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OK, first of all, we technically chose our nominee by the vote at the convention, by the delegates. Usually, the result will be known in advance, and it will just be a formality, but it can theoretically take multiple rounds of voting, etc., etc. Now, there are 2 types of delegates: commited and uncommited (also known as the superdelegates). The former are elected by primaries/caucuses, and are required by law to vote for the proper candidate on the first ballot in the convention. The latter are part bigwigs -- former presidents, current congressmen, governors, etc., and they can vote however they wish. The tradition is to vote w/the majority of commited delegates, though, but theoretically they can make the difference if there is no clear winner (i.e. if the convention actually matters).
The commited delegates are allocated per state as follows: one takes the fraction of electoral votes the state has, the fraction of the popular vote for the democratic nominee in the last 3 presidential elections it contributed, averages them out, and multiplies by 3000, w/some rounding. So "blue" states get a bit more power than their electoral college standing.
At the primaries, the winners are allocated delegates proportionally. Some are allocated per each congressional district, some are allocated in the state at large. In each case, the results are split for all the candidates who go over 15%. So if one candidate gets 15%, the other 30%, the first will get a third, and the second 2/3rds.
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