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 discard comparison information, or exploit it at prohibitive cost. 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 an induced 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 the current top-$m$ output 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, BlitzRank achieves Pareto dominance over existing approaches: matching or exceeding accuracy while requiring 25--40% fewer tokens than comparable methods; against pairwise reranking, it achieves near-identical quality with 7$\times$ fewer tokens. Code available at https://github.com/ContextualAI/BlitzRank.

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