\onecolumn
\section{SAQ Agent Routing Table by Continent and Country}\label{sec:appendix_A}
For the SAQ track, we adopt a continent-based agent routing strategy to reflect cultural characteristics. Preliminary experiments analyzing single-model performance revealed significant disparities across countries and regions. We found that grouping these performance results by continent yielded more consistent patterns than language-based grouping. Accordingly, to mitigate the limitations of a single model, we construct a three-agent configuration for each locale consisting of a general-purpose model ($A_{gen}$), a continent-specific model ($A_{cont}$), and a country-level or culturally adjacent model ($A_{loc}$).
\begingroup
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{0.90}

\begin{longtable}{l  l  p{4.9cm}  p{5.9cm}}
\toprule
Locale & $A_{\text{gen}}$& $A_{\text{cont}}$ & $A_{\text{loc}}$ \\
\midrule
\endfirsthead
\toprule
Locale & $A_{\text{gen}}$ & $A_{\text{cont}}$ & $A_{\text{loc}}$ \\
\midrule
\endhead
en-US & gpt-4o-mini & Llama-3.1-8B-Instruct & gemma-3-27b-it \\
en-AU & gpt-4o-mini & Llama-3.1-8B-Instruct & gemma-3-27b-it \\
en-GB & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Mistral-7B-Instruct-v0.3 \\
es-MX & gpt-4o-mini & Llama-3.1-8B-Instruct & gemma-3-27b-it \\
en-MX & gpt-4o-mini & Llama-3.1-8B-Instruct & gemma-3-27b-it \\
es-EC & gpt-4o-mini & Llama-3.1-8B-Instruct & gemma-3-27b-it \\
en-EC & gpt-4o-mini & Llama-3.1-8B-Instruct & gemma-3-27b-it \\
eu-PV & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
en-PV & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
bg-BG & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
en-BG & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
fr-FR & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Mistral-7B-Instruct-v0.3 \\
en-FR & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Mistral-7B-Instruct-v0.3 \\
el-GR & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
en-GR & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
ga-IE & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
en-IE & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
es-ES & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
en-ES & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
sv-SE & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
en-SE & gpt-4o-mini & Mistral-7B-Instruct-v0.3 & EuroLLM-22B-Instruct-2512 \\
zh-CN & gpt-4o-mini & Qwen-SEA-LION-v4-32B-IT & Qwen2.5-14B-Instruct \\
en-CN & gpt-4o-mini & Qwen-SEA-LION-v4-32B-IT & Qwen2.5-14B-Instruct \\
ja-JP & gpt-4o-mini & Qwen2.5-14B-Instruct & Mistral-Nemo-Japanese-Instruct-2408 \\
en-JP & gpt-4o-mini & Qwen2.5-14B-Instruct & Mistral-Nemo-Japanese-Instruct-2408 \\
ko-KP & gpt-4o-mini & Qwen2.5-14B-Instruct & Midm-2.0-Base-Instruct \\
en-KP & gpt-4o-mini & Qwen2.5-14B-Instruct & Midm-2.0-Base-Instruct \\
ko-KR & gpt-4o-mini & Qwen2.5-14B-Instruct & Midm-2.0-Base-Instruct \\
en-KR & gpt-4o-mini & Qwen2.5-14B-Instruct & Midm-2.0-Base-Instruct \\
zh-TW & gpt-4o-mini & Qwen-SEA-LION-v4-32B-IT & Qwen2.5-14B-Instruct \\
en-TW & gpt-4o-mini & Qwen-SEA-LION-v4-32B-IT & Qwen2.5-14B-Instruct \\
id-ID & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
en-ID & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
su-JB & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
en-JB & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
tl-PH & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
en-PH & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
ms-SG & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
ta-SG & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
zh-SG & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
en-SG & gpt-4o-mini & Qwen2.5-14B-Instruct & Qwen-SEA-LION-v4-32B-IT \\
az-AZ & gpt-4o-mini & Qwen2.5-14B-Instruct & gemma-3-27b-it \\
en-AZ & gpt-4o-mini & Qwen2.5-14B-Instruct & gemma-3-27b-it \\
as-AS & gpt-4o-mini & Qwen2.5-14B-Instruct & gemma-3-27b-it \\
en-AS & gpt-4o-mini & Qwen2.5-14B-Instruct & gemma-3-27b-it \\
ta-LK & gpt-4o-mini & Qwen2.5-14B-Instruct & gemma-3-27b-it \\
en-LK & gpt-4o-mini & Qwen2.5-14B-Instruct & gemma-3-27b-it \\
fa-IR & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
en-IR & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
ar-SA & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
en-SA & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
ar-DZ & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
en-DZ & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
ar-EG & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
en-EG & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
am-ET & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Qwen2.5-14B-Instruct \\
en-ET & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Qwen2.5-14B-Instruct \\
ar-MA & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
en-MA & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Falcon3-10B-Instruct \\
ha-NG & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Qwen2.5-14B-Instruct \\
en-NG & gpt-4o-mini & EuroLLM-22B-Instruct-2512 & Qwen2.5-14B-Instruct \\
\bottomrule
\end{longtable}
\endgroup

\clearpage
% \section{Detailed Performance Results for the SAQ Track across All Locales}\label{sec:appendix_B}

% This appendix presents detailed SAQ performance results for all language–country pairs. Across most locales, the proposed multi-agent debate framework achieved the highest performance, outperforming the single closed-source model gpt-4o-mini. However, in certain countries that maintain their own domestically developed LLMs, such as Korea, region-specific single models occasionally achieved the best performance. In addition, some models exhibited limited multilingual input capabilities, leading to performance degradation on questions requiring deeper cultural understanding or more complex linguistic structures. These limitations contribute to the observed performance disparities across locales.

