Hey, some actual contextual analysis. Congratulations, you're on your way. Except you're still reading it backwards and beginning with what you understand election to be speaking of, and ignoring the larger point which Paul is speaking to which is answering challengers who say because God changed the plan from the nation of Israel He failed because Israel failed. Paul is demonstrating that the whole process was God's purpose in election, the remnant that persisted stood in achieving what Israel was intended to achieve. The word "elect" has many meanings, and Paul uses it in a couple of different senses across his writings. Who is God's elect? Jesus Christ, who by faith achieved what Israel was chosen to achieve. Paul has a single point throughout Romans and doesn't deviate from it, throughout revealing how God's purposes are fulfilled in Jesus first through the law itself proceeding from how nature condemns men, proceeding to the revelation of the law to bring consciousness of sin, finally ending with Jesus as the fulfillment of the law then through Jesus as the representation of Israel, beginning with highlighting how God's plan for Israel from the beginning was to show mercy to the whole world, then revealing how Israel did not fail but succeeded in God's election of Jesus Christ.
If you would draw your word meanings based on their immediate context you would understand these things, but instead you begin with a definition and then distort the writing to fit that definition.
