Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs

TL;DR

This paper analyzes the stability of HodgeRank estimators under different crowdsourced sampling strategies using random graph theory, providing practical recommendations for small and large item sets.

Contribution

It introduces a new estimate of the Fiedler value for random graph models in crowdsourced pairwise comparisons and validates it asymptotically.

Findings

Two-stage sampling strategy for small item sets improves stability.

Random sampling with replacement is effective for large item sets.

Experimental results support the theoretical analysis.

Abstract

Crowdsourcing platforms are now extensively used for conducting subjective pairwise comparison studies. In this setting, a pairwise comparison dataset is typically gathered via random sampling, either \emph{with} or \emph{without} replacement. In this paper, we use tools from random graph theory to analyze these two random sampling methods for the HodgeRank estimator. Using the Fiedler value of the graph as a measurement for estimator stability (informativeness), we provide a new estimate of the Fiedler value for these two random graph models. In the asymptotic limit as the number of vertices tends to infinity, we prove the validity of the estimate. Based on our findings, for a small number of items to be compared, we recommend a two-stage sampling strategy where a greedy sampling method is used initially and random sampling \emph{without} replacement is used in the second stage. When a large number of items is to be compared, we recommend random sampling with replacement as this is computationally inexpensive and trivially parallelizable. Experiments on synthetic and real-world datasets support our analysis.