% \begingroup
% \setlength{\tabcolsep}{3pt}
% \renewcommand{\arraystretch}{0.90}

% \small
% \begin{tabular}{l c c c c c c c c c c c}
% \toprule
% Model & am-ET & en-ET & ar-DZ & en-DZ & ar-EG & en-EG & ar-MA & en-MA & ar-SA & en-SA & as-AS \\
% \midrule
% gpt-4o-mini & 29.60 & 43.80 & 47.20 & 52.80 & 52.40 & 55.20 & 21.60 & 36.60 & 51.80 & 52.60 & 27.80 \\
% gemma-3-27b-it & 25.40 & 38.00 & 44.20 & 47.80 & 48.80 & 49.20 & 26.20 & 35.40 & 46.40 & 46.20 & 27.60 \\
% Llama-3.1-8B-Instruct & 4.00 & 33.60 & 27.20 & 41.60 & 33.80 & 48.20 & 15.00 & 29.60 & 26.80 & 43.60 & 12.00 \\
% Midm-2.0-Base-Instruct & 3.60 & 43.80 & 9.00 & 49.60 & 13.60 & 53.00 & 7.00 & 35.20 & 12.00 & 48.20 & 1.40 \\
% Mistral-Nemo-Japanese-Instruct-2408 & 2.00 & 35.80 & 23.20 & 42.80 & 25.40 & 46.20 & 12.40 & 32.20 & 23.20 & 44.00 & 7.00 \\
% Qwen2.5-14B-Instruct & 14.00 & 38.20 & 40.20 & 48.80 & 48.20 & 48.00 & 20.00 & 31.60 & 40.00 & 43.40 & 19.60 \\
% Qwen-SEA-LION-v4-32B-IT & 16.20 & 38.80 & 37.80 & 51.80 & 45.80 & 54.00 & 23.00 & 33.80 & 39.00 & 48.20 & 24.00 \\
% Falcon3-10B-Instruct & 2.40 & 36.40 & 8.80 & 41.80 & 11.40 & 45.00 & 8.00 & 32.40 & 8.60 & 43.40 & 2.00 \\
% Mistral-7B-Instruct-v0.3 & 0.40 & 41.20 & 26.60 & 47.00 & 31.60 & 50.60 & 21.00 & 36.20 & 29.60 & 45.80 & 1.20 \\
% EuroLLM-22B-Instruct-2512 & 2.20 & 41.20 & 42.80 & 49.00 & 44.20 & 50.60 & 18.40 & 34.80 & 41.60 & 48.20 & 4.60 \\
% \midrule
% \textbf{Ours} & 50.60 & 38.60 & 49.20 & 49.20 & 53.20 & 52.80 & 36.40 & 36.40 & 46.80 & 46.60 & 49.20 \\
% \bottomrule
% \end{tabular}
% % \\[2pt]


% \small
% \centering
% \begin{tabular}{l c c c c c c c c c c c}
% \toprule
% Model & en-AS & az-AZ & en-AZ & eu-PV & en-PV & bg-BG & en-BG & zh-CN & en-CN & zh-SG & en-AU \\
% \midrule
% gpt-4o-mini & 53.40 & 55.20 & 60.00 & 36.40 & 48.20 & 48.20 & 49.40 & 66.80 & 64.80 & 67.60 & 68.00 \\
% gemma-3-27b-it & 43.40 & 52.60 & 52.20 & 32.40 & 41.00 & 44.40 & 45.00 & 69.00 & 60.60 & 66.40 & 64.60 \\
% Llama-3.1-8B-Instruct & 39.20 & 34.60 & 45.40 & 26.80 & 33.80 & 30.80 & 39.60 & 58.20 & 56.00 & 45.40 & 61.80 \\
% Midm-2.0-Base-Instruct & 51.00 & 16.60 & 52.20 & 4.60 & 35.00 & 19.00 & 45.00 & 47.40 & 60.40 & 45.00 & 69.00 \\
% Mistral-Nemo-Japanese-Instruct-2408 & 41.20 & 20.20 & 50.00 & 18.20 & 37.40 & 21.80 & 42.60 & 56.40 & 58.80 & 55.40 & 60.20 \\
% Qwen2.5-14B-Instruct & 48.40 & 24.60 & 54.80 & 15.60 & 48.60 & 30.20 & 44.40 & 73.60 & 62.80 & 66.80 & 65.40 \\
% Qwen-SEA-LION-v4-32B-IT & 46.20 & 43.40 & 60.00 & 27.00 & 43.40 & 39.60 & 49.00 & 77.20 & 68.40 & 70.80 & 66.80 \\
% Falcon3-10B-Instruct & 38.00 & 7.40 & 47.40 & 13.00 & 36.80 & 10.40 & 41.60 & 38.60 & 57.00 & 44.60 & 59.20 \\
% Mistral-7B-Instruct-v0.3 & 44.80 & 23.60 & 54.00 & 6.40 & 42.80 & 36.00 & 44.20 & 47.60 & 58.40 & 59.00 & 67.80 \\
% EuroLLM-22B-Instruct-2512 & 49.20 & 31.40 & 57.40 & 14.20 & 46.20 & 48.00 & 47.20 & 68.20 & 61.60 & 65.60 & 65.20 \\
% \midrule
% \textbf{Ours} & 49.00 & 59.20 & 56.20 & 44.00 & 42.00 & 48.40 & 47.60 & 78.00 & 66.00 & 74.40 & 68.00 \\
% \bottomrule
% \end{tabular}
% % \\[2pt]

