If God would elect some for salvation, it follows both logically and theologically that He would be electing others for damnation. But since the offer of eternal life is to "whosoever will" it should be crystal clear that God elects no one for salvation. Rather He offers salvation to all of humanity, since all have sinned and come short of the glory of God, and there is none righteous, no, not one.
As to whether sinners "decide" to respond to the Gospel, it is perfectly clear from Scripture that it is a decision involving repentance toward God and faith toward our Lord Jesus Christ. This is confirmed in Acts 2.
37 Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do?
38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
39 For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.
40 And with many other words did he testify and exhort, saying, Save yourselves from this untoward generation.
41 Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls.
The question "What shall we do?" confirms that sinners must do something. And about 3,000 people responded to the Gospel that day and were baptized the same day.