I voted Republican on Tuesday.

While I am coming clean about my biases, I should probably also confess: I haven’t voted for a Democrat in any of the past four presidential elections.

This will puzzle some of my Republican friends, because I have been rather critical of the party’s nominees. So perhaps I should add a couple of asterisks.

The first asterisk: I live in the District of Columbia, so it doesn’t really matter how I vote; We have no voting representative in Congress, and the Democratic nominee invariably wins in just about every race. (At my daughter’s suggestion Tuesday morning, I wrote in the name of the family dog for D.C. “shadow senator,” figuring the canine could handle the nonexistent responsibilities of the position as well as anybody.)

Asterisk No. 2: I don’t vote for anyone who is actually listed on the ballot. I think about who would be the best president, and I write in that person.

This is a variation of the Len Downie method. The Post’s former executive editor, who is still a vice president of The Washington Post Co., had a policy of refusing to vote in elections so that he wouldn’t shed his journalistic impartiality, even in the sanctity of the voting booth. I think it’s my obligation to vote — in down-ballot races, where my vote might make a difference, I select actual candidates — but I’d rather not align myself with either party’s presidential nominees.

This turns out not to be much of a sacrifice, because neither party has in the past four cycles put forward the sort of giant who could bring the country together. What’s needed is an iconoclast, a candidate who will defy his or her own party in working out compromise. There hasn’t been much defiance of any kind since George H.W. Bush raised taxes and Bill Clinton reformed welfare.

In recent years, this has been mostly a Republican problem. Democratic leaders have been more willing to break with party orthodoxy on spending than Republicans have been on taxes. Since the tea party, Grover Norquist, the Club for Growth and the like have purged the GOP of ideological heretics, Democrats are the only ones who still have even a small amount of ideological diversity.

My challenge, therefore, is to pick a Republican leader with the stature and courage to push fellow Republicans to bend.

In 2000, the choice was obvious: I wrote in John McCain. Back then, fresh from his primary fight against George W. Bush, McCain remained a maverick Republican fighting for campaign-finance reform and challenging leaders of the Christian right. This was long before McCain, in pursuit of the 2008 presidential nomination, embraced conservative dogma.

In 2004, I voted for Chuck Hagel, the Republican senator from Nebraska who became a brave critic of the Bush administration. A Vietnam War hero, Hagel used his unquestionable military credentials to question the administration’s handling of Iraq.

In 2008, I went with Mike Bloomberg, who had been elected mayor of New York as a Republican. He had by then switched his party registration to unaffiliated, raising false hope that he would run for president as an independent.

This year, I thought of breaking my no-Democrats rule and writing in Hillary Clinton, because I continue to believe she would have been a stronger president than the man who beat her in the 2008 primaries. I also toyed with a vote for Jon Huntsman, whose attempt to run as a moderate in the GOP primaries went nowhere.

But that all changed last week, when New Jersey Gov. Chris Christie, the man many Republicans hoped would be their presidential nominee, infuriated Rush Limbaugh when he effusively praised President Obama’s response to Hurricane Sandy. This was Christie’s second sacrilege, following his keynote speech at the Republican convention in which he went on for 17 minutes before mentioning Mitt Romney’s name.

With characteristic bravado, Christie declared that he doesn’t “give a damn about presidential politics” during a time of crisis. Don’t believe that: His actions, though harmful to Romney, have put him in a solid position to run for president himself in 2016.

To win that nomination, Christie, like McCain, may need to shed his image as a Republican heretic. And I will need to find a new Republican to write in.