This fall’s election may determine more than New Haven’s next mayor — an escalating debate between mayoral candidates over party primaries and public financing could redefine the procedure at the very heart of city elections.

On the steps of City Hall Thursday, Connecticut State Rep. Gary Holder-Winfield laid out the terms of his “Clean Primary Pledge,” promising to adhere to the public financing system established by the New Haven Democracy Fund, reject special interest money and abide by the results of the Democratic primary. He asked his opponents to do the same.

But Ward 10 Alderman Justin Elicker FES ’10 SOM ’10 and Henry Fernandez LAW ’94, CEO of the consulting firm Fernandez Advisors, have opted for somewhat different strategies. Elicker — who, like Holder-Winfield, has already promised to use the Democracy Fund — announced that he would run in November’s general election as an independent should he lose the Democratic primary scheduled for Sept. 10. Fernandez has taken the opposite tack, agreeing to abide by the results of the primary but passing on the Democracy Fund, which limits individual campaign donations to $370 or less in return for a $19,000 grant and matching funds of up to $125,000. A fourth registered mayoral candidate and plumber, Sundiata Keitazulu, could not be reached for comment.

In a city dominated by registered Democrats, the Democratic primary has determined the winner come November in every election since 1954. Elicker said this process disenfranchises thousands of people, as there are currently 18,700 unaffiliated voters and 494 belonging to minority parties, compared to 48,887 registered Democrats, according to the New Haven Independent.

“The city has a strange situation where generally the only viable candidates are Democrats. That means elections are decided in the primary,” Elicker said. “But there are nearly 20,000 people in New Haven who are not registered Democrats, and those people need to have a voice in who our next mayor should be.”

Elicker’s move has precedent. In 2011, Jeffrey Kerekes lost the Democratic primary only to re-enter the fray as an independent and give Mayor John DeStefano Jr. his toughest re-election challenge in his 20-year-tenure.

Elicker said his decision was motivated by his concern that a candidate could win the primary, and thus functionally clinch the mayor’s office, with less than 50 percent of the vote. With four official candidates and two more — probate Judge Jack Keyes and Hillhouse High School Principal Kermit Carolina — likely to enter, Elicker said that’s a distinct possibility. The scenario Elicker described played out in 1979, when Biagio DiLieto ousted incumbent Mayor Frank Logue after winning the primary with only 47 percent of the vote.

James Campbell, a political consultant and clean-campaign finance advocate who is managing Holder-Winfield’s campaign, assailed Elicker’s strategy as disingenuous and unfair to city taxpayers.

“If you’re already planning on losing the primary and then running again in the general, why run? It’s crazy,” he said. “You’re using New Haven taxpayer dollars under the Democracy Fund to subsidize a dry run.”

Under Democracy Fund rules, a candidate is not allowed to stay on with public financing in the general election after losing the primary, Campbell said. That means Elicker would have to switch to entirely private funding should he run as an independent.

“We’re not going to say, well, we’re going to run in the primary and then we’re going to run in the general election,” Holder-Winfield said outside of City Hall on Thursday. “We’re going to do what we say we’re going to do.”

Fernandez also said he would abide by the results of the Democratic primary, adding that he would “not switch parties.” He also challenged Elicker’s suggestion of disenfranchisement by emphasizing that two elections are still held and that everyone gets to vote in November.

Though he praised the Democracy Fund for expanding the potential field of candidates, Fernandez said he would not be using the system due to time constraints as a “late-entering candidate.” Under the fund, candidates must collect 200 contributions of $10 or more from registered voters to qualify for public financing. Elicker said he fulfilled that requirement in five days.

Fernandez also condemned the idea of campaign pledges, telling the New Haven Independent they were “silly” and saying they distract from the substantive issues of the campaign.

“I’m not going to focus on these process questions,” Fernandez told the News Sunday. “I plan on focusing on reducing crime, improving our schools, creating youth centers for our kids and creating jobs.”

Meanwhile, the Holder-Winfield and Elicker campaigns are casting issues of process in a different light, saying they determine whether government is efficient and accountable to people.

Campbell cited criticisms of DeStefano’s 20-year tenure in office as evidence of a desire for more accountability and democracy in campaign finance. He said how candidates choose to finance their campaigns influences how they govern.

“This is not a process issue — it’s a governance issue,” he said. “If you have contractors spending $1,000 a pop to buy the mayor, that guy won’t represent the average New Haven resident. Who signs onto the Democracy Fund is an indication of who will be supportive of the popular will of the people.”

Elicker agreed, saying the Democracy Fund is a way of “leveling the playing field.” He added that he is having no trouble fundraising without special-interest money, breaking his own $50,000 fundraising goal for the March 31 filing deadline.

Fernandez declined to comment on fundraising strategy, but said that Connecticut’s election laws made funding streams “highly transparent” even without the clean-finance pledges embraced by his opponents.

The general election will be held on Nov. 5.