Republics

 Another stupid thing that I keep hearing from Electoral College fans (which seem to all be Trump fans as well) is that we can't have direct, i.e. popular vote elections for President because "we're a Republic, not a Democracy". Both the terms refer to rule by the people. "Republic" comes to us from the Latin res publica, i.e. a matter of the people; "Democracy" comes from demokratia, Greek for "power by the people". "Republic" came to mean a government of elected representatives, as distinct from a monarchy. "Democracy" indicated a political system where 'the people' had a vote. Most early republics did not have universal suffrage, even the United States limited voting rights to white, male landowners at its founding. "Democracy" was often used to refer to direct democracy or mob rule, the tyranny of the majority. However, over time, Republics where the representatives weren't elected by the people became common; examples include Socialist Republics and Islamic Republics, where there were representatives that were elected, or more precisely selected by the ruling party or by religious elites. The term Democratic Republic came to be used for systems where the people elected their representatives, and often "Democracy" was used as a shorthand. Those who attempt to make a distinction between a Democracy and a Republic are defining "Democracy" as "Direct Democracy" when in fact most people are not using the term that way.

Even if the Trumpists were correct in their claim that we're not a Democracy, there is nothing about being a Republic that prima facie precludes it from directly electing a President. The people are still electing their representative, the President.