Peter and the other ten apostles had searched the Scriptures and found God’s words concerning the vacancy that the death of Judas Iscariot had left in their circle.   (Acts 1:20)
  What was their conclusion?   

  Peter stood in the midst of the gathered men and women and said:
(NASB) Acts 1:21-26 “‘Therefore it is necessary that of the men who have accompanied us all the time that the Lord Jesus went in and out among us –
22 beginning with the baptism of John until the day that He was taken up from us – one of these must become a witness with us of His resurrection.’
23 So they put forward two men, Joseph called Barsabbas (who was also called Justus), and Matthias.
24 And they prayed and said, ‘You, Lord, who know the hearts of all men, show which one of these two You have chosen
25 to occupy this ministry and apostleship from which Judas turned aside to go to his own place.’
26 And they drew lots for them, and the lot fell to Matthias; and he was added to the eleven apostles.” 

From man’s point of view, they thought the requirements of God were: 
a man who loved the Lord Jesus and chose to obey His words
a reasonable conclusion
a logical choice
one that fit the criteria of the eleven men’s own experience. 

  What criteria did the eleven establish out of their own experience?
1- two men who had followed Jesus from the beginning of His ministry and ended with the ascension of Jesus into heaven
2- both men had been eye-witnesses of the resurrection of Jesus 

  How was Matthias chosen?
1- through prayer – they asked the Lord who He had chosen
2- lots were drawn and the lot fell to Matthias
3- Matthias was then added to this circle of apostles 

  How did God respond to this decision?
I believe God accepted the decision and continued with His own plans without demeaning Matthias.  God was gracious to the eleven and to Matthias.
  Later in the book of Acts we will ‘see’ that the Lord Jesus chose Saul (changing his name to Paul) and called him to be an apostle.  (Acts 9:1-19) 

  Graciousness of God can also be thought of as kindness, benevolence of God. 

  The followers of Christ are to be encouraged because:
  The graciousness of God continues to work in the lives of His followers for His glory.