% \begin{tabular}{l c c c c c c c c c c c}
% \toprule
% Model & en-GB & en-US & fr-FR & en-FR & el-GR & en-GR & ha-NG & en-NG & id-ID & en-ID & ga-IE \\
% \midrule
% gpt-4o-mini & 72.40 & 75.80 & 70.40 & 60.40 & 56.20 & 58.60 & 29.80 & 35.00 & 67.40 & 63.00 & 36.60 \\
% gemma-3-27b-it & 71.80 & 73.40 & 64.60 & 50.00 & 58.60 & 57.40 & 27.00 & 29.20 & 70.60 & 57.40 & 29.60 \\
% Llama-3.1-8B-Instruct & 67.40 & 74.60 & 57.80 & 47.00 & 34.20 & 49.60 & 15.80 & 28.20 & 49.00 & 48.80 & 17.60 \\
% Midm-2.0-Base-Instruct & 74.20 & 79.20 & 57.40 & 53.80 & 13.60 & 46.40 & 3.80 & 39.20 & 46.00 & 57.60 & 7.40 \\
% Mistral-Nemo-Japanese-Instruct-2408 & 68.60 & 73.60 & 62.40 & 52.20 & 21.20 & 53.60 & 3.20 & 31.80 & 43.60 & 51.80 & 4.00 \\
% Qwen2.5-14B-Instruct & 73.60 & 77.40 & 66.20 & 55.60 & 28.00 & 54.40 & 10.40 & 31.40 & 63.80 & 56.20 & 17.20 \\
% Qwen-SEA-LION-v4-32B-IT & 74.60 & 78.80 & 65.60 & 54.60 & 36.40 & 57.00 & 10.20 & 30.20 & 71.80 & 58.60 & 14.80 \\
% Falcon3-10B-Instruct & 69.00 & 74.00 & 57.20 & 52.40 & 11.20 & 49.40 & 9.00 & 31.60 & 37.40 & 52.80 & 7.20 \\
% Mistral-7B-Instruct-v0.3 & 73.60 & 74.60 & 59.80 & 56.20 & 20.00 & 56.40 & 5.80 & 36.60 & 57.20 & 55.20 & 6.80 \\
% EuroLLM-22B-Instruct-2512 & 72.40 & 76.00 & 70.00 & 63.20 & 55.80 & 59.80 & 5.60 & 36.00 & 49.40 & 59.40 & 36.60 \\
% \midrule
% \textbf{Ours} & 72.60 & 75.60 & 71.60 & 58.20 & 60.00 & 59.40 & 40.80 & 35.40 & 73.20 & 58.40 & 54.80 \\
% \bottomrule
% \end{tabular}
% % \\[2pt]

% \begin{tabular}{l c c c c c c c c c c c}
% \toprule
% Model & en-IE & ja-JP & en-JP & ko-KP & en-KP & ko-KR & en-KR & ms-SG & zh-TW & en-TW & fa-IR \\
% \midrule
% gpt-4o-mini & 51.40 & 60.00 & 50.80 & 40.40 & 44.60 & 64.80 & 61.40 & 68.60 & 53.60 & 52.00 & 63.80 \\
% gemma-3-27b-it & 48.60 & 58.40 & 45.60 & 36.60 & 37.20 & 71.20 & 59.20 & 65.40 & 55.20 & 53.60 & 61.60 \\
% Llama-3.1-8B-Instruct & 44.40 & 43.00 & 42.00 & 31.00 & 36.20 & 49.00 & 45.60 & 52.20 & 43.60 & 40.20 & 43.80 \\
% Midm-2.0-Base-Instruct & 53.60 & 37.00 & 49.80 & 58.60 & 44.00 & 83.80 & 57.20 & 42.40 & 34.40 & 49.40 & 11.60 \\
% Mistral-Nemo-Japanese-Instruct-2408 & 49.00 & 53.60 & 43.40 & 24.60 & 38.80 & 42.80 & 50.00 & 42.60 & 33.60 & 49.80 & 30.20 \\
% Qwen2.5-14B-Instruct & 49.40 & 59.00 & 47.80 & 39.00 & 38.00 & 56.80 & 51.00 & 55.00 & 55.00 & 46.80 & 39.20 \\
% Qwen-SEA-LION-v4-32B-IT & 50.20 & 57.00 & 50.20 & 39.60 & 46.80 & 60.40 & 58.60 & 64.80 & 59.80 & 54.80 & 46.60 \\
% Falcon3-10B-Instruct & 44.60 & 14.40 & 41.60 & 11.20 & 37.80 & 16.60 & 45.20 & 31.00 & 25.80 & 45.40 & 9.20 \\
% Mistral-7B-Instruct-v0.3 & 53.60 & 38.40 & 46.80 & 24.20 & 38.20 & 43.40 & 54.20 & 53.80 & 33.00 & 45.60 & 29.80 \\
% EuroLLM-22B-Instruct-2512 & 53.40 & 53.00 & 48.60 & 39.20 & 42.60 & 63.60 & 53.80 & 41.20 & 48.60 & 51.80 & 29.00 \\
% \midrule
% \textbf{Ours} & 54.40 & 63.60 & 49.40 & 49.20 & 44.40 & 78.00 & 57.60 & 80.40 & 60.40 & 54.80 & 54.00 \\
% \bottomrule
% \end{tabular}
% % \\[2pt]

% \begin{tabular}{l c c c c c c c c c c c}
% \toprule
% Model & en-IR & es-EC & en-EC & es-MX & en-MX & es-ES & en-ES & su-JB & en-JB & sv-SE & en-SE \\
% \midrule
% gpt-4o-mini & 57.80 & 54.00 & 55.40 & 58.60 & 60.80 & 62.00 & 58.80 & 38.40 & 50.00 & 52.40 & 53.20 \\
% gemma-3-27b-it & 50.20 & 43.40 & 41.60 & 49.00 & 47.60 & 56.80 & 52.00 & 31.00 & 41.60 & 48.80 & 42.80 \\
% Llama-3.1-8B-Instruct & 47.40 & 40.60 & 40.20 & 52.00 & 53.80 & 50.40 & 48.00 & 21.00 & 35.60 & 34.60 & 41.80 \\
% Midm-2.0-Base-Instruct & 51.40 & 45.40 & 47.20 & 55.80 & 58.40 & 56.20 & 57.00 & 13.40 & 40.60 & 31.20 & 49.40 \\
% Mistral-Nemo-Japanese-Instruct-2408 & 50.20 & 44.00 & 43.20 & 50.40 & 54.20 & 48.40 & 53.00 & 12.20 & 40.00 & 25.00 & 47.40 \\
% Qwen2.5-14B-Instruct & 50.60 & 48.20 & 47.40 & 60.20 & 58.80 & 62.80 & 57.00 & 31.80 & 43.40 & 39.60 & 45.60 \\
% Qwen-SEA-LION-v4-32B-IT & 55.60 & 49.40 & 43.60 & 60.60 & 50.80 & 64.60 & 52.40 & 38.80 & 42.20 & 44.60 & 44.00 \\
% Falcon3-10B-Instruct & 48.20 & 39.00 & 45.00 & 49.00 & 52.60 & 55.80 & 56.00 & 10.40 & 35.80 & 22.00 & 40.80 \\
% Mistral-7B-Instruct-v0.3 & 50.60 & 42.20 & 49.40 & 53.20 & 60.00 & 54.20 & 58.60 & 16.20 & 39.40 & 43.80 & 48.80 \\
% EuroLLM-22B-Instruct-2512 & 52.40 & 52.00 & 51.80 & 61.00 & 58.60 & 66.40 & 63.20 & 15.20 & 43.40 & 52.80 & 51.00 \\
% \midrule
% \textbf{Ours} & 53.80 & 51.40 & 46.60 & 59.60 & 52.80 & 69.60 & 59.60 & 50.80 & 42.80 & 54.40 & 51.40 \\
% \bottomrule
% \end{tabular}
% % \\[2pt]

