Monte Carlo Sort for unreliable human comparisons

TL;DR

This paper introduces a novel Monte Carlo sorting algorithm designed for subjective human comparisons, accounting for errors and optimizing the sequence of queries to minimize human effort in subjective ranking tasks.

Contribution

It presents a new sorting method that effectively handles unreliable human judgments by using a Discrete Adiabatic Monte Carlo approach to minimize comparison costs.

Findings

The algorithm accurately sorts with high probability despite comparison errors.

It reduces the number of human comparisons needed for reliable ranking.

The approach is applicable to subjective and complex judgment-based sorting tasks.

Abstract

Algorithms which sort lists of real numbers into ascending order have been studied for decades. They are typically based on a series of pairwise comparisons and run entirely on chip. However people routinely sort lists which depend on subjective or complex judgements that cannot be automated. Examples include marketing research; where surveys are used to learn about customer preferences for products, the recruiting process; where interviewers attempt to rank potential employees, and sporting tournaments; where we infer team rankings from a series of one on one matches. We develop a novel sorting algorithm, where each pairwise comparison reflects a subjective human judgement about which element is bigger or better. We introduce a finite and large error rate to each judgement, and we take the cost of each comparison to significantly exceed the cost of other computational steps. The algorithm must request the most informative sequence of comparisons from the user; in order to identify the correct sorted list with minimum human input. Our Discrete Adiabatic Monte Carlo approach exploits the gradual acquisition of information by tracking a set of plausible hypotheses which are updated after each additional comparison.