Miles, in the Bible the elect will often refer to israel. Elect just means 'chosen'.
Calvinists will try and push wacky theories about who the elect is. But its quite clear in the Bible God chose Abraham and his descendants Isaac and Jacob to make a covenant with. From which comes the seed of Christ i.e Jesus, and all who believe in Him. So if we believe in Jesus we are chosen in Him.
God did not choose the children of Israel because they were stronger or mightier than anyone else, but because He loved them. He wanted to make a holy nation out of them, a light to the gentiles. JEsus is king of this nation, but when his own family rejected him, he offered salvation to the gentiles i.e people not born from Israel in the flesh..that is why everyone must be born again. We become adopted into Israel.
When God adopts someone, He chooses first. A adoptee cant choose their parents - its the parents who choose the child. But He had already chosen Israel as His firstborn, and Jesus as the firstfruit of many. When we believe in Jesus we become co-heirs. Because God has already chosen Jesus as his only BEGOTTEN firstborn son (he knew even before Jesus was born) Jesus is elect.
In the letter to ephesians, Paul talks about the apostles being elect, because Jesus chose them. They also chose to follow Him...they could have turned away, they had free will. But Jesus chose them first. They didnt put up their hands when Jesus walked by..Jesus hand picked them and called them to 'follow me'. And they did.