The Bible believing, God obeying, Spirit filled, NOT the worldly, should decide matters between believers.

Who ought not decide...

When there is a problem among or between believers, who ought not decide are such who don't know the Lord. When there is a dispute, we shouldn't ask those who are not walking in God's word and being filled with His Spirit to judge in spiritual matters. The non-spiritually alive should not be called on to judge in cases dealing with the spiritually alive (see 1 Corinthians 6:1-8).

Who, then, are the spiritually alive?

You and I both know when one believes on the name of Jesus and receives Him in truth and in sincerity, we are given the right to be the sons and daughters of God (see John 1:12). However, how can we know such a confession and reception is sincere? A sincere confession and a true reception of Jesus's life leads to a continued confession and continued reception of Jesus's life. In other words, we keep confessing and we keep surrendering so that we keep becoming like Jesus. A person who is spiritually alive is a person who is continually putting away the works of the flesh and taking up the life of the Spirit.

When there is a dispute, believers aren't to take their case before the world. They are to work it out among the transformed! They are to work the problem out among those who know what it's like to be changed by God. They are to take the case to those who are agreeing with God about what is right and wrong and who are allowing God to change their lives. They are to take the case to those who are sharing in the same inheritance as they are.

Paul said, "Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived: neither the sexually immoral, nor idolaters, nor adulterers, nor men who practice homosexuality, nor thieves, nor the greedy, nor drunkards, nor revilers, nor swindlers will inherit the kingdom of God. And such were some of you. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God." (1 Corinthians 6:9-11 ESV)

Take the case to those who it can be said "And such were some of you..." (emphasis on the WERE...changed people...people touched by God's Spirit!).

Why?
(1) Such people do not look at situations with only the reasoning of the world.
(2) Such people do not look at situations by what this person or that person wants, but by what God says.
(3) Such people know the mercy and grace of God personally.
(4) Such people are coming to grips with danger of ignoring the commands of God; there is a holy trembling among such people at the thought of facing God.
(5) Such people are seeking the leading and wisdom of the Spirit.
(6) Such people are comparing lives and situations not to human precedence but according to the person of Jesus.
(7) Actually, the list could be even longer, but the main point is that such people bring Father, Son and Holy Ghost into the discerning and deciding process.

Who ought not decide? In its notes on 1 Corinthians 6:9-10, the ESV Study Bible says those who ought not be called on to judge in the lives of believers are those "...indistinguishable from the unbelieving world..." Wow! That simplifies what I've been saying! How do you know who to invite into the assessment and reconciliation process? We invite those who we can clearly tell are walking with God and who we can clearly tell have forsaken worldliness.