Class Discussion: Are Elections legitimate?

With the upcoming election, my AP Government class has been talking more and more about the mechanisms of how elections really work. One of our debates included whether we agree with the book when it says that elections are legitimate, meaning that they are accepted as the real voice of the people and whether the theory of the mandate of the people can be truly used to make life-changing decisions.

Pros:
*Elections are a peaceful way for people to voice out their opinions, instead of rioting or performing acts of violence.
*Election is a big part of democracy; this is how we decide what the majority wants.
*We, the people, elect the delegates and the representatives that elect the president, therefore we have a hand in selecting the person that leads us.
*Making decisions by voting in general elections are our right. We decide which acts or propositions can be passed by state legislature or the houses.

Cons:
*During elections, the candidates that we choose from are the ones that were not weeded out by the primaries or caucuses, therefore we have a limited choice.
*Most voters vote using retrospective voting,meaning that we vote for the person closest to what we want because there is no candidate that entirely supports our cause of beliefs.
*Election turn outs are dismal, the number of people that actually vote is nothing compared to the total number of the population. How can it be considered the "majority?"
*The Electoral College does not fully represent the views of the people. Take the 2000 Election for example, Al Gore won the popular vote but George Bush took the presidency.

These are only a few of the arguments discussed in my group. What do you think? Are elections legitimate? Do they give the real mandate of the people to the elected candidate? What are some ways that we can improve this process?