NT Greek in Plato's Cratylus: Ananke and Hekousion

Socrates: .. But I still want to investigate 'ananke' (compulsion), and 'hekousion' (voluntary), since they are next. The name 'hekousion' expresses the fact that it signifies yielding and not resisting, but yielding, as I said before, to the motion (eikon toi ionti)—the one that comes into being in accord with our wish. ‘Anankaion’ (compulsory) and ‘antitupnon’ (resistant), on the other hand since they signify motion contrary to our wish, are associated with ‘error’ and ‘ignorance.’ (Cratylus, 420d-e)

Plato defines ‘ananke’ as something that is contrary to our wishes, and ‘hekousion’ as something that yields, instead of resisting. 

Paul uses these two words in his letter to Philemon:

Whom I would have retained with me, that in thy stead he might have ministered unto me in the bonds of the gospel: But without thy mind would I do nothing; that thy benefit should not be as it were of necessity (‘ananke’), but willingly (‘hekousion’) (Philem 13-14, KJV).

What is it that Paul wants Philemon to do willingly? He is asking him to take back his former slave, Onesimus; not as a slave, but as a beloved brother.

Therefore, although in Christ I could be bold and order you to do what you ought to do, yet I appeal to you on the basis of love. I then, as Paul-an old man and now also a prisoner of Christ Jesus- I appeal to you for my son Onesimus, who became my son while I was in chains. Formerly he was useless to you, but now he has become useful both to you and to me. I am sending him-who is my very heart-back to you. I would have liked to keep him with me so that he could take your place in helping me while I am in chains for the gospel. But I did not want to do anything without your consent, so that any favor you do will be spontaneous and not forced. Perhaps the reason he was separated from you for a little while was that you might have him back for good- no longer as a slave, but better than a slave, as a dear brother. He is very dear to me but even dearer to you, both as a man and as a brother in the Lord (Philem 8-16, NIV).

Paul says he could order ('epitasso') Philemon to do the right thing, but instead of ordering him, Paul appeals to him for love's sake. Love does not force, it waits for others to act.

Had Paul ordered Philemon to receive Onesimus the way he would've received Paul, Philemon would not have been able to consent, and without his consent, his obedience would be forced, instead of willing. Paul says he has confidence that Philemon will obey, and do even more than he has asked, because of love.

Two things become evident from this.

1) Slaves were considered to be brothers in the Lord
2) Willing obedience is better than forced obedience 

This points to mutual submission of all believers, for if love compels us to consider the interests of others, and let others join in the decision making in matters that concern them, there can be no hierarchy in which some force others to obey without allowing for willing obedience.
 
Authority in the church is given only for one reason: to build others up in their faith (2 Cor 10:8). It is not given in order to allow some make all the decisions.

Because authority in the church is given to build others up, we ought to seek to please others instead of only ourselves (Rom 15:2). If we ought to please others we cannot force others to obey us against their consent.

Yet, mutual submission means also that we stop being difficult. We shouldn't resist those who seek to please us, instead we should be easily entreated, and considerate (Jas 3:17). We should be willing to obey.

And because authority is given to build others up in the church, those who have authority serve as slaves.

1 Cor 9:19-23 Though I am free and belong to no man, I make myself a slave to everyone, to win as many as possible. To the Jews I became like a Jew, to win the Jews. To those under the law I became like one under the law (though I myself am not under the law), so as to win those under the law. To those not having the law I became like one not having the law (though I am not free from God's law but am under Christ's law), so as to win those not having the law. To the weak I became weak, to win the weak. I have become all things to all men so that by all possible means I might save some. I do all this for the sake of the gospel, that I may share in its blessings (NIV).

When all serve one another in love, mutual submission isn't only an ideal, it is a reality (Gal 5:13).