Don Johnson

On 2, lots may be votes or they might be random, it is not clear.  Even if random the lot is in the hands of the Lord as they were acting in faith.

Rev 21:14

And the wall of the city had twelve foundations, and on them were the twelve names of the twelve apostles of the Lamb.

Here we see there were 12 and only 12 names of the 12 apostles of the Lamb.  We both agree Judas is not there.  John wrote Rev around 90-100, in other words after the events in Acts, where Matthias was chosen.  Who would anyone think was the 12th apostle?  Before one might think Paul was the 12th you need to knock Matthias out of the running.  The question does not even come up if Matthias is the 12th.

Mat 28:16

But the eleven disciples went to Galilee, to the mountain which Jesus appointed [or, designated] to them.

Mat 28:17

And having seen Him, they prostrated themselves in worship before Him, but some were doubtful.
Mat 28:18

Mat 28:19

“When you* have gone, make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,

Mat 28:20

teaching them to be observing all [things], as many as I commanded you*. And listen! _I_ am with you* all the days, until the conclusion of the age! So be it!” [Gr. amen, and throughout NT].

And having approached, Jesus spoke to them, saying, “All authority in heaven and on earth was given to Me.
Here Jesus promised to be with the 11 (the you is plural) always.  Here is one reason I claim the 11 acting as the 11 COULD NOT make a mistake in choosing Matthias.

On the authority to do so, there is the bind and loose verse.
Mat 18:18

“Positively, I say to you*, whatever [things] you* bind on the earth will have been bound in heaven, and whatever [things] you* loose on the earth will have been loosed in heaven.

This is using rabbinic terms to say that they (you plural again) can make decisions on things that have not already been decided.  They use this authority in Acts 15 and I claim they also use this authority in choosing Matthias.