**Consensus Verdict on Strategies for Reducing LLM Inference Costs**

**1. Areas of Agreement:**
All debaters recognize the importance of optimizing LLM inference costs and agree that prompt caching and batching are effective strategies. They also acknowledge the potential of model distillation and quantization, albeit with differing views on their practicality and effectiveness.

**2. Areas of Disagreement:**
The primary disagreement lies in the prioritization of strategies. Alice argues for model distillation and quantization as superior long-term solutions, while Bob and Carol emphasize prompt caching and batching for their immediate cost-effectiveness and ease of implementation. Carol also highlights routing to cheaper models as a viable strategy, which Alice does not prioritize.

**3. Strongest Evidence-Backed Strategies:**
- **Model Distillation and Quantization:** Supported by NVIDIA and MarkTechPost, these methods offer significant long-term cost reductions with minimal quality loss, though they require more upfront investment.
- **Prompt Caching and Batching:** Backed by Clarifai and CalmOps, these strategies provide immediate cost savings and efficiency improvements, making them attractive for quick implementation.
- **Routing to Cheaper Models:** Supported by Aiveda, this adaptive approach allows for cost optimization based on task complexity, enhancing resource utilization.

**4. Final Recommendation:**
Based on the arguments presented, the recommendation is to prioritize **prompt caching and batching** for immediate cost reductions, supplemented by **routing to cheaper models** for adaptive efficiency. Organizations should consider **model distillation and quantization** as longer-term strategies for sustained cost-effectiveness, particularly as their needs evolve. 

**Confidence Level:** High. The consensus reflects a balanced view of both immediate and long-term strategies, ensuring adaptability in various production environments.