What were the conditions of Ibn Majah, Abu Dawud, al-Tirmidhi and al-Nasa'i for including a hadith?

Imam Al-Nasa'i's Sunan is given precedence over the other four Sunans due to his meticulous scrutiny of narrators. His conditions are stricter than those of Al-Bukhari and Muslim. He does not include any narration from a narrator who has been unanimously abandoned (as unreliable). Therefore, his narrations are closer to authenticity, and his book contains the fewest weak narrations after the two Sahihs (Al-Bukhari and Muslim).

Sunan Abi Dawud is comparable to it in strength and authenticity. His condition is to narrate the soundest Hadith (definition) he possesses concerning a particular topic, and that the report be well-known, not odd (gharib). He does not include narrations from abandoned (matruk) narrators. If he mentions a report with severe weakness, he clarifies it. What he remains silent about (without comment) he considers acceptable for consideration.

Following these in terms of the strength of conditions is Sunan Al-Tirmidhi. His main criterion for selecting Hadiths is that they have been acted upon. He does not confine himself to mentioning only authentic reports; rather, he includes Hadiths from narrators who have some weakness, while clarifying their degree of weakness. His rank is lower than that of Sunan Al-Nasa'i and Abi Dawud due to his inclusion of Hadiths from a group of severely weak narrators.

As for Sunan Ibn Majah, no specific condition has been mentioned for it. It contains the most weak narrations among the four Sunans, and it includes fabricated (mawdu') narrations. He has narrated Hadiths from abandoned narrators whom the other authors of the four Sunans did not include.