Inclusion-of-Thoughts: Mitigating Preference Instability via Purifying the Decision Space

1. Problem Statement

While Large Language Models (LLMs) have shown success in reasoning tasks via Chain-of-Thought (CoT) prompting, they remain vulnerable to preference instability in Multiple-Choice Question (MCQ) settings.

• The Core Issue: Even when an LLM possesses the correct knowledge and reasoning steps, its final prediction often oscillates between the correct answer and plausible distractors. This instability arises not from a lack of reasoning capability, but from cognitive load induced by the presence of multiple plausible options.
• Limitations of Existing Methods: Current test-time scaling methods (e.g., Self-Consistency, Tree-of-Thoughts, or iterative elimination like Exclusion-of-Thoughts) often rely on expensive sampling, complex search algorithms, or extensive feedback loops. These approaches increase computational overhead significantly without necessarily addressing the root cause: the model's inability to stabilize its preference among top candidates when distractors are present.

2. Methodology: Inclusion-of-Thoughts (IoT)

The authors propose Inclusion-of-Thoughts (IoT), a lightweight, zero-shot, self-filtering framework designed to "purify" the decision space. Instead of expanding the reasoning space, IoT isolates the model's highest-confidence hypotheses to test their stability.

The framework operates via a three-stage pipeline:

• Stage 1: Initial Preference Elicitation

  • The model is prompted with the original MCQ (all options) using standard CoT.
  • It generates a reasoning trace and selects a top-choice candidate ($o^*_1$).

• Stage 2: Second Plausibility Assessment (Perturbation)

  • The model is queried again, but the option set is perturbed. The initial top choice ($o^*_1$) is removed and replaced with a neutral placeholder: "none of the options."
  • The model selects a new top candidate ($o^*_2$) from this modified set.
  • Logic: If $o^*_1$ was robustly correct, the model should select "none of the options" (indicating no other option is better). If the model switches to a different option, it reveals a preference instability between $o^*_1$ and the new candidate.

• Stage 3: Confined Final Inference

  • The framework constructs a reduced MCQ containing only the two most plausible candidates identified in Stages 1 and 2 (i.e., $\{o^*_1, o^*_2\}$).
  • The model performs a final comparative judgment on this "distractor-free" set.
  • Early Stopping Mechanism: If Stage 2 results in the selection of "none of the options," the process terminates immediately, confirming $o^*_1$ as the final answer without incurring the cost of Stage 3.

3. Key Contributions

1. Novel Framework (IoT): A zero-shot, unsupervised method that improves MCQ reasoning by isolating and comparing a model's top two candidates, rather than expanding the search space through sampling or complex tree searches.
2. Stability-Oriented Perspective: The paper reframes MCQ errors as preference instability among plausible options rather than missing knowledge. It demonstrates that many errors occur because models cannot consistently rank the correct answer against high-quality distractors.
3. Diagnostic Utility: The three-stage structure allows for a granular transition analysis (e.g., TTT, FTT, TFF patterns). This helps diagnose whether errors stem from model failure, genuine question ambiguity, or noisy ground-truth labels.
4. Efficiency: IoT achieves performance gains with minimal computational overhead (approx. 2.2x tokens of standard CoT), significantly outperforming Self-Consistency (SC) which requires ~4.6x tokens.

4. Experimental Results

The authors evaluated IoT across four models (Llama-3.3-8B, Olmo-2-7B/13B, GPT-4o-mini) and seven diverse benchmarks (Commonsense, Educational, and Mathematical reasoning).

• Performance Gains: IoT consistently outperformed standard CoT and Self-Consistency (SC) baselines.
  • Olmo-2-7B: Achieved State-of-the-Art (SOTA) on Commonsense tasks (e.g., +3.40% on OBQA, +2.05% on CSQA) and Math (GSM8K-MC +3.95%).
  • Overall: IoT secured the highest average accuracy across all models and domains, with a margin of ~1.64% over the nearest competitor.
• Robustness: IoT significantly reduced sensitivity to option ordering (a known weakness in LLMs), demonstrating a more stable underlying preference structure.
• Computational Efficiency:
  • Token Cost: IoT generates ~2.2x the tokens of CoT, whereas SC generates ~4.6x.
  • Early Stopping: In many cases (TTT pattern), the process skips Stage 3, further reducing costs.
• Transition Analysis:
  • The method successfully converted many "False-True-False" (FTF) and "True-False-False" (TFF) trajectories into correct final answers (FTT).
  • It also identified ambiguous questions where external judges agreed that the "incorrect" final answer was actually plausible, suggesting IoT can serve as a tool for dataset auditing.

5. Significance and Impact

• Paradigm Shift: IoT challenges the prevailing notion that better reasoning requires more computation (more samples, deeper search). Instead, it suggests that purifying the decision space to reduce cognitive load is a more efficient path to stability.
• Scalability: As a zero-shot, plug-and-play method, IoT can be applied to any pre-trained LLM without fine-tuning, making it highly scalable for real-world applications.
• Interpretability: By explicitly documenting the filtering process and transition patterns, IoT provides a transparent window into the model's decision-making, distinguishing between reasoning failures and dataset ambiguities.
• Complementarity: While IoT is powerful on its own, the paper shows it can be combined with Self-Consistency (IoT+SC) for marginal additional gains, though at a higher computational cost.

In conclusion, Inclusion-of-Thoughts offers a cost-effective, interpretable, and robust solution to the problem of preference instability in LLMs, proving that stabilizing the model's internal ranking of top candidates is often more effective than generating diverse reasoning paths.