On what basis is the Jewish remnant chosen?
The Jewish remnant is chosen on the basis of election by grace, not law and not Judaism. Paul explains that in this present age of grace, a small percentage of Jews become believers of the gospel of grace, and they constitute a remnant according to the election of grace.
Les teaches that Scripture contains a doctrine of the remnant, and God has always kept a remnant. In Christ's earthly ministry this is pictured by the broad way and the narrow way: the mass of humanity goes the broad way, but the remnant takes the narrow way. Paul says that in this age of grace, which is predominantly Gentile with some Jewish exceptions, there is still a remnant—a small percentage of Jews who have become believers of the gospel of grace. They are a remnant according to the election, not of law, not of Judaism, but of grace. Les also notes testimonies of Jews from many backgrounds who came to believe Jesus of Nazareth was the Messiah who died for their sins. As Elijah was shown 7,000 who had not fallen to idolatry, so today there is a remnant of Jews who recognize the gospel of grace and the election of grace.
Even so then at this present time also there is a remnant according to the election of grace.