The ESV Study Bible note on Gen 9:9-11 (p. 65) embodies the perspective that underlies the concept of corporate election: “A covenant formally binds two parties together in a relationship, on the basis of mutual personal commitment, with consequences for keeping or breaking the commitment. God makes this kind of covenant with a group of people by covenanting with one who represents them: everyone else then experiences the covenant by virtue of being included ‘in’ the representative.”
Corporate election simply recognizes that Jesus is the seed of Abraham and the head of the covenant people of God, taking his place in the line of Abraham, Isaac, and Jacob, and that people experience the New Covenant by virtue of being included “in Christ.” This supports Arminian theology, specifically, conditional election, because inclusion in Christ is conditioned on faith in Christ.
The ESV Study Bible note on Luke 11:4 (p. 1978) also takes a corporate perspective:
“The use of the second person plural (‘us’) throughout emphasizes that the petitions of ‘The Disciples’ Prayer’ are not primarily for the individual but for the entire community of believers.”
Obviously, the prayers do apply to the individual. But as the note says, these are for the community primarily. The implication would then be that they are for the individual believer secondarily, by virtue of his membership in the community. The same is true of election unto salvation in the New Testament. Passages that speak of election typically use plural language. It is the Church as a community that is elect primarily, and individual believers are elect secondarily, as members of the elect community. To use an example of the second person plural “us” like the ESV Study Bible note, when Ephesians 1:4 say that God chose us in Christ, it means that he chose the Church primarily, and individual believers secondarily as members of the elect community.