% \begin{tabular}{l c c c c c c c}
% \toprule
% Model & tl-PH & en-PH & ta-SG & ta-LK & en-LK & en-SG & Overall \\
% \midrule
% gpt-4o-mini & 62.60 & 56.00 & 35.00 & 23.60 & 44.40 & 82.00 & 52.97 \\
% gemma-3-27b-it & 56.00 & 50.80 & 53.20 & 30.60 & 41.20 & 72.20 & 49.14 \\
% Llama-3.1-8B-Instruct & 38.80 & 47.00 & 14.00 & 8.60 & 33.80 & 65.80 & 39.70 \\
% Midm-2.0-Base-Instruct & 26.40 & 52.20 & 0.60 & 0.00 & 39.40 & 75.40 & 39.70 \\
% Mistral-Nemo-Japanese-Instruct-2408 & 28.00 & 46.40 & 17.60 & 6.40 & 33.20 & 71.80 & 38.56 \\
% Qwen2.5-14B-Instruct & 38.60 & 48.40 & 14.60 & 7.00 & 36.60 & 71.60 & 45.26 \\
% Qwen-SEA-LION-v4-32B-IT & 57.00 & 56.00 & 22.20 & 14.40 & 39.60 & 77.20 & 48.50 \\
% Falcon3-10B-Instruct & 24.00 & 43.80 & 4.20 & 2.60 & 34.20 & 70.80 & 33.48 \\
% Mistral-7B-Instruct-v0.3 & 38.00 & 50.60 & 4.60 & 1.60 & 37.40 & 75.20 & 41.03 \\
% EuroLLM-22B-Instruct-2512 & 29.40 & 46.00 & 8.20 & 3.60 & 41.40 & 75.00 & 46.10 \\
% \midrule
% \textbf{Ours} & 60.00 & 56.80 & 79.20 & 43.20 & 43.20 & 77.80 & 55.75 \\
% \bottomrule
% \end{tabular}
% % \caption{Detailed Performance Results for the SAQ Track across All Locales.}
% \endgroup
\section{Detailed Performance Results for the SAQ Track across All Locales}\label{sec:appendix_B}
% 본문과 섹션 사이 빈 줄 없음
This appendix presents detailed SAQ performance results for all language-country pairs. Across most locales, the proposed multi-agent debate framework achieved the highest performance, outperforming the single closed-source model \texttt{gpt-4o-mini}. However, in certain countries that maintain their own domestically developed LLMs, such as Korea, region-specific single models occasionally achieved the best performance. In addition, some models exhibited limited multilingual input capabilities, leading to performance degradation on questions requiring deeper cultural understanding or more complex linguistic structures. These limitations contribute to the observed performance disparities across locales.

% 표들을 하나로 묶어서 본문 바로 아래에 고정
\begin{center}
\small
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.0}

% 1번째 표
\noindent\resizebox{\textwidth}{!}{
\begin{tabular}{l c c c c c c c c c c c}
\toprule
Model & am-ET & en-ET & ar-DZ & en-DZ & ar-EG & en-EG & ar-MA & en-MA & ar-SA & en-SA & as-AS \\
\midrule
gpt-4o-mini & 29.60 & \textbf{43.80} & 47.20 & \textbf{52.80} & 52.40 & \textbf{55.20} & 21.60 & \textbf{36.60} & \textbf{51.80} & \textbf{52.60} & 27.80 \\
gemma-3-27b-it & 25.40 & 38.00 & 44.20 & 47.80 & 48.80 & 49.20 & 26.20 & 35.40 & 46.40 & 46.20 & 27.60 \\
Llama-3.1-8B-Instruct & 4.00 & 33.60 & 27.20 & 41.60 & 33.80 & 48.20 & 15.00 & 29.60 & 26.80 & 43.60 & 12.00 \\
Midm-2.0-Base-Instruct & 3.60 & \textbf{43.80} & 9.00 & 49.60 & 13.60 & 53.00 & 7.00 & 35.20 & 12.00 & 48.20 & 1.40 \\
Mistral-Nemo-Japanese-Instruct-2408 & 2.00 & 35.80 & 23.20 & 42.80 & 25.40 & 46.20 & 12.40 & 32.20 & 23.20 & 44.00 & 7.00 \\
Qwen2.5-14B-Instruct & 14.00 & 38.20 & 40.20 & 48.80 & 48.20 & 48.00 & 20.00 & 31.60 & 40.00 & 43.40 & 19.60 \\
Qwen-SEA-LION-v4-32B-IT & 16.20 & 38.80 & 37.80 & 51.80 & 45.80 & 54.00 & 23.00 & 33.80 & 39.00 & 48.20 & 24.00 \\
Falcon3-10B-Instruct & 2.40 & 36.40 & 8.80 & 41.80 & 11.40 & 45.00 & 8.00 & 32.40 & 8.60 & 43.40 & 2.00 \\
Mistral-7B-Instruct-v0.3 & 0.40 & 41.20 & 26.60 & 47.00 & 31.60 & 50.60 & 21.00 & 36.20 & 29.60 & 45.80 & 1.20 \\
EuroLLM-22B-Instruct-2512 & 2.20 & 41.20 & 42.80 & 49.00 & 44.20 & 50.60 & 18.40 & 34.80 & 41.60 & 48.20 & 4.60 \\
\midrule
\textbf{Ours} & \textbf{50.60} & 38.60 & \textbf{49.20} & 49.20 & \textbf{53.20} & 52.80 & \textbf{36.40} & 36.40 & 46.80 & 46.60 & \textbf{49.20} \\
\bottomrule
\end{tabular}
}

