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

Mohammad Reza Ghasemi Madani; Soyeon Caren Han; Shuo Yang; Jey Han Lau

cs.CLMar 15, 2026

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

Authors: Mohammad Reza Ghasemi Madani, Soyeon Caren Han, Shuo Yang, Jey Han Lau

Organizations: School of Computing and Information Systems, The University of Melbourne

Abstract

Multiple-choice questions (MCQs) are widely used to evaluate large language models (LLMs). However, LLMs remain vulnerable to the presence of plausible distractors. This often diverts attention toward irrelevant choices, resulting in unstable oscillation between correct and incorrect answers. In this paper, we propose Inclusion-of-Thoughts (IoT), a progressive self-filtering strategy that is designed to mitigate this cognitive load (i.e., instability of model preferences under the presence of distractors) and enable the model to focus more effectively on plausible answers. Our method operates to reconstruct the MCQ using only plausible option choices, providing a controlled setting for examining comparative judgements and therefore the stability of the model's internal reasoning under perturbation. By explicitly documenting this filtering process, IoT also enhances the transparency and interpretability of the model's decision-making. Extensive empirical evaluation demonstrates that IoT substantially boosts chain-of-thought performance across a range of arithmetic, commonsense reasoning, and educational benchmarks with minimal computational overhead.

Figures & tables

Figure 1: Inclusion-of-Thoughts Framework is a self-filtering strategy that reconstructs multiple-choice questions using only plausible options to mitigate model instability and enhance performance.

Figure 2: Inclusion-of-Thoughts Framework. The pipeline allows the model to choose up to two options. Then the model looks at its preferences and decides the final answer in isolation.

Figure 3: The figure illustrates the effect of options on the accuracy of Olmo-2-7B across different datasets. The y-axis indicates the number of options passed with the question.

Model	Method	Commonsense			Education		Math		Avg.
Model	Method	SIQA (3)	OBQA (4)	CSQA (5)	ARC (4)	MMLU (4)	GSM8K-MC (4)	AQUA (5)	Avg.
	CoT	70.42	80.80	74.53	84.21	65.62	89.08	62.99	75.38
	SC	71.36	75.80	76.42	79.22	64.91	89.39	66.54	74.81
Olmo-2-7B	EoT	69.91	74.60	73.79	79.69	62.62	87.06	55.82	71.93
	IoT	70.88	84.20	76.58	87.54	66.78	91.66	63.78	77.35
	CoT	71.60	85.40	79.69	85.32	70.59	91.36	67.32	78.75

Table 1: Accuracy of multiple LLMs across various benchmarks using CoT, Self-Consistency (SC), EoT, detecting plausible answers, and IoT. The second best performance is underlined . Note: EoT cannot be applied directly to closed-source models (GPT), and GPT-4o SC is excluded due to computational costs.

Figure 4: Results of Olmo-2-7B categorized by benchmarks type. While the margin in Commonsense or Education is more significant, IoT achieves performance comparable to self-consistency (SC) with much lower computational cost.

Figure 5: Answer transition process of Olmo-2-7B over OBQA dataset. The final improvement is the difference between FTT and TFF.

Figure 6: Gold answer average ranking for FFF cases.

Figure 7: The portion of noisy samples agreed across different benchmarks in TFF and FTF agreed by external judges. The Agreement rate shown in the plot is the average rate over Gemini-3-pro , and GPT-5 agreement.

Dataset	top-1+random	logit-based	IoT
SIQA	75.79	90.78	88.02
OBQA	83.00	86.80	92.40
CSQA	79.28	87.14	89.19
ARC	86.94	89.85	93.86
GSM8K-MC	91.89	58.68	94.54
AQUA	74.02	42.23	73.23

Table 2: Top-2 accuracy of match-budget baselines compared to IoT.

Dataset	CoT	SC (3 samples)	SC (5 samples)	IoT
SIQA	70.42	68.73	71.36	70.88
OBQA	80.80	80.80	75.80	84.20
CSQA	74.53	74.12	76.42	76.58
ARC	84.21	84.38	79.22	87.54
MMLU	65.62	N/A	64.91	66.78
GSM8K-MC	89.08	93.32	89.39	91.66

Table 3: Comparison of self-consistency with different numbers of samples to IoT.

Dataset	CoT	Inclusion-of-Thoughts
Dataset	CoT	w/ 2 Chances	w/ 3 Chances
SIQA	70.09	70.29	N/A
OBQA	77.70	81.30	80.70
CSQA	73.34	76.41	75.67
ARC	82.64	85.67	84.81
MMLU	65.59	66.54	66.92

Table 4: Comparison of IoT performance given a second and third chance. The results are average over Olmo-2-7B and Llama-3.3-8B performance.

