BLITZRANK: Principled Zero-shot Ranking Agents with Tournament Graphs

Selecting the top $m$ from $n$ items via expensive $k$-wise comparisons is central to settings ranging from LLM-based document reranking to crowdsourced evaluation and tournament design. Existing methods either rely on heuristics that fail to fully exploit the information each comparison reveals, or are inefficient when they do. We introduce a tournament graph framework that provides a principled foundation for $k$-wise ranking. Our key observation is that each $k$-item comparison reveals a complete tournament of $\binom{k}{2}$ pairwise preferences; aggregating these into a global preference graph and computing its transitive closure yields many additional orderings without further oracle calls. We formalize when an item's rank is certifiably determined and design a greedy query schedule that maximizes information gain towards identifying the top-$m$ items. The framework also gracefully handles non-transitive preferences (cycles induced by real-world oracles) by collapsing them into equivalence classes that yield principled tiered rankings. Applied to LLM reranking across 14 benchmarks and 5 models, our method achieves Pareto dominance over existing approaches: matching or exceeding accuracy while requiring 25-40% fewer tokens than comparable methods, and $7\times$ fewer than pairwise reranking at near-identical quality.