My understanding is Mormons hold to something similar to libertarian free will, the belief that a person’s choices are free from the determination or constraints of human nature and free from any predetermination by God.
Since I don’t understand the position very well, perhaps a brief explanation of the view would be helpful to me, but primarily this question is concerned with what case can be made for the LDS view from Scripture (whether the Bible or other LDS Scriptures).
The LDS church does not teach predestination.
To Latter-day Saints, the idea of predestination is unscriptural. Not only does it deny what Paul and other prophets taught about agency, but it also limits God’s love to only a select few. Elder Joseph Fielding Smith stated emphatically that “no person is ever predestined to salvation or damnation. Every person has free agency.” Similarly, the Book of Mormon prophet Jacob taught that “one being is as precious in [God’s] sight as the other.” (Jacob 2:21.)
The LDS church teaches about foreordination.
Foreordination is thus different from predestination. There is no divine compulsion to ensure that a person who is foreordained to a particular calling will fulfill his or her tasks.
So why does the church teach foreordination and not predestination. Predestination removes from us responsibility and agency. If a person is predestined to become a minister or sorts, nothing will stop that even if they blatantly disobey God's commands. One could be foreordained to be a minister and live in a way that is not condusive to that calling and never become a minister. Agency is central to the doctrine of God.
Agency is the ability and privilege God gives us to choose and to act for ourselves. Agency is essential in the plan of salvation. Without agency, we would not be able to learn or progress or follow the Savior. With it, we are “free to choose liberty and eternal life, through the great Mediator of all men, or to choose captivity and death, according to the captivity and power of the devil” ( 2 Nephi 2:27).
If you read the last bullet point under sources, that will give you a solid understanding of what The Church of Jesus Christ of Latter-day Saints believe concerning predestination and foreordination.
Sources