Figure 8: Cost-Benefit. Vertical axes illustrate the accuracy of each method, while the horizontal axes show the average number of tokens per sample that each method costs. “IoT w/o ES” means IoT without early stopping. The detailed number of tokens generated by each dataset is given in Appendix D .

Dataset	CoT			IoT
Dataset	Mean	Std	Entropy	Mean	Std	Entropy
SIQA	69.63	0.49	0.76	71.89	0.61	0.43
OBQA	80.64	0.84	0.79	84.28	0.73	0.24
CSQA	72.64	1.13	0.72	76.89	0.52	0.19
ARC	83.43	0.50	0.78	86.82	0.53	0.26
MMLU	64.58	0.64	0.72	66.84	0.29	0.27

Table 5: Robustness of IoT compared to CoT w.r.t. shuffling options. Results are obtained from Olmo-2-7B . The best performance is bold .

Dataset	CoT	SC	IoT	IoT+SC
SIQA	70.42	71.36	70.88	66.63
OBQA	80.80	75.80	84.20	84.40
CSQA	74.53	76.42	76.58	71.82
ARC	84.21	79.22	87.54	83.53
GSM8K-MC	89.39	89.39	91.66	93.02
AQUA	62.99	66.54	63.78	64.96

Table 6: IoT complements existing methods such as SC. While SC shows improvements by sampling more forward reasoning, integrating IoT further improves the performance.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Train	Dev	Test
SIQA	33410	1954	-
OBQA	7.69K	500	500
CSQA	9.74K	1.22K	1.14K
ARC	1.12K	299	1.17K
MMLU	-	-	14K
GSM8K-MC	7.47K	-	1.32K

Appendix

Table 7: Number of samples each dataset contains for train, dev, and test splits.

Dataset	CoT	SC	EoT	IoT	IoT w/o ES
SIQA	164	797	335	359	531
OBQA	173	833	360	369	562
CSQA	159	712	326	427	501
ARC	200	1,000	404	494	643
MMLU	261	1,336	529	636	805
GSM8K-MC	162	895	340	258	542

Appendix

Table 8: Average tokens generated per sample. SC generates roughly

4.6\times

the tokens of CoT, and EoT generates

2.1\times

, while IoT is approximately

2.2\times

the cost of CoT.

Dataset	Stage 1 (First Pref Acc)	Stage 2 (Top-2 Acc)	Stage 3 (Final Acc)
OBQA	80.80	92.40	84.20
CSQA	74.53	89.19	76.58
SIQA	70.42	88.02	70.88
ARC	84.21	93.86	87.54
MMLU	65.62	81.03	66.78
GSM8K-MC	89.08	94.54	91.66

Appendix

Table 9: Stage-wise performance of Olmo-2-7B using IoT across different datasets.

Panel of Figure 9 — Figure 9: Example of TFT case from IoT (OBQA, Olmo-2-7b).

Panel of Figure 10 — Figure 10: Example of TTT case from IoT (CSQA, Olmo-2-7b). Here, the IoT stops the process and skips stage 3 since the model confirms its answer in stage 2.

Panel of Figure 11 — Figure 11: Example of FTT case from IoT (CSQA, Olmo-2-7b).

Panel of Figure 12 — Figure 12: Example of FFF case from IoT (AQUA, Olmo-2-7b). Here, the IoT stops the process and skips stage 3 since the model confirms its answer in stage 2.

Panel of Figure 13 — Figure 13: Example of FTT case from IoT (GSM8K-MC, Olmo-2-7b).

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Open paper AskPDF arXiv

Large language models (LLMs) can achieve strong reasoning performance through chain-of-thought (CoT) reasoning, yet they often generate unnecessarily long reasoning paths that incur high inference cost. Self-consistency-based approaches push accuracy higher still, but they require sampling and aggregating multiple reasoning trajectories, leading to substantial computational overhead. In this paper, we introduce a confidence-aware selective sampling framework that, at inference time, analyzes a single reasoning trajectory to adaptively determine whether to rely on that trajectory alone or trigger multi-path sampling. The framework uses trajectory-level numeric features and sentence-level linguistic features extracted from reasoning states to guide selective multi-path reasoning. We train it on MedQA and evaluate it in-domain on MedQA and under calibration-only transfer on MathQA, MedMCQA, and MMLU, without further fine-tuning. Experimental results show that the proposed framework maintains comparable performance to full and efficient multi-path reasoning baselines, with accuracy changes of

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Abstract

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