Saved not by works but by work?

8 For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, 9 not a result of works, so that no one may boast.  Ephesians 2:8-9

Suppose you agree with me that we are saved by grace through faith and not by works.  Now suppose you make the decision to follow Christ and that decision results in authentic faith that saves you.  Could you not then argue "I was not saved by my works but by my work of deciding"?  In other words, while Christ's death on the cross made you saveable, it was your decision to believe that actually saved you.  (I'm speaking hypothetically)  And if you can claim that, is that not something you could boast about?  How then is salvation "not a result of works, so that no one may boast" as Ephesians 2:9 says it is?

My point being, if our salvation is conditional on a choice (or even God's foreknowledge of a choice we would have made) and not on God's election then we are ultimately saved by our own volition.  However, if our salvation is conditional on God's election irrespective of anything we do or choice we make (though if elected you will respond to the call of the gospel with belief) then we are saved by God alone "and this is not [our] own doing".

The Spirit gives life; the flesh counts for nothing. The words I have spoken to you—they are full of the Spirit and life.  John 6:63

The person without the Spirit does not accept the things that come from the Spirit of God but considers them foolishness, and cannot understand them because they are discerned only through the Spirit.  1 Corinthians 2:14