# Unsolvability Ceiling in Multi-LLM Routing: An Empirical Study of Evaluation Artifacts

arXiv: https://arxiv.org/abs/2605.07395 · HTML: https://mlsanity.com/paper/2605.07395/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 11 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 9 of 9)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (2023)
- [RouterArena: An Open Platform for Comprehensive Comparison of LLM Routers](https://mlsanity.com/paper/2510.00202/) (2025)
- [R2-Router: A New Paradigm for LLM Routing with Reasoning](https://mlsanity.com/paper/2602.02823/) (2026)
- [MoDEM: Mixture of Domain Expert Models](https://mlsanity.com/paper/2410.07490/) (2024)

## Built on by (most cited first, 4 of 4)

- [What Does a Routing Oracle Measure Under Stochastic Decoding? Coupling, Scorer Choice, and Single-Commit Ceilings](https://mlsanity.com/paper/2607.03436/) (2026)
- [Separating perception from reasoning in vision-language models: a model-free render ceiling for crystal structures](https://mlsanity.com/paper/2609.00663/) (2026)
- [On the Limits of Metacognitive Monitoring in LLMs](https://mlsanity.com/paper/2609.34864/) (2026)
- [False Floors: LLM Safety Routing Evaluations Break Under Distribution Shift](https://mlsanity.com/paper/2610.01535/) (2026)

## Abstract (arXiv)

Efficient routing across multiple LLMs enables cost-quality tradeoffs by directing queries to the cheapest capable model. Prior work attributes routing headroom to an "unsolvability ceiling", queries no model in the pool can solve. We present a large-scale study of multi-tier LLM routing with 206,000 query-model pairs across six benchmarks (MMLU, MedQA, HumanEval, MBPP, Alpaca, ShareGPT) using the Gemma 4 and Llama 3.1 families. Evaluating with both LLM-as-a-judge and exact-match metrics, we show that a substantial portion of reported unsolvability stems from evaluation artifacts: (i) systematic judge biases favoring verbosity over correctness, (ii) truncation under fixed generation budgets, and (iii) output format mismatches. Through dual-judge validation and exact-match grounding, we reduce measured unsolvability across tasks. We introduce a decomposition framework attributing failures to these artifacts, revealing consistent patterns across domains and model families. These artifacts also distort router training signals: standard routers collapse to majority-class prediction (~79% smallest-tier optimal), confirmed via random-feature and shuffled-label controls, incurring a 13-17 percentage point opportunity cost. We provide actionable recommendations including dual-judge validation, exact-match anchoring, and cost-sensitive objectives. Our findings suggest existing routing headroom estimates are substantially inflated, underscoring the need for reliable evaluation protocols in multi-LLM systems.