Before Tuesday's debate -- best described as a political circus with the moderators all but losing control -- I identified four main questions that needed to be answered. And to the extent these contests matter now that Americans are actually voting, they may have a bearing on what is to come.

The first is a simple matter of arithmetic -- mainly subtraction. Now that there are actual votes and delegates distributed, how do the candidates who do not have a particularly good night and who lagged behind in Iowa, New Hampshire and Nevada justify staying in race? Tom Steyer and Mike Bloomberg have deep pockets and can ride it out even though their road may lead nowhere. But what about Amy Klobuchar and Elizabeth Warren, and even Pete Buttigieg? They all had strong performances, but will they have any momentum coming out of South Carolina and into Super Tuesday?

Aaron David Miller
Aaron David Miller is a senior fellow at the Carnegie Endowment for International Peace, focusing on U.S. foreign policy.
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Second, what kind of night did Bloomberg have? Not bad compared to his last performance. He did make a compelling point on the logic of electability and scored points on his record in New York City. (Nonetheless, Warren came for him a second time.) But Bloomberg just doesn't project empathy, his rhetorical skills are terrible, he has no sense of humor and his efforts to bond and relate on a personal level largely fall flat.

Third, did Joe Biden have the much-needed debate of his life? Not exactly. But his interventions were strong and confident. He projected strength, experience and comfort being on the debate stage in a way we have not seen before.

Fourth, and perhaps most important, was Bernie Sanders hurt? He was hammered -- and was hit hard especially by Buttigieg and Warren. But he survived. The attacks on Bloomberg deflected much of the heat. Where Sanders disappointed was his failure to explain what his democratic socialism really means -- and to separate it from his past positive comments on Cuba and Nicaragua.

This article was originally published by CNN.