Both systems seek to solve a simple problem with the system that the United States (and most nations) currently use, which is called Plurality Voting (PV). That problem is that PV forces voters into two opposed camps, each camp taking one candidate as their "champion". This results in what often turns out to be a maximum of unhappy voters. For example, if you place people's views on a scale from 1 to 10 with 1 being the most liberal and 10 being the most conservative, PV tends to foster candidates that fall around the 2-4 and 7-9 range However, if your goal is to elect someone who represents the majority of Americans, it would certainly make much more sense to elect someone that falls into the 4-7 range and let the end-points tug that center-line back and forth. The problem is that centrists are essentially blocked out of PV systems because they are seen as "spoilers" for the extremes.
