-MaxEnt does. Overall, these initial results are promising, and RC merits further investigation as a constraint-ranking method in experimental linguistics.
Highlights
One way of testing hypotheses about linguistic competence is to collect judgment data in an experiment
How can we extract an overall rank/weight hierarchy for {C1, ...Cn} based only on the proportion of Ci » Cj responses for each Ci, Cj pair—especially if each actual Ci, Cj domination relation has the potential to be variable? I evaluate the ability of the general-purpose rank-aggregation algorithm RANK CENTRALITY (RC; Negahban et al 2017) to do just this, and I show that the RC results are promisingly similar to those of the state-of-the-art Gradual Learning Algorithm (GLA; Boersma & Hayes 2001)
RC was developed to model both the ordering of, and the distance between, items in a set, given data from comparisons between pairs of items. This ranking algorithm is designed to be computationally simple, to require only pairwise comparison data rather than having explicit scores assigned a priori to items in the set, and to perform at least as well as existing algorithms (Negahban et al 2017: §1)
Summary
One way of testing hypotheses about linguistic competence is to collect judgment data in an experiment. The forced-choice experiment results to be used for the comparison between the Rank Centrality and GLA-MaxEnt ranking algorithms are those from the study described in Smith & Tashiro (2019).
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