Recent advances in large language models (LLMs) have enabled zero-shot automated essay scoring (AES), providing a promising way to reduce the cost and effort of essay scoring in comparison with manual grading. However, most existing zero-shot approaches rely on LLMs to directly generate absolute scores, which often diverge from human evaluations owing to model biases and inconsistent scoring. To address these limitations, we propose LLM-based Comparative Essay Scoring (LCES), a method that formulates AES as a pairwise comparison task. Specifically, we instruct LLMs to judge which of two essays is better, collect many such comparisons, and convert them into continuous scores. Considering that the number of possible comparisons grows quadratically with the number of essays, we improve scalability by employing RankNet to efficiently transform LLM preferences into scalar scores. Experiments using AES benchmark datasets show that LCES outperforms conventional zero-shot methods in accuracy while maintaining computational efficiency. Moreover, LCES is robust across different LLM backbones, highlighting its applicability to real-world zero-shot AES.