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(Note also that Peter is exercising his infallible interpretation of scripture here. No one objects to Peter's unilateral exercise of authority.)

Except God!

Note that the Apostles cast lots to see who would be "chosen". Note also that this is before Pentecost. Note also that it is Jesus who a few chapters later Regenerates Saul to be his Apostle.

Paul, a servant of Jesus Christ, called to be an apostle and separated unto the Gospel of God,
1 Corinthians 1 Paul, called to be an apostle of Jesus Christ through the will of God, and Sosthenes our brother,
2 Corinthians 1 Paul, an apostle of Jesus Christ by the will of God, and Timothy our brother, Unto the church of God which is at Corinth, with all the saints who are in all Achaia:
Galatians 1 Paul, an apostle (not of men, neither by man, but by Jesus Christ and God the Father, who raised Him from the dead),
Ephesians 1 Paul, an apostle of Jesus Christ by the will of God, To the saints who are at Ephesus, and to the faithful in Christ Jesus:
Colossians 1 Paul, an apostle of Jesus Christ by the will of God, and Timothy our brother,
1 Timothy 1 Paul, an apostle of Jesus Christ by the commandment of God our Savior, and Lord Jesus Christ, who is our hope,
2 Timothy 1 Paul, an apostle of Jesus Christ by the will of God, according to the promise of life which is in Christ Jesus,
Titus 1 Paul, a servant of God and an apostle of Jesus Christ, according to the faith of God's elect, and the acknowledging of the truth which is according to godliness,

And they cast their lots, and the lot fell upon Matthias; and he was numbered with the eleven apostles. Word search on the Apostle Matthias: 0. Seems like God had something different in mind than casting lots; namely Paul, an apostle (not of men, neither by man, but by Jesus Christ and God the Father...).