A standard paradigm for sentiment analysis is to rely on a singular LLM and makes the decision in a single round under the framework of in-context learning. This framework suffers the key disadvantage that the single-turn output generated by a single LLM might not deliver the perfect decision, just as humans sometimes need multiple attempts to get things right. This is especially true for the task of sentiment analysis where deep reasoning is required to address the complex linguistic phenomenon (e.g., clause composition, irony, etc) in the input. To address this issue, this paper introduces a multi-LLM negotiation framework for sentiment analysis. The framework consists of a reasoning-infused generator to provide decision along with rationale, a explanation-deriving discriminator to evaluate the credibility of the generator. The generator and the discriminator iterate until a consensus is reached. The proposed framework naturally addressed the aforementioned challenge, as we are able to take the complementary abilities of two LLMs, have them use rationale to persuade each other for correction. Experiments on a wide range of sentiment analysis benchmarks (SST-2, Movie Review, Twitter, yelp, amazon, IMDB) demonstrate the effectiveness of proposed approach: it consistently yields better performances than the ICL baseline across all benchmarks, and even superior performances to supervised baselines on the Twitter and movie review datasets.