As the story is told, a little boy sat on a curbstone in Jersey City on Election Day, tears streaming from his eyes. "What's the matter?" his friend said.

"My father was in town today and he didn't come see me," the boy sniffled.

To which the startled friend replied, "But your dad's been dead for years."

"Yeah, well he voted," said the boy.

Voting fraud is, of course, more serious than that. But is it really the biggest problem we face with regard to administering elections in a land where voter participation approaches new lows with each passing campaign? Or do we use fear of fraud as a way to cling to outmoded rules and systems that end up discouraging legitimate potential voters from exercising the franchise?

Suppose, for example, you had never bothered to vote before but something about this year's US Senate race has your blood up. For once you want to take a stand. Or maybe your hatred of one candidate is so intense that you just have to help elect the other.

So you run down to the local election board tomorrow and register to vote. What happens next depends on where you live.

If you want to vote for John E. Sununu or Jeanne Shaheen, you will get the chance to do so. But if you want to vote for former US Sen. Frank Lautenberg or his opponent, Doug Forrester, you are plumb out of luck.

That's because Shaheen and Sununu in New Hampshire, where you can sign up to vote anytime you want, even on Election Day. Lautenberg and Forrester, of course, are running in New Jersey, where the law says you had to sign up by October 7, a month before Election Day. Oh, you still can register now if you like-you just can't vote until 2003.

If it sounds like we're doing something wrong in New Jersey, that's because we are. We are stifling democracy. Just when the people who don't focus on politics most of the year start to tune in, New Jersey freezes them out-one of 37 states that cut off registration 20 to 30 days before the election. Indeed, the Gallup Poll found that in 2000, 59 percent of people during Sept. 18-24 said they were giving "quite a lot" of thought to the election, with the rate climbing to 62 percent Oct. 2-8, 70 percent Oct. 16-22 and then hitting 75 percent Oct. 30 - Nov. 5, long after New Jersey closed the door.

Six states allow registration on Election Day, and guess what: turnout in Idaho, Maine, Minnesota, New Hampshire, Wisconsin and Wyoming in 2000 averaged just over 68 percent, beating the national average by almost 10 points. That tells you something.

A skeptic might counter that those are relatively small states where tracking names and fighting fraud are easier than would be the case in a densely populated state like New Jersey. Fair enough, except that a study this year in California done for Demos, a national research and advocacy organization, showed otherwise. Two scholars on election rules and voting systems strongly concluded that fraud would be no more of a problem than it already is. Indeed, they felt that same-day registration could even make it easier to ferret out illegal or multiple voters-since most voter registrations would occur at the polling place and require some form of ID.

Keys to the system include well-trained polling place staffs, increased penalties to deter fraud and a computerized statewide voter database, the latter already under consideration in New Jersey. And, the report found, administering same-day registration seems not to cost any more than the old system.

The report concluded not only that voter participation in California rise with same-day registration, but the largest increases would be among groups that now have particularly low turnout: 18-to-25 year-olds; those with a grade school education or less; ethnic and racial minorities; and those who have lived at their currently address for less than six months.

Before long, New Jersey might somewhat ease the currently over-restrictive system. The state's Law Revision Commission has been looking at election administration and its preliminary recommendations include allowing registration closer to Election Day, but not as close as in the least restrictive states.

We should go further. Let's at least try same-day registration for a year or two and see how it works, rather than conclude in advance that it won't. Let's see if there really is a downside to letting more people vote. And let's ask those who want anything short of the highest possible turnout to explain why.

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