mormons do not elect their leaders. this is how it goes.
every mormon should have a basic testimony that joseph smith was a prophet of god through whom god restored his church which had apostized to the point that it had to be restored, not reformed. god restored the priesthood in him, the same priesthood that paul and all the other apostles held. joseph then appointed apostles the same as christ did. when joseph died, god chose (and chooses apparently) the next prophet from among the apostles. all is done by direct revelation from god. every mormon believes that this has led over time to the current prophet. they believe in him because he was (and is) chosen by god to lead the church. he chooses apostles when they die, and other high church authorities when needed to govern the church, by inspiration from heavenly father.
these other governing authorities then choose area authorities by inspiration, and area authorities choose district authorities and they choose church authorities, all by inspiration. the members are not expected to believe that any of them are perfect, or that the decisions are perfect. they only are expected to support their leaders, and to accept calls made to them when they can.
it is important to remember that none of these people recieve ANY MONETARY REIMBURSMENT for serviice they perform.
the members of individual congregations are asked for a sustaining vote on callings rendered. one or two hands in dissent are plenty to throw back a calling if they are backed up by information that would not allow someone to take the calling. for example, i knew once a woman who dissented to a man being called to a position because they were having an affair and he was unworthy to hold the position.
in many cases the calling does not seem right. maybe a woman who does not have children and has less than a cheery disposition is asked to work with children. some parents may not even want her around their children. but in many cases, such as this, the person may not be right for the calling, but the calling is right for the person. the calling is so that the person will learn and grow from it. this lady may learn to love children because she fulfilled the calling to the best of her ability.
as i said, mormons are only asked to support and trust the authorities in what callings they ask memebers to do, they do not vote on them and decide for themselves.