To Lay Hands or Not to Lay Hands?

Yosi ben Yoezer says: One should not lay their hands; Yosi ben Yoḥanan says: One should lay their hands.

Joshua ben Peraḥya says: One should not lay their hands; Nitai ha-Arbeli says: One should lay their hands.

Judah ben Tabbai says: One should not lay their hands; Simeon ben Shetaḥ says: One should lay their hands.

Shemaiah says: One should lay their hands; Avtalyon says: One should not lay their hands.

Hillel and Menaḥem did not disagree [on the matter]. Menaḥem left and Shammai entered. Shammai says: One should not lay their hands; Hillel says: One should lay their hands. The first [of each of these pairs] were patriarchs and the second [of each of these pairs] were heads of the court.