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Evaluating large language model (LLM) is a complex task. Pairwise ranking has emerged as state-of-the-art method to evaluate human preferences by having humans compare pairs of LLM outputs based on predefined criteria, enabling ranking across multiple LLMs by aggregating pairwise results through algorithms like Elo. However, applying these ranking algorithms in the context of LLM evaluation introduces several challenges, such as inconsistent ranking results when using ELO. Currently there is a lack of systematic study of those ranking algorithms in evaluating LLMs. In this paper, we explore the effectiveness of ranking systems for head-to-head comparisons of LLMs. We formally define a set of fundamental principles for effective ranking and conduct extensive evaluations on the robustness of several ranking algorithms in the context of LLMs. Our analysis uncovers key insights into the factors that affect ranking accuracy and efficiency, offering guidelines for selecting the most appropriate methods based on specific evaluation contexts and resource constraints.