You may have encountered an initiative to end primary elections for political parties, turning them in to one preliminary election where you can vote for as many people as you want, then the top two, regardless of party, face off in the general election. Although it may sound tempting, it makes for a cure worse than any disease that Mark Frohnmayer talks about in that letter.
Think about the scenario for a second: you can vote for as many people as you want in the preliminary election, and only the top two will advance. What incentives does that give you? Obviously, you have an incentive to vote for your favorite candidate, and maybe a few other good ones, hoping that at least one of them advances. So far, it sounds fine. However, you now also have an incentive to vote for the most beatable candidate on the other side, so your candidate has the best chance. Likewise, those on the other side have an incentive to vote for their favorites, and the most beatable candidate on your side.
Usually, the most beatable candidate is the most extreme ideologically. Such candidates will get the votes of people who agree with them, and who wholeheartedly disagree with them but want them to advance because they will be easy to beat. This will make the general elections between the extremes, and make for greater polarization in government officials.