Every once in a while you see a Frankenstein monster of a house on a suburban street. The original structure might have a bumped-out second story too heavy for its foundation, an addition that looks tacked on, a sunroom around back meant for a different place entirely. And that's before you even get to the gazebo. From a commonsense standpoint, the whole thing is a mess.

That's the equivalent of the American election system, at least if you added a couple of cars on cinder blocks in the side yard. Piecemail, arbitrary, even downright wacky, turning the nation's most important task into a jerry-built mess. The first time Mao met Nixon, the Chinese leader said he'd voted for him. The way we pick a president is so random the big guy might almost have been believed.

The official season kicks off with a rite so arcane that even many of those participating don't understand it. The Iowa caucuses are like evening coffee klatsches with a serving of trigonometry. Those who show up at one of the state's 1,784 precincts huddle in various corners of the room depending on whom they're supporting. Then the folks in each "preference group" are counted and the math begins: multiplying that number by the number of delegates allotted to a precinct, then dividing by the number attending the caucus. Or at least I think that's right. Even veterans admit confusion, and tutorials are routinely offered. Keep that in mind when you hear the deceptively straightforward news that a candidate won in Iowa.

Caucus participants like to talk about how it's participatory democracy at its grittiest, but they represent a very small sliver of voters, since lots of people don't have the time, the patience or perhaps the computational skills to participate. In 2004 about 125,000 Iowans took part, and naysayers complained that that wasn't representative of Iowa, and Iowa wasn't representative of America. Ditto New Hampshire, whose primary follows and which, like Iowa, is not particularly representative of a new, more polyglot America. A former speechwriter for Dick Gephardt, whose presidential ambitions once turned to dust in these early contests, wrote of the aftermath, "One-half of one per cent of the nation's Democrats will have decisively shaped the race."

That speechwriter, Matthew Dallek, proposed a national primary or a series of regional primaries instead. It's a notion that dovetails nicely with the hobbyhorse of a professor of political science at NYU, Steven Brams, who has long promoted a method called approval voting. This might be his year, since on both sides of the political spectrum many voters seem to be persuaded—or unpersuaded—by more than one candidate. Approval voting would let them reflect that on their ballots, choosing any and all of those they would find acceptable. Torn between Huckabee and Romney, Clinton and Obama? Approval voting would allow you to put a check next to both names. Brams argues that this would elect the candidate most acceptable to the largest number of voters, instead of the one beloved by one segment and despised by another. It would also allow special-interest voters to have it both ways, since they could cast a statement vote for a third-party candidate as well as a strategic vote for a front runner. So far, approval voting is used mainly to elect the officers of such organizations as the Mathematical Association of America, and Brams admits he has an uphill slog: "Politicians are risk-averse."

How else to explain their continued allegiance—or inertia—in the face of our quaint 19th-century election customs? Oregon and Washington were free-thinking enough to institute voting by mail, and Texas and Georgia allow ballots to be cast in advance of Election Day at polling places. But most other states still require voters to show up in person on the first Tuesday after the first Monday in November. Why? The fall harvest, silly. The beginning of November was when the crops were in but roads were still passable, and Tuesday gave those coming in buggies from outlying towns plenty of time to attend church on Sunday before their departure. Which means that today Tuesday voting makes even less sense than Daylight Saving Time.