Our Election by God is ultimately to His own Glory.
This is clear from every passage where the concept of Election is mentioned, referred to, or implied. It is for God's glory alone.
In Romans 8 and 9, Election is a display of God's glory in His love. It is a display of His glory in love because John says "we love Him because He first loved us." God's love is a previous love. He loved us first. He knew and He loved us. This is no cause for boasting though, because His love is also a merciful love. He knew us and still He loved us. This is an amazing fact, because as any Christian will tell you, there is nothing lovable about any of us. So while we were unlovable, God loved us. Before we had done anything good He loved us. And He proved that love by choosing us for Himself.
Election is also a display of God's glory in His wisdom. 1 Corinthians 1:18-31 makes this very clear. God did not choose many mighty, noble, strong, wise, beautiful, or good people, but rather, in His infinite wisdom, He chose powerless, poor, weak, ignorant, ugly, and bad people to confound the wisdom of this world. He chose the weak things to destroy the strong things. And all of this is so that no one can stand in His presence and boast of anything about themselves that caused God to choose them. Our goodness, riches, wisdom, and even our faith were not factors in His choice of the Elect. It was His own wisdom and divine prerogative that moved Him to look on us with favor. Ephesians 1:3-14 also make this clear. But look especially at verse 11.
"In him we have obtained an inheritance, having been predestined according to the purpose of him who works all things according to the counsel of his will..." (Eph 1:11)
He did this according to His own purpose because He works all things after the counsel of His own will. Nothing in me, you, or anyone else changes that. His sovereign choice is based solely in Himself.
When we look at 1 Peter however we come away with a different way God is glorified in Electing sinners to salvation.
"But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light. Once you were not a people, but now you are God's people; once you had not received mercy, but now you have received mercy. Beloved, I urge you as sojourners and exiles to abstain from the passions of the flesh, which wage war against your soul. Keep your conduct among the Gentiles honorable, so that when they speak against you as evildoers, they may see your good deeds and glorify God on the day of visitation." (1Pe 2:9-12)
God is glorified in Election by His Elect. His Elect are to proclaim the excellencies of the one who through His sovereign mercy and grace had called them out of darkness into light. And the Elect are also to live lives that call attention to God's glory. We are to proclaim His glory and live in such a way that when others see our lives as God's chosen people the result is that they glorify Him. Not that they say, "What a good person Jeremy is!" Rather that they would say, "What a God Jeremy serves!"
These two acts of giving God glory cannot be separated. If we do not speak of our God, then they will not know that God works in us to will and to do of His good pleasure. If we talk much of God but do not live lives that glorify God, then we will be seen as though we were speaking lies about our God.
There is a quote, often attributed to Saint Francis, although it is not recorded in any of his works, that says, "Preach the Gospel at all times, when necessary use words." But may I submit that words and deeds walk hand in hand and one element is not to be elevated above the other. Preach with deeds and words and God will get glory.
Soli Deo Gloria