Mr. Trump’s arsenal was far more fearsome. Combining modern-day fame and an age-old demagogy, he bypassed the ossified gatekeepers and appealed directly to voters through a constant Twitter stream that seemed interrupted only by television appearances.

In doing so, he seemed to grasp that a new twist on direct democracy was in the offing: that disaffected voters who tune out the traditional modes of political communication might be reachable through their smartphones, and Twitter messages or Reddits might be more relevant to those voters than the findings of a more scientific poll.

On the left, too, Senator Bernie Sanders has built his own movement with millions of voters, and $210 million in fund-raising, by using online tools as simple as email to seek support. Yet Mr. Trump’s celebrity has been an enormous asset with voters who feel gratified and inspired that he would lavish them with attention and bluntly express some of the ideas and attitudes they share.