the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
Ibn al-Qayyim says in I`lâm al-Muwaqq`în (1/21): "The third principle of Ahmad’s school of thought is: “If the Companions disagree on an issue, we should select what is closer to Qur’ân and Sunnah. We may not neglect their sayings. If we cannot give preference to one of their sayings by way of the Qur’ân or Sunnah, we declare: It is a matter of disagreement and we do not know which one is the right opinion."
If the Companions disagree, the strongest opinion will be chosen. It is the one which is best supported by the Qur’ân, Sunnah, juristic analogy, some other evidence, the general objectives of Islamic Law, or any other means of making a determination of preference.
If a determination cannot be made in this way, then the opinion of the Rightly Guided Caliphs will take precedence over the saying of others.
Preference will thereafter be given to Abû Bakr and `Umar together, then to `Umar, then to those praised by the Prophet (peace be upon thme) for their knowledge. Otherwise, it will remain a matter of disagreement.
And Allah knows best.
Source: Islam Today