Where do you find "family" as a unit in the Bible? As far as I can tell, neither the Hebrew nor the Greek of the Bible have a word that means "nuclear family." Two words that the NRSV does translate (sometimes) with "family" in the New Testament are γενός and πατρία.
While πατρία is translated "family" or "families" all three times in the NRSV, it refers to a group much larger than mom, dad, and children. Luke 2:4 it refers to "the family of David" all the offspring from David's time down to Joseph. Acts 3:25, quoting Genesis 12:3, refers to "all the families of the earth." Similarly, Ephesians 3:15 refers to "every family in heaven and on earth."
γενός is much more complex.
Three times it is translated "family" (Acts 4:6; 7:13; 13:26) referring to an extended family - perhaps better translated "clan".
Four times it is translated "kind."
"kind of fish" (Matthew 13:47)
"this kind" (of unclean spirit) (Mark 9:29)
"kinds of tongues" (1 Corinthians 12:10, 28)
"kinds of sounds" (1 Corinthians 14:10)
Three times with "native" (Acts 4:13; 18:2, 24)
Three times with "people" (2 Corinthians 11:26; Galatians 1:14; Philippians 3:5)
Twice with "race" (Acts 7:19; 1 Peter 2:9)
Twice with "offspring" (Acts 17:28, 29)
Once with "origin" (Mark 7:26)
Once with "descendant" (Revelation 22:11)
Neither of these words carries quite the same meaning as the English word, "family," especially as you are using it in reference to a nuclear family of mom, dad, and children.
I also don't believe that you'll find the concept of a democracy in the Bible. The biblical world was not a democratic world.
We don't read about any sort of vote at the Jerusalem Council in Acts 15. After a period of discussion, where Peter, Paul, and Barnabas, and perhaps others have their say, James declares what the church will do. In fact, he says, "I conclude …" or "I judge …" (v. 19). James made the decision for the whole church.
There is one mistake you have made. You have forgotten the Greek terms οἶκος and οἰκία to express the idea of a household, especially with respect to the family that lives there and whose head of that family is the head of that household. What does the usage of these terms (οἶκος, οἰκία) in the Bible say about whether the electoral unit of representation in the Voter Assembly of a local congregation is the individual or the family?
Again, Luther's writings in so many places plead earnestly for the right of the congregation to elect their own pastors by popular congregational vote.
"Let this passage be your sure foundation, [1Cor.14:31 because it gives such an overwhelming power to the Christian congregations to preach, to permit preaching, and to call. Especially if there is a need, it [this passage] calls everyone with a special call-without a call for men-so that we should have no doubt that THE CONGREGATION WHICH HAS THE GOSPEL MAY AND SHOULD ELECT AND CALL FROM AMONG ITS MEMBERS someone to teach the word in its place." (LW 39:311)
"The other way of sending is indeed also one by God, but it is done through the instrumentality of man. . . . Now a new way of sending was instituted, which works through man but is not of man. We were sent according to this method; according to it we ELECT AND SEND others, and we install them in their ministry to preach and to administer the Sacraments. This type of sending is also of God and commanded by God. Even though God resorts to our aid and to human agency, it is He Himself who sends laborers into His vineyard." LW22:482
"Let this passage be your sure foundation, [1Cor.14:31] because it gives such an overwhelming power to the Christian congregations to preach, to permit preaching, and to call. Especially if there is a need, it [this passage] calls everyone with a special call-without a call from men-so that we should have no doubt that the congregation which has the gospel may and SHOULD ELECT AND CALL from among its members someone to teach the word in its place." LW39:311
"Neither Titus nor Timothy nor Paul ever instituted a priest without the CONGREGATION'S ELECTION AND CALL." LW39:312
"Moreover, if there were really decent bishops who want to have the gospel and wanted to institute decent preachers, they still could not and should not do so without the will, THE ELECTION, AND CALL OF THE CONGREGATION-except in those cases where need made it necessary so that souls would not perish for lack of the divine word." LW39:312
"Again, we even read in Acts 4 [6:1-6] regarding an even lesser office, that the apostles were not permitted to institute a person as deacon without the knowledge and consent of the congregation. Rather, THE CONGREGATION ELECTED AND CALLED the seven deacons, and the apostles confirmed them." LW39:312
"But the community rights demand that one, or as many as the COMMUNITY CHOOSES, shall be chosen or approved who, in the name of all with these rights, shall perform these functions publicly." LW40:34
"How much more, then, does not a certain community as a whole have both right and command to commit BY COMMON VOTE such an office to one or more, to be exercised in its stead. With the approval of the community these might then delegate the office to others." LW40:36
". . . then it but remains either to let the church perish without the Word or to let those who come together CAST THEIR BALLOTS and elect one or as many as are needed of those who are capable." [2Tim. 2; Acts 18: 24ff; 1Cor.14: 30; Ti.1: 6ff.] LW40:37