Majority voting is considered an effective method to enhance chain-of-thought reasoning, as it selects the answer with the highest ”self-consistency” among different reasoning paths (Wang et al., 2023). However, previous chain-of-thought reasoning methods typically generate only a single answer in each trial, thereby ignoring the possibility of other potential answers. As a result, these alternative answers are often overlooked in subsequent voting processes. In this work, we propose to generate ranked answers in each reasoning process and conduct ranked voting among multiple ranked answers from different responses, thereby making the overall self-consistency more reliable. Specifically, we use three ranked voting methods: Instant-runoff voting, Borda count voting, and mean reciprocal rank voting. We validate our methods on six datasets, including three multiple-choice and three open-ended question-answering tasks, using both advanced open-source and closed-source large language models. Extensive experimental results indicate that our proposed method outperforms the baselines, showcasing the potential of leveraging the information of ranked answers and using ranked voting to improve reasoning performance. Code and logs will be released.

In attempts to develop sample-efficient and interpretable algorithms, researcher have explored myriad mechanisms for collecting and exploiting feature feedback, auxiliary annotations provided for training (but not test) instances that highlight salient evidence. Examples include bounding boxes around objects and salient spans in text. Despite its intuitive appeal, feature feedback has not delivered significant gains in practical problems as assessed on iid holdout sets. However, recent works on counterfactually augmented data suggest an alternative benefit of supplemental annotations, beyond interpretability: lessening sensitivity to spurious patterns and consequently delivering gains in out-of-domain evaluations. We speculate that while existing methods for incorporating feature feedback have delivered negligible in-sample performance gains, they may nevertheless provide out-of-domain benefits. Our experiments addressing sentiment analysis, show that feature feedback methods perform significantly better on various natural out-of-domain datasets despite comparable in-domain evaluations. By contrast, performance on natural language inference remains comparable. Finally, we compare those tasks where feature feedback does (and does not) help.