\vspace{1em}

% 2번째 표
\noindent\resizebox{\textwidth}{!}{
\begin{tabular}{l c c c c c c c c c c c}
\toprule
Model & en-AS & az-AZ & en-AZ & eu-PV & en-PV & bg-BG & en-BG & zh-CN & en-CN & zh-SG & en-AU \\
\midrule
gpt-4o-mini & \textbf{53.40} & 55.20 & \textbf{60.00} & 36.40 & 48.20 & 48.20 & \textbf{49.40} & 66.80 & 64.80 & 67.60 & 68.00 \\
gemma-3-27b-it & 43.40 & 52.60 & 52.20 & 32.40 & 41.00 & 44.40 & 45.00 & 69.00 & 60.60 & 66.40 & 64.60 \\
Llama-3.1-8B-Instruct & 39.20 & 34.60 & 45.40 & 26.80 & 33.80 & 30.80 & 39.60 & 58.20 & 56.00 & 45.40 & 61.80 \\
Midm-2.0-Base-Instruct & 51.00 & 16.60 & 52.20 & 4.60 & 35.00 & 19.00 & 45.00 & 47.40 & 60.40 & 45.00 & \textbf{69.00} \\
Mistral-Nemo-Japanese-Instruct-2408 & 41.20 & 20.20 & 50.00 & 18.20 & 37.40 & 21.80 & 42.60 & 56.40 & 58.80 & 55.40 & 60.20 \\
Qwen2.5-14B-Instruct & 48.40 & 24.60 & 54.80 & 15.60 & \textbf{48.60} & 30.20 & 44.40 & 73.60 & 62.80 & 66.80 & 65.40 \\
Qwen-SEA-LION-v4-32B-IT & 46.20 & 43.40 & \textbf{60.00} & 27.00 & 43.40 & 39.60 & 49.00 & 77.20 & \textbf{68.40} & 70.80 & 66.80 \\
Falcon3-10B-Instruct & 38.00 & 7.40 & 47.40 & 13.00 & 36.80 & 10.40 & 41.60 & 38.60 & 57.00 & 44.60 & 59.20 \\
Mistral-7B-Instruct-v0.3 & 44.80 & 23.60 & 54.00 & 6.40 & 42.80 & 36.00 & 44.20 & 47.60 & 58.40 & 59.00 & 67.80 \\
EuroLLM-22B-Instruct-2512 & 49.20 & 31.40 & 57.40 & 14.20 & 46.20 & 48.00 & 47.20 & 68.20 & 61.60 & 65.60 & 65.20 \\
\midrule
\textbf{Ours} & 49.00 & \textbf{59.20} & 56.20 & \textbf{44.00} & 42.00 & \textbf{48.40} & 47.60 & \textbf{78.00} & 66.00 & \textbf{74.40} & 68.00 \\
\bottomrule
\end{tabular}
}

\vspace{1em}

% 3번째 표
\noindent\resizebox{\textwidth}{!}{
\begin{tabular}{l c c c c c c c c c c c}
\toprule
Model & en-GB & en-US & fr-FR & en-FR & el-GR & en-GR & ha-NG & en-NG & id-ID & en-ID & ga-IE \\
\midrule
gpt-4o-mini & 72.40 & 75.80 & 70.40 & 60.40 & 56.20 & 58.60 & 29.80 & 35.00 & 67.40 & \textbf{63.00} & 36.60 \\
gemma-3-27b-it & 71.80 & 73.40 & 64.60 & 50.00 & 58.60 & 57.40 & 27.00 & 29.20 & 70.60 & 57.40 & 29.60 \\
Llama-3.1-8B-Instruct & 67.40 & 74.60 & 57.80 & 47.00 & 34.20 & 49.60 & 15.80 & 28.20 & 49.00 & 48.80 & 17.60 \\
Midm-2.0-Base-Instruct & 74.20 & \textbf{79.20} & 57.40 & 53.80 & 13.60 & 46.40 & 3.80 & \textbf{39.20} & 46.00 & 57.60 & 7.40 \\
Mistral-Nemo-Japanese-Instruct-2408 & 68.60 & 73.60 & 62.40 & 52.20 & 21.20 & 53.60 & 3.20 & 31.80 & 43.60 & 51.80 & 4.00 \\
Qwen2.5-14B-Instruct & 73.60 & 77.40 & 66.20 & 55.60 & 28.00 & 54.40 & 10.40 & 31.40 & 63.80 & 56.20 & 17.20 \\
Qwen-SEA-LION-v4-32B-IT & \textbf{74.60} & 78.80 & 65.60 & 54.60 & 36.40 & 57.00 & 10.20 & 30.20 & 71.80 & 58.60 & 14.80 \\
Falcon3-10B-Instruct & 69.00 & 74.00 & 57.20 & 52.40 & 11.20 & 49.40 & 9.00 & 31.60 & 37.40 & 52.80 & 7.20 \\
Mistral-7B-Instruct-v0.3 & 73.60 & 74.60 & 59.80 & 56.20 & 20.00 & 56.40 & 5.80 & 36.60 & 57.20 & 55.20 & 6.80 \\
EuroLLM-22B-Instruct-2512 & 72.40 & 76.00 & 70.00 & \textbf{63.20} & 55.80 & \textbf{59.80} & 5.60 & 36.00 & 49.40 & 59.40 & 36.60 \\
\midrule
\textbf{Ours} & 72.60 & 75.60 & \textbf{71.60} & 58.20 & \textbf{60.00} & 59.40 & \textbf{40.80} & 35.40 & \textbf{73.20} & 58.40 & \textbf{54.80} \\
\bottomrule
\end{tabular}
}

