two functions of eidus

Last week we discussed the principle of "lo te'hey shemiya gedolah m'reiya," i.e. dayanim who witnesses an event can pasken on the basis of their observations without hearing testimony. For example (R"H 25), three dayanim who see the new moon can declare rosh chodesh without other witnesses having to come forward and say that they saw the moon.

The Rashba (B"K 90) writes that although a single judge who is a mumche (expert) is allowed to pasken alone, the principle of "lo te'hey shemiya gedolah m'reiya" does not apply to him. Question: if the observation of a dayan serves as its own evidence and proof, why can one judge not pasken on that basis but three can?

The Ketzos (7:5) explains that a single judge who observes an event is not more authoritative than any other single witness. Since a ba'al din can contradict an eid echad and get off by just taking a shevua, the ba'al din can also contradict the judge serving as his own eid echad and is therefore never bound by the final psak.

R' Shimon Shkop (Sha’arei Yosher 7:1) explains the Rashba differently. He writes that witnesses serve a dual function: 1) they clarify the facts of the case before the court; 2) their testimony empowers the court to act. While a single judge’s observation is sufficient to allow him to decide who is chayav and who is patur, it is only “al pi shenayim eidim yakim davar,” only two witnesses which can empower the court with the authority to mete our punishment or to compel one of the parties to pay.

A final question for thought: the halacha is that "ain eid na'asah dayan," i.e. a witness can not serve as a judge on the same case he is testifying in. How then does "lo te'hey shemiya gedolah m'reiya" work? How can people who observe an event simultaneously serve as judges and witnesses? Is this a klutz kashe or something to think about?