Three Facts About the Doctrine of Election.

1.  You can know if someone else is elect.  1 Thessalonians 1:5-10.

• The person receives the gospel. 1:5.
• The person begins imitating the Lord. 1:6.
• The person openly confesses Christ. 1:8.
• The person turns from their false religion to God and Christ. 1:9-10.
• But this knowledge is only after-the-fact. You cannot know if someone is elect prior to their trusting in Christ.

2.  Election is not beyond comprehension.  2 Thessalonians 2:13-14.

• Election is a cause for thanksgiving.
• Election expresses God's love.
• God initiates the choosing.
• God chose before anything or anyone existed.
• God chose actual people.
• Election is unto salvation. 
• Election takes effect through the sanctifying influences of the Holy Spirit, and the person's response of faith.

3.  Election has two objectives, or effects.  1 Peter 1:1-2.

• God intends the chose person to live a life of obedience to Jesus Christ.
• God intends to remit the person's sins, through the merit of Christ's blood, received by faith.   

My opinion is that Romans 9 does not teach unconditional election. This puts me at odds with traditional Reformed-Calvinist thinkers. Here are some reasons for my opinion.

1. The Jacob & Esau example (9:10-13) isn't an allegory of salvation. Paul was reinforcing his case that Jews have no bloodline title to God's favor. God chose to give Jacob a privilege, even as God was giving Gentiles the privilege to be saved. Being physically born of Abraham did not gain a Jew the free gifts of God.
2. God is free to show mercy to whomever He wishes (9:15). He gave a free gift to Moses (a vision of His glory), but judged Pharaoh. But this doesn't mean that God's mercy is disconnected from human response. God showed mercy to Nineveh because 120,000 of their citizens were ignorant -- probably children (Jonah 4:11). God showed Paul saving mercy, similarly, because he was sinning ignorantly (1 Timothy 1:12-13). Sinning ignorantly is a condition. God told Jeremiah that He would show mercy to pagan nations if they repented (Jeremiah 18:7-8), and He would punish Israel if they did not. Repentance and rebellion are conditions. God hardened the hearts of the Pharisees, not because they were irresistibly preordained by God to sin, but because they sinned against their knowledge of the Gospel knowingly and willfully (John 12:36-40). 
3. Paul rebukes theological fatalism. Paul, in Romans 9:20, quotes Isaiah 29; so you must look back at the original quotation. The pot made by the potter in Isaiah 29:15-16 is not a member of the "non-elect." The pot of Isaiah 29 is a wicked person who deeply hides his plans from the Lord, whose evil deeds are done in dark places, and who says to himself, "Who sees us? Who knows us?" So, Paul is not saying that the person's objection against being blamed is correct but "how dare the person complain." Paul rebukes the imaginary person for blaming his sins on God's sovereignty at all. That is nothing but a twisted, false doctrine, used to give rebellious back-talk to God. Paul is slapping down anyone who teaches that God irresistibly foreordained their sins.
4. Paul's final conclusion is not that "the elect obtain saving righteousness because God unconditionally chose them." He never says that. Paul's conclusion is that Gentiles were obtaining saving righteousness by faith, and Jews, who  were pursuing righteousness by works, all failing to attain it (9:30-31). That's the bottom-line of Romans 9. 
5. Finally, in Romans 10:1, Paul prays for the salvation of every Jew without exception. This shows that Paul believed every Israelite, without exception, could possibly be won to the Lord.  And that prayer reflects backward into Romans 9. Paul doesn't know who the elect are. But that fact is irrelevant. Paul's prayer is a revelation of what's possible. If Paul believed that God by an eternal decree had rendered some unspecified section of Israel into a state of irresistible and irreversible unbelief, he would not have prayed for all Israel to be saved. God does not have us pray for the metaphysically impossible -- for example, we don't pray for God to let the people in Hell go free. We know from Scripture that cannot possibly happen. By the same reasoning, Paul prayed for all Israel to be saved because none of Israel had been eternally reprobated.