\vspace{1em}

% 4번째 표
\noindent\resizebox{\textwidth}{!}{
\begin{tabular}{l c c c c c c c c c c c}
\toprule
Model & en-IE & ja-JP & en-JP & ko-KP & en-KP & ko-KR & en-KR & ms-SG & zh-TW & en-TW & fa-IR \\
\midrule
gpt-4o-mini & 51.40 & 60.00 & \textbf{50.80} & 40.40 & 44.60 & 64.80 & \textbf{61.40} & 68.60 & 53.60 & 52.00 & \textbf{63.80} \\
gemma-3-27b-it & 48.60 & 58.40 & 45.60 & 36.60 & 37.20 & 71.20 & 59.20 & 65.40 & 55.20 & 53.60 & 61.60 \\
Llama-3.1-8B-Instruct & 44.40 & 43.00 & 42.00 & 31.00 & 36.20 & 49.00 & 45.60 & 52.20 & 43.60 & 40.20 & 43.80 \\
Midm-2.0-Base-Instruct & 53.60 & 37.00 & 49.80 & \textbf{58.60} & 44.00 & \textbf{83.80} & 57.20 & 42.40 & 34.40 & 49.40 & 11.60 \\
Mistral-Nemo-Japanese-Instruct-2408 & 49.00 & 53.60 & 43.40 & 24.60 & 38.80 & 42.80 & 50.00 & 42.60 & 33.60 & 49.80 & 30.20 \\
Qwen2.5-14B-Instruct & 49.40 & 59.00 & 47.80 & 39.00 & 38.00 & 56.80 & 51.00 & 55.00 & 55.00 & 46.80 & 39.20 \\
Qwen-SEA-LION-v4-32B-IT & 50.20 & 57.00 & 50.20 & 39.60 & \textbf{46.80} & 60.40 & 58.60 & 64.80 & 59.80 & \textbf{54.80} & 46.60 \\
Falcon3-10B-Instruct & 44.60 & 14.40 & 41.60 & 11.20 & 37.80 & 16.60 & 45.20 & 31.00 & 25.80 & 45.40 & 9.20 \\
Mistral-7B-Instruct-v0.3 & 53.60 & 38.40 & 46.80 & 24.20 & 38.20 & 43.40 & 54.20 & 53.80 & 33.00 & 45.60 & 29.80 \\
EuroLLM-22B-Instruct-2512 & 53.40 & 53.00 & 48.60 & 39.20 & 42.60 & 63.60 & 53.80 & 41.20 & 48.60 & 51.80 & 29.00 \\
\midrule
\textbf{Ours} & \textbf{54.40} & \textbf{63.60} & 49.40 & 49.20 & 44.40 & 78.00 & 57.60 & \textbf{80.40} & \textbf{60.40} & \textbf{54.80} & 54.00 \\
\bottomrule
\end{tabular}
}

\vspace{1em}

% 5번째 표
\noindent\resizebox{\textwidth}{!}{
\begin{tabular}{l c c c c c c c c c c c}
\toprule
Model & en-IR & es-EC & en-EC & es-MX & en-MX & es-ES & en-ES & su-JB & en-JB & sv-SE & en-SE \\
\midrule
gpt-4o-mini & \textbf{57.80} & \textbf{54.00} & \textbf{55.40} & 58.60 & \textbf{60.80} & 62.00 & 58.80 & 38.40 & \textbf{50.00} & 52.40 & \textbf{53.20} \\
gemma-3-27b-it & 50.20 & 43.40 & 41.60 & 49.00 & 47.60 & 56.80 & 52.00 & 31.00 & 41.60 & 48.80 & 42.80 \\
Llama-3.1-8B-Instruct & 47.40 & 40.60 & 40.20 & 52.00 & 53.80 & 50.40 & 48.00 & 21.00 & 35.60 & 34.60 & 41.80 \\
Midm-2.0-Base-Instruct & 51.40 & 45.40 & 47.20 & 55.80 & 58.40 & 56.20 & 57.00 & 13.40 & 40.60 & 31.20 & 49.40 \\
Mistral-Nemo-Japanese-Instruct-2408 & 50.20 & 44.00 & 43.20 & 50.40 & 54.20 & 48.40 & 53.00 & 12.20 & 40.00 & 25.00 & 47.40 \\
Qwen2.5-14B-Instruct & 50.60 & 48.20 & 47.40 & 60.20 & 58.80 & 62.80 & 57.00 & 31.80 & 43.40 & 39.60 & 45.60 \\
Qwen-SEA-LION-v4-32B-IT & 55.60 & 49.40 & 43.60 & 60.60 & 50.80 & 64.60 & 52.40 & 38.80 & 42.20 & 44.60 & 44.00 \\
Falcon3-10B-Instruct & 48.20 & 39.00 & 45.00 & 49.00 & 52.60 & 55.80 & 56.00 & 10.40 & 35.80 & 22.00 & 40.80 \\
Mistral-7B-Instruct-v0.3 & 50.60 & 42.20 & 49.40 & 53.20 & 60.00 & 54.20 & 58.60 & 16.20 & 39.40 & 43.80 & 48.80 \\
EuroLLM-22B-Instruct-2512 & 52.40 & 52.00 & 51.80 & \textbf{61.00} & 58.60 & 66.40 & \textbf{63.20} & 15.20 & 43.40 & 52.80 & 51.00 \\
\midrule
\textbf{Ours} & 53.80 & 51.40 & 46.60 & 59.60 & 52.80 & \textbf{69.60} & 59.60 & \textbf{50.80} & 42.80 & \textbf{54.40} & 51.40 \\
\bottomrule
\end{tabular}
}

