An umpire or arbiter or judge (Job 9:33). This word is formed from the Latin diem dicere, i.e., to fix a day for hearing a cause. Such an one is empowered by mutual consent to decide the cause, and to "lay his hand", i.e., to impose his authority, on both, and enforce his sentence.
These dictionary topics are from M.G. Easton M.A., D.D., Illustrated Bible Dictionary, Third Edition, published by Thomas Nelson, 1897. Public Domain, copy freely.
Easton, Matthew George. "Entry for 'Daysman'". "Easton's Bible Dictionary".