U.S. Presidential primary elections could benefit greatly by adding a run-off.  The mathematical problem of choosing a single candidate from a list of candidates is obvious. A simple example is the case of three candidates—two who are moderate and one extreme (left or right). Imagine—and this is more a likelihood than a matter of conjecture—that the two moderate candidates each receive 30% of the votes, while the extreme candidate receives 40%. In this case, 60% of the voters sought a moderate candidate, while the winner ended up being the extreme candidate. This problem would nearly always be solved by a run-off vote that considered only the top two vote getters. 

Another solvable election problem is the matter of electorate education. The December, 2019 issue of Atlantic Magazine included this quote from co-authors Jonathan Rauch and Ray La Raja: “In other words, the nomination process makes unrealistic demands on voters, not because they are lazy or stupid—they’re not—but because they are human.” Rauch and La Raja are kind to say voters are not lazy or stupid. The truth is, voters generally are lazy and quite a few others vote on the basis of hairstyle, or charm, or the volume of t.v. ads. But, if we are honest, we must admit that it really is difficult to be informed about candidates. The news media tends to present 2 or 3 factoids about candidates, and it is very good at belaboring all actions, statements, and accusations that are controversial. (Ironically, though the media and Trump are at odds, it was the media that got him elected. It could not restrain itself from amplifying every bizarre tweet that leaked from his sophomoric fingertips, thus providing him with an enormous amount of free publicity.) 

The media is not good at providing easy to understand, comprehensive input on candidate platforms. Why is it that we can access useful testing data on virtually any high-value consumer product but we must conduct time-intensive research ourselves to obtain useful information about important political candidates? How hard would it be to create a set of, say, 20 questions that address national and international issues? How hard would it be to call on candidates to provide their own (brief, limited) statements on all these questions? How hard would it be to collect 1/2 page resumes, again supplied by the candidates themselves? What if theses documents were made available on a website paid for with government funds? Perhaps we should stop complaining about how ill-informed the public is and face the fact that most of us are ill-informed.  And then we should do something about it.