The $700 billion financial bailout is front and center again, with the U.S. auto industry campaigning for a piece of the pie this week. So now seems like an appropriate time to review the House’s two votes on the Wall Street rescue plan, where we find a compelling case study for anyone who wants to better understand how to change a lawmaker’s mind.

A closer look at some of the 58 Members of Congress who changed their votes from no to yes illustrates what I have described as “key predictors” of effective persuasion tactics.

The predictors of success are based on original research that my firm conducted with more than 20 government relations professionals at top lobbying organizations in 2006 and 2007. Most of the participants were from organizations on Fortune’s Power 25, which includes well-known grass-roots organizations like the National Rifle Association, AARP and the U.S. Chamber of Commerce. Participants were asked to account for more than 70 variables that predict an organization’s ability to influence the hardest political target of all: undecided legislators.

The most powerful example from the bailout vote involved the margin of victory. Our experience and research show there are several predictors that can cause legislators to change their minds. The most prominent is that they are more likely to change their minds if they won their last election by a wide margin.

Of the 58 who changed their minds, 50 were unopposed or won their seats by comfortable or wide margins in 2006. So it follows that of the 41 Members in competitive races, 34 refused to vote for the controversial bailout package both times.

Our survey showed that freshman legislators were more strident in their views and less likely to change their minds than seasoned legislators. So I wasn’t surprised that all of the 15 freshman Republicans voted against the rescue package twice despite a full court press by President George W. Bush, Treasury Secretary Henry Paulson and Sen. John McCain (R-Ariz.).

It gets even more interesting when you look at the lawmakers who did change their minds and their reasons why.

Our survey showed that undecided lawmakers are more likely to change their minds if they hear from people they trust. We call those people “key influentials” — personal friends, local elected officials and opinion leaders in the legislator’s district.

At least10 of the lawmakers who changed their minds and voted “yes” on the second vote said they were influenced by phone calls or other communication from constituents or opinion leaders, all of whom could be defined as “key influentials.” Several said they changed their minds after talking to the presidential candidates, McCain and Sen. Barack Obama (D-Ill.), who are certainly considered to be “key influentials” of the highest order.

Rep. Howard Coble (R-N.C.), a fiscal conservative, told the New York Times that he changed his vote after receiving a torrent of telephone calls and e-mails that had swung in favor of the bill. He also said he heard from Leo Lambert, the president of Elon University, who said the school had been squeezed by the credit crisis.

Rep. Elijah Cummings (D-Md.) told the Washington Post that his change of heart was influenced by a small-business owner who makes wire baskets in Baltimore and feared he couldn’t make payroll because a bank had cut his line of credit.

Rep. Jean Schmidt (R-Ohio) changed her vote after she heard from some of the largest employers in her district who were struggling to make payroll, according to the Cleveland Plain Dealer.

Rep. Joe Knollenberg (R-Mich.), who faced one of the toughest re-election fights in the House, told the Associated Press that he changed his mind after he received telephone calls from General Motors Corp. chief executive officer G. Richard Wagoner Jr. and other auto and corporate executives. “I’ve never talked to as many bank presidents in my life, over my entire life,” he said.

Knollenberg has received $131,500 from GM since he started serving in Congress in 1993, according to Federal Election Commission records, illustrating another “predictor of influence success.” Our survey showed that giving a legislator the maximum allowable political action committee contribution is a predictor of persuasion success.

Lobbyists representing the housing, financial, auto and other business sectors pushed hard for the bailout bill. Several of the lawmakers who changed their minds have received campaign contributions from those industry PACs.

Schmidt has received $70,100 from American Financial Group Inc., a Cincinnati-based insurance holding company, and $16,500 from the American Bankers Association since she was elected to Congress in 1989.

Rep. Judy Biggert (R) was the only Illinois lawmaker to change her mind about the bailout package. Since she began representing her suburban Chicago district in 1989, she has received $45,000 from the National Association of Realtors, $39,500 from the National Automobile Dealers Association and $37,548 from the ABA.

Most lawmakers say they aren’t influenced by campaign contributions, but the recent bailout votes suggest otherwise. We found that the most successful influence attempts typically include campaign contributions. In other words, a PAC contribution represents “exchange” and cements relationships.

Amy Showalter is president of the Showalter Group Inc., which advises trade associations, Fortune 500 companies and nonprofit organizations on how to increase their grass-roots and political action committee effectiveness.