What is a brokered convention?A candidate must secure a majority - not just a plurality - of votes prior to the convention. If a candidate has not secured a majority of votes prior to the convention, then there will be a first ballot at the convention. Delegates must vote to their pledged candidate on the first ballot. If after the first ballot, there is still no majority, then the convention becomes brokered. At this time, the delegates are released from their pledges and the deal making begins.
The last GOP brokered convention was in 1948. The last Democratic brokered convention was in 1952.
Before primaries became the norm, brokered conventions happened often.
Once primaries, with their winner-take-all formula became the norm, brokered conventions went away.
The Democratic party did away with winner-take-all primaries in 2008, forcing all states to have proportional primaries.
In the case of the Republicans, they have both winner-take-all and proportional primaries.
In the 2016, the proportional primaries will be held first. Then the winner-take-all primaries will be held. Those will be the larger states in number of delegates.
Winner-take-all vs proportional2016 Republican Primaries: How Delegates Will be Awarded