text: will be evaluated with respect to this pair, which we refer to as LLM pair 1. We performed more limited experiments with 
  the original strong, weak model pair (LLM pair 4) and had similar success in rerouting. 
  
  We additionally performed experiments with two further weaker models, in order to better evaluate the case where weak 
  models produce much lower-quality responses for queries (compared to the strong model). In particular, we define LLM 
  pair 2 as the strong model plus Mistral-7B-Instruct-v0.3 [38] and LLM pair 3 as the strong model plus Llama-2-7B-chat- 
  hf [63]. The weaker models in pairs 2 and 3 were chosen to represent smaller (Mistral 7B) and older-generation (Llama-2) 
  models: according to the Chatbot Arena LLM ranking leaderboard [1, 21], Llama-3.1-8B is ranked in the 58th place, 
  Mixtral 8x7B at the 88th place, Mistral-7B at the 108th place, and Llama-2-7B at the 125th place. 
  
  The LLM strong-weak pairs with which we performed experiments are summarized in Figure 3. 