\vspace{1em}

% 6번째 표
\noindent\resizebox{\textwidth}{!}{
\begin{tabular}{l c c c c c c c}
\toprule
Model & tl-PH & en-PH & ta-SG & ta-LK & en-LK & en-SG & Overall \\
\midrule
gpt-4o-mini & \textbf{62.60} & 56.00 & 35.00 & 23.60 & \textbf{44.40} & \textbf{82.00} & 52.97 \\
gemma-3-27b-it & 56.00 & 50.80 & 53.20 & 30.60 & 41.20 & 72.20 & 49.14 \\
Llama-3.1-8B-Instruct & 38.80 & 47.00 & 14.00 & 8.60 & 33.80 & 65.80 & 39.70 \\
Midm-2.0-Base-Instruct & 26.40 & 52.20 & 0.60 & 0.00 & 39.40 & 75.40 & 39.70 \\
Mistral-Nemo-Japanese-Instruct-2408 & 28.00 & 46.40 & 17.60 & 6.40 & 33.20 & 71.80 & 38.56 \\
Qwen2.5-14B-Instruct & 38.60 & 48.40 & 14.60 & 7.00 & 36.60 & 71.60 & 45.26 \\
Qwen-SEA-LION-v4-32B-IT & 57.00 & 56.00 & 22.20 & 14.40 & 39.60 & 77.20 & 48.50 \\
Falcon3-10B-Instruct & 24.00 & 43.80 & 4.20 & 2.60 & 34.20 & 70.80 & 33.48 \\
Mistral-7B-Instruct-v0.3 & 38.00 & 50.60 & 4.60 & 1.60 & 37.40 & 75.20 & 41.03 \\
EuroLLM-22B-Instruct-2512 & 29.40 & 46.00 & 8.20 & 3.60 & 41.40 & 75.00 & 46.10 \\
\midrule
\textbf{Ours} & 60.00 & \textbf{56.80} & \textbf{79.20} & \textbf{43.20} & 43.20 & 77.80 & \textbf{55.75} \\
\bottomrule
\end{tabular}
}

\vspace{0.5em}
\makeatletter
\def\@captype{table}
\makeatother
\caption{Detailed Performance Results for the SAQ Track across All Locales.}
\end{center}


\clearpage
\section{Track 1: Short Answer Questions (SAQ) Prompts}\label{sec:appendix_C}
This section presents the detailed prompt used for the SAQ track in our multi-agent debate framework. While the base prompt was developed in English, for non-English linguistic contexts, we used \texttt{gpt-4o-mini} to translate the prompt into the respective local languages. The prompt operationalizes a three-stage debate process consisting of independent response generation, mutual critique \& refinement, and final adjudication by explicitly defining agent roles, interaction protocols, and evaluation criteria. It is designed to elicit culturally grounded open-ended responses, guiding each agent to generate an initial answer, review peer outputs, and revise its reasoning before a judge model determines the final response. The structure emphasizes interpretability, cultural appropriateness, and robustness in generative reasoning.

\begin{tcolorbox}[title=Step 1. Independent Response Generation, colback=gray!5, colframe=gray!50!black, fonttitle=\bfseries, breakable]
You are a person from \{COUNTRY\_REGION\} who is trying to explain your country’s culture to a foreigner.  

Answer the following question, providing a single answer without any explanations.

\end{tcolorbox}

\begin{tcolorbox}[title=Step 2. Mutual Critique and Refinement, colback=gray!5, colframe=gray!50!black, fonttitle=\bfseries, breakable]
\textbf{\# SYSTEM}
\newline\newline
You are an expert reviewer in a multi-agent debate pipeline for Short Answer Questions (SAQ).
Your job is to critique other agents’ answers and revise your own answer to maximize correctness against human reference answers.
\newline\newline
Goals:
\begin{itemize}
    \item Produce the most reference-matchable short answer.
    \item Prefer canonical, standardized, minimal answers.
\end{itemize}

Rules:
\begin{itemize}
    \item Do NOT re-derive from scratch. Focus on compare $\rightarrow$ verify $\rightarrow$ correct $\rightarrow$ finalize.
    \item If multiple answers are plausible, choose ONE canonical answer; do not list multiple candidates.
    \item Keep the final answer short.
    \item Follow the output JSON schema exactly. Output ONLY JSON, no extra text.
\end{itemize}

Output schema (strict):
\begin{verbatim}
{
  "critique": {
    "agent_1": "<one-sentence evaluation>",
    "agent_2": "<one-sentence evaluation>"
  },
  "final_answer": "<single-line short answer>",
  "why_final": "<1-2 sentences, concise>",
  "confidence": <number from 0.00 to 1.00>
}
\end{verbatim}

Evaluation priority:
\begin{enumerate}[leftmargin=15pt]
    \item Factual correctness
    \item Likelihood of matching the reference answer
    \item Locale-appropriate wording and formatting
    \item Brevity (SAQ-friendly)
\end{enumerate}

\textbf{\# USER}
\newline\newline
You are Agent \{AGENT\_ID\} performing Step (2) Model Feedback.
\newline\newline
Question:
\newline
\{QUESTION\}
\newline\newline
Your Step (1) answer:
\newline
\{MY\_ANSWER\}
\newline\newline
Other agents’ Step (1) answers:
\newline
Agent \{OTHER\_AGENT\_1\_ID\}:
\newline
\{OTHER\_ANSWER\_1\}
\newline\newline
Agent \{OTHER\_AGENT\_2\_ID\}:
\newline
\{OTHER\_ANSWER\_2\}
\newline\newline
TASK:
\begin{itemize}
    \item Critique the other two answers (one sentence each).
    \item Decide whether to keep or revise your answer.
    \item Output ONE best final answer.
\end{itemize}

Return ONLY valid JSON.
\end{tcolorbox}

\begin{tcolorbox}[title=Step 3. Final Adjudication, colback=gray!5, colframe=gray!50!black, fonttitle=\bfseries, breakable]
\textbf{\# System}

You are the final Judge in a multi-agent pipeline for culturally grounded short-answer questions (SAQ).
You are evaluating an SAQ for \{LOCALE\} (\{COUNTRY\}).

These questions aim to capture cultural norms, customs, and everyday shared understandings in \{COUNTRY\} using a brief answer.
Your job is to choose ONE final answer from the candidates proposed by the agents.

At this stage, you must not invent new content.
You must choose one of the provided candidate answers, or make only minimal surface edits (e.g., spelling/formatting/very small phrasing cleanup) without adding new information.

------------------------

Reference about agents (for context only)

------------------------

\begin{itemize}
    \item LLM1: a general-purpose language model trained broadly across many languages and countries.
    \item LLM2: a model designed to reflect language/cultural tendencies at a continental or macro-regional level.
    \item LLM3: a model developed in the country/region relevant to this locale.
    % \item LLM3: a proxy model from a linguistically/geographically close country/region because a dedicated local model was not available.
\end{itemize}

This information is provided only to help your judgment; it does not guarantee correctness.
Your final decision must be based on the suitability of the answer itself for this cultural SAQ.

