A language model must choose the best response from a set of three options: A, B, and C. A reward function provides the following scores for each option: Option A has a score of 2.0, Option B has a score of 1.0, and Option C has a score of 0.5. Assuming the probability of selecting an option is calculated by normalizing its exponentiated reward score against the sum of all exponentiated scores, what is the approximate probability of the model selecting Option A?

Impact of Uniform Reward Shift on Selection Probabilities

Consider a model that selects a response from a set of options, where the probability of selecting any given response is proportional to the exponential of its reward score. If response Y has a reward score that is exactly twice the reward score of response Z, the model's probability of selecting Y will be exactly twice its probability of selecting Z.