Josiah gave some good reasons why Mitt Romney was selected as the Republican party's nominee, but there is a good chance that Romney was selected simply because the system is designed to select someone and Romney was essentially an arbitrary choice. Hard to believe? Maybe not, because in any system of voting there is a measure of arbitrariness. Here's an example.
Voter First Preference Second Preference Third Preference
Voter 1 A B C
Voter 2 C A B
Voter 3 B C A
In this case, if the voters vote on their options in pairs, they can get a winner. Between A and B, A will win and move on. Between A and C, C wins. So, clearly since everyone voted on it, C is the will of the people. But what if they changed the order of the voting. If they vote between A and C first, C wins but loses to B. So, is B the will of the people? The important factor in this system is not the desires of the voters, but the order of voting. This particular example is known as Condorcet's paradox.
This example was very simple, but unfortunately the fundamental problem doesn't go away when you add more voters. That was proven mathematically by economist Kenneth Arrow. In his impossibility theorem, Arrow showed with the certainty of mathematics, that there is no possible voting system that always satisfies the following principles:
1. If everyone prefers X to Y, the group prefers X to Y
2. If everyone's preference of X to Y doesn't change, the groups preference of X to Y doesn't change.
3. There is no dictator (no one person always decides the outcome)
Every system though has to have a winner, so voting systems sometimes return results that contradict principle 1 or 2. What becomes important quite often, is the order of voting. This is a real problem when selecting nominees from a group of several candidates.
What are the implications of this? Perhaps Mitt Romney's nomination does not represent any sort of "choice" by voters, but is actually just an artifact of a flawed system. Beyond the Republicans, with this knowledge, can we really say with certainty that in 2008 the majority of Americans preferred Obama to Hillary Clinton for president, or was that just a product of our particular system? Can an elected politician really claim a "mandate" if there is a real chance that he was just the beneficiary of a flawed system?
To be clear, I am not saying that all elections are illegitimate. Sometimes our voting systems satisfy the three principles, just not always and they are most likely to fail when the elections are tightest. Sometimes, the "will of the people" is not reflected in the outcome of an election and sometimes "the will of the people" does not exist. Sometimes voting is like shaking a magic 8-ball; you'll always get an answer, but it may be nonsense and should be treated as such.