Acts 1

Luke records the process that the early apostles used to select a new apostle to provide a full quorum of twelve apostles with the falling away of Judas Iscariot. Peter taking the lead, obvious as the leader or president of the twelve taught -

"...and his bishoprick let another take..." (New Testament | Acts 1:20)

...or his calling or position, let another fill. And obviously after some discussion two were nominated for -

"...they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias." (New Testament | Acts 1:23)

And with a desire that the Lord's will be manifest -

"...they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen,
25 That he may take part of this ministry and apostleship..." (New Testament | Acts 1:24 - 25)

And Luke then records (I wonder if he was actually present) -

"...they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles." (New Testament | Acts 1:26)

At first, one might think that they drew straws so to speak or even cast their ballot. But I have wondered if things may have not been like that at all. In referencing the dictionary, one of the definitions for "lot" is -

"...the resulting choice" even -

"...something that comes to one upon whom a lot has fallen..." (Merriam-Webster)

It would seem more logical to me that after much prayer, Peter stood with and inspired choice that the lot was to befall Mathias. In turn, being inspired, the twelve also cast their unanimous sustaining vote or choice that this lot should also fall on Mathias. And in this manner was Matthais called and numbered amoung the eleven. This would seem to be the order that Luke was recording.