As of this writing, the top four candidates in the Denver race for mayor show the following vote totals:
Chris Romer: 28.5%
Michael Hancock: 27.1%
James Mejia: 25.7%
Doug Linkhart: 9.4%
The Denver Post reports, "If no candidate receives more than 50 percent of the vote in the May 3 election, the top two vote-getters advance to a June 7 runoff."
But if you think about it, that's a pretty foolish way to run an election. For example, what if Linkhart's voters prefer Mejia over the other two? Too bad: Mejia is out (assuming the percentages hold). Or what if the voters of either Romer or Hancock far preferred Mejia over the alternative? Again, the outcome will be that a less-favored candidate will win anyway.
In addition, holding a runoff vote costs taxpayers more money (and taxes their patience as well).
The way to solve both problems -- to pick the most-favored candidate and to do it with a single vote -- is to institute approval voting. The basic idea is that voters can cast more than one vote. For instance, you could vote for Romer only, Linkhart and Romer, Romer and Hancock, or whatever other combination of candidates you think you could live with.
As it stands, chances are pretty good that the next Denver mayor will not be the candidate with the most support among the voters, though we'll never really know. Even if the results turn out "right" in this case, inevitably the less-favored candidate will win in certain other races. I can think of lots of good reasons to institute approval voting, and no good reason not to.