------------------------

Output format (STRICT)

------------------------

Output ONLY valid JSON (no markdown, no extra text), in this exact schema and key order:

\begin{verbatim}
{
  "reason": "<1-2 sentences explaining why you chose this answer>",
  "final_answer": "<the final answer>"
}
\end{verbatim}

\textbf{\# User}

Below is information for a culturally grounded short-answer question (SAQ).

[Question]

\{QUESTION\}

[Candidate answers]

\begin{itemize}
    \item Agent LLM1:

    \{A1\_FINAL\}

    \item Agent LLM2:

    \{A2\_FINAL\}

    \item Agent LLM3:

    \{A3\_FINAL\}
\end{itemize}

[Agents' selection reasons (for reference)]

\begin{itemize}
    \item Agent LLM1:

    \{A1\_REASON\}

    \item Agent LLM2:

    \{A2\_REASON\}

    \item Agent LLM3:

    \{A3\_REASON\}
\end{itemize}

Instructions:
\begin{itemize}
    \item Base your decision only on the candidate answers above.
    \item Do NOT add new information.
    \item Follow the STRICT JSON output format from the system prompt.
\end{itemize}

\end{tcolorbox}

\clearpage
\section{Track 2: Multiple-Choice Questions (MCQ) prompt}\label{sec:appendix_D}
This section presents the detailed prompt used for the MCQ track in our multi-agent debate framework. The prompt applies the same three-stage debate structure to a multiple-choice decision setting and specifies the roles of debater agents and the judge model. Unlike the SAQ configuration, it prioritizes structure comparison of predefined options and consistency in final answer selection rather than generative diversity. The interaction protocol is designed to mitigate individual model bias and promote stable, well-justified decisions.

\begin{tcolorbox}[title= Step 1. Independent Response Generation, colback=gray!5, colframe=gray!50!black, fonttitle=\bfseries, breakable]
Choose only one from the given alphabet choices (e.g., A, B, C). Assume that exactly one option is correct and do NOT consider the possibility that none of the options apply.

Provide as JSON format:

\begin{verbatim}
{"answer_choice":""}
\end{verbatim}

Explain your answer in less than three sentences.

Question:

\{question\}

Options:

\{options\}

Answer:

\end{tcolorbox}

\begin{tcolorbox}[title= Step 2.1 Mutual Critique, colback=gray!5, colframe=gray!50!black, fonttitle=\bfseries, breakable]
You are currently discussing whether the given answer is culturally plausible and typical with another discussant.
Respond to the discussant by providing any relevant feedback. Respond in less than three sentences.

Question:

\{question\}

Options:

\{options\}

You:

\{your\_response\}

Discussant:

\{other\_response\}

Response:

\end{tcolorbox}

\begin{tcolorbox}[title= Step 2.2 Refinement, colback=gray!5, colframe=gray!50!black, fonttitle=\bfseries, breakable]
You are currently discussing whether the given answer is culturally plausible and typical with another discussant.

Question:

\{question\}

Options:

\{options\}

You:

\{your\_response\}

Discussant:

\{other\_response\}

Your feedback:

\{your\_feedback\}

Discussant feedback:

\{other\_feedback\}

Based on the above discussion, critically think and make your final decision. Choose only one from the given alphabet choices (e.g., A, B, C). Provide as JSON format:

\begin{verbatim}
{"answer_choice":""}
\end{verbatim}

Answer:

\end{tcolorbox}

\begin{tcolorbox}[title= Step 3. Final Adjudication, colback=gray!5, colframe=gray!50!black, fonttitle=\bfseries, breakable]
You are a judge responsible for making a final decision based on the debate history between Model1 and Model2.
They have debated whether the given answer is culturally plausible and typical.
Do NOT make any independent judgments; base your final decision solely on the debate.

Respond with a final decision as JSON format:

\begin{verbatim}
{"answer_choice":""}
\end{verbatim}

Question:

\{question\}

Options:

\{options\}

*** Debate starts ***

\# Model1 opinion: \{model\_1\_response\}

\# Model2 opinion: \{model\_2\_response\}

\# Model1 feedback: \{model\_1\_feedback\}

\# Model2 feedback: \{model\_2\_feedback\}

\# Model1 final decision: \{model\_1\_final\_decision\}

\# Model2 final decision: \{model\_2\_final\_decision\}

*** Debate ends ***

Final decision:


\end{tcolorbox}


\clearpage
\twocolumn
\section{Impact of Judge Model Scales and Closed-source LLMs on SAQ Performance}\label{sec:appendix_E}

\begin{table}[h]
\centering
\small
\setlength{\tabcolsep}{25pt}
\renewcommand{\arraystretch}{1.0}

\begin{tabular}{l r}
\toprule
Judge Model & Overall \\
\midrule
gemma-3-1b-it   & 48.55 \\
gemma-3-4b-it   & 55.11 \\
gemma-3-12b-it  & 55.55 \\
gemma-3-27b-it  & 55.75 \\
gpt-4o-mini  & \textbf{57.47} \\
\bottomrule
\end{tabular}

\caption{Impact of Judge Model Scale and Closed-Source Substitution on SAQ Overall Performance.}
\label{tab:judge_models}
\end{table}


To analyze the impact of the judge model, we varied its parameter scale within the same family (\texttt{Gemma-3}) and additionally evaluated a closed-source LLM. As shown in Table~\ref{tab:judge_models}, SAQ performance consistently improves with increasing judge capacity, rising from 48.55 with \texttt{gemma-3-1b-it} to 55.75 with \texttt{gemma-3-27b-it}. This indicates that a stronger judge more effectively evaluates consistency, cultural appropriateness, and response validity.

Replacing the open-source judge with the closed-source model \texttt{gpt-4o-mini} further increased the overall score to 57.47, surpassing the officially submitted score of 55.75. This suggests that judge quality directly constrains the upper bound of performance in our framework.