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After last month’s Republican National Convention, a Gallup poll showed President Barack Obama nursing a 1 percentage-point advantage over challenger Mitt Romney while Romney was up 3 points in a Rasmussen poll. CNN had the two even.

Fast-forward past the Democratic National Convention and Gallup and CNN had Obama leading by 6 points, and Rasmussen by 5 on one day and 3 the next.

Meanwhile, a Washington Post/ABC News poll pegged the president’s post-convention bounce at a 1-point advantage among likely voters. Since then, the numbers have bounced around even more.

Up and down, in and out, to a layman the gyrating numbers might suggest more of a statistical polls dance than a clear and rational way to gauge the trajectory of a seesaw contest that could alter the fate of a nation — and even the world.

Are voters that fickle? Did they see something they liked more in Charlotte, N.C., than Tampa, Fla.? Or, as Romney’s pollster tried to spin it, did they merely experience a brief “sugar high” from the Democratic confab that may quickly wear off.

Maybe, maybe and maybe, admittedly unsatisfying answers in an era when Americans increasingly are fed a diet of snap judgments from politicians, journalists, bloggers and opinion makers.

The only concrete shot at clarity comes Nov. 6 when ballots are cast, a reality that gives rise to the less-than-sincere cliche uttered by many a politician that the only poll they care about is the one on Election Day.

Don’t believe it.

Until then, however, voters will be left to grope through a blizzard of often-confusing and seemingly contradictory numbers — some of them self-serving interpretations from the campaigns — that nonetheless could actually point to something meaningful.

That is an irony not lost on Frank Newport, editor-in-chief of the Gallup organization, who compares the gobs of polling data to research on critical health care topics such as the value of mammograms or prostate-specific antigen tests.

“There are lots of studies that are sometimes conflicting, and it’s very difficult to say which ones I should pay attention to,” he said.

At their best, election polls capture the shifting impressions of Americans toward the candidates seeking to lead them.

Borrowing from the science of statistics and probability theory, polls can render the impressions of a few hundred or a few thousand randomly selected individuals a valid stand-in for the thoughts of millions.

For voters, poll results define the horse race. For campaigns, they serve as a guide on what issues to highlight and where support is soft or solid.

In a nation where people like to back a winner, a good poll can build on itself, generating more support and financial backing.

But polling is as much art as science and no two are done the same way, leading to sometimes subtle and sometimes gaping differences in results.

Yet, as Marquette University polling expert Charles Franklin put it: “Every pollster claims to be the most accurate pollster in America. That’s actually not a joke.”

So to appreciate the validity of political polls it’s also important to understand their differences and limitations.

Polls today measure opinions and voting preferences as they stand today, not on Election Day.

What’s more, some use registered voters as a measuring stick while others sample a narrower pool of those who say they are likely to vote, a potentially significant distinction.

Obama’s recent lead over Romney is smaller when taking into account voters who plan to cast ballots.

And no poll can take into account the effectiveness of partisan get-out-the-vote drives that can sway outcomes in tight races.

Likewise, no poll could take into account the potential impact of new voter-identification laws in some battleground states, which Republicans say will prevent fraud and Democrats argue will suppress the votes of minorities who typically vote Democratic.

Polls show Obama with a healthy lead in Pennsylvania, for example, but the Republican House leader in that state has boasted that a voter ID requirement will “allow Governor Romney” to win there. (This week, the state Supreme Court indicated it was troubled with the voter ID law and sent it to a lower court for further review.)

When it comes to presidential politics, there’s also the quirky nature of the Electoral College to keep in mind. Nationwide preference polls are fine, and typically the winner of the popular vote in all 50 states wins the election as well. But not always (see George W. Bush vs. Al Gore in 2000).

As things stand now, only eight or nine states are considered tossups — the list in the Midwest includes Iowa, Ohio and Wisconsin — so paying attention to the polls in those states could be more telling than getting hung up on the national numbers.

Perhaps the biggest divide in polls is methodology.

Many, including the Tribune/WGN-TV poll in Illinois, survey voters over the telephone, with interviewers reading from a prepared script.

Other polls use computers to make the calls and ask questions through prerecorded messages.

A few compile responses through the Internet, relying on preselected pools of people to query.

Advantages and drawbacks are baked into each of those methods.

One of the most controversial involves cellphones, with many pollsters in recent years adding wireless numbers to the samples they survey along with land lines.

The reason is simple: More than 1 in 4 U.S. homes have cut the cord and now are cellphone-only. This is especially true for younger voters, so leaving cellphones out of the polling mix could undervalue their viewpoints.

The problem is that federal rules bar computer-generated calls to cellphones, so calling them is generally off limits for operators of automated robopolls.

The variations in polling techniques don’t end with hardware.

“Every polling organization uses slightly different methodology in the way they write questions, choose their samples and weight the data (to better reflect the demographic makeup of the voting public),” said Humphrey Taylor, chairman of the Harris Poll.

Then there’s the question of what is often referred to as margin of error, a term Taylor thinks is misleading because it suggests a range of precision that no pollster can absolutely be sure of.

What it means, however, is that all poll numbers come with statistical wiggle room of 2, 3 and 4 points up or down.

In a close race that could be significant, and by all accounts, the Obama-Romney battle figures to be a close one.

For all the pitfalls inherent in polls, there is evidence that the overall accuracy has come a long way since 1948, when Thomas Dewey was widely projected to beat Harry Truman and the Tribune famously got the outcome wrong in its initial headline.

Research by the National Council on Public Polls, an association of polling organizations, shows that the final pre-election polls of national media organizations in presidential elections dating to the 1950s varied little from the vote tallies and appear to get ever more precise.

Averaging the results of 19 major nationwide polls at the end of the 2008 presidential battle, the group found the surveys varied less than 1 percent from the actual results of the election, in which Obama beat Republican John McCain by 7.3 percentage points.

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