Is it scripturally correct for elders to choose another elder and have him installed by an outside evangelist? The process I'm speaking of was one where two elders announced to a group of the members that the elders would be "selecting" the new elder(s) and deacon(s). Shouldn't the "selection process" be left up to the congregation as it was in Acts 6 with the deacons? Seeing as how the elders are definitely part of the congregation, they will obviously have a say in the selection; however, should their input be the only real say in the matter? The elders initially recanted and said they misspoke when they said that "they would be doing the selecting." Then later on in further discussion, they claimed that they had the right to do the selecting. Thanks for your insight in this matter. (I should add that surveys were sent out to "selected families" about who should be an elder, but I'm afraid they were only given tacit consideration.)
When looking to establish God's will on a matter, we must look to see what has been directly commanded, shown by example to be approved, and implied by an inescapable conclusion. In a prior question, "Who appoints elders?" it was shown that you first had to have men who aspired to serve as elders and who have stretched themselves to show they meet the qualifications listed for an elder.
Using the example of the selection of deacons found in Acts 6, we see that the current leadership of the church -- the apostles, did not chose the deacons, but gave the qualifications to the church and asked the church to select men who met those qualifications. The apostles then appointed those selected men to their duties.
We don't find a direct reference to the church selecting elders. We do find the list of qualifications given to preachers in I Timothy 3 and Titus 1. And, we find that preachers appointed elders (Acts 14:23; Titus 1:5). But the step in between, the actual selection of the men to be appointed is not mentioned.
Lacking additional direction, we must assume the selection of elders was done in a similar manner to the selection of deacons. The church is taught what to look for in man considered for the eldership and the church then offers up men for appointment by the preacher.
Since Paul warned Timothy, "Do not lay hands on anyone hastily, nor share in other people's sins; keep yourself pure" (I Timothy 5:22), we conclude that the preacher is not to blindly give approval to whoever is selected, but must double check that the man mets the qualifications laid down by the Holy Spirit.
I find no indication that elders selected additional elders or elders selected deacons. Rather there is an implication in Acts 6:2-4 that it was not for the leadership to do the selection. As leaders in a congregation, it would be the elders' responsibility to help guide the congregation toward finding qualified men. Their wisdom ought to carry weight with the congregation; however, the congregation as a whole must find men to whom they are willing to submit (I Peter 5:5).
I think much of the problem you are seeing stems from a prevalent view that the elders not only represent the congregation but are the congregation. Such is not taught in the Bible. Elders oversee a congregation (Hebrews 13:7, 17). Their rule is by shepherding or guiding the congregation into making correct decisions. For a eldership to decide for a church is to violate what Peter stated, "Shepherd the flock of God which is among you, serving as overseers, not by compulsion but willingly, not for dishonest gain but eagerly; nor as being lords over those entrusted to you, but being examples to the flock" (I Peter 5:2-3). They cannot be be lords (those who exercise dominion) over the church.