Third-party candidates Gary Johnson Gary Earl JohnsonWhat the numbers say about Trump's chances at reelection Presidential race tightens in Minnesota as Trump plows resources into state The Hill's Campaign Report: Biden condemns violence, blames Trump for fomenting it l Bitter Mass. primaries reach the end l Super PAC spending set to explode MORE's and Jill Stein's rights were not violated when they were excluded from presidential debates during the 2012 campaign, a federal appeals court ruled on Tuesday.

The pair, who also ran for the White House in 2016 as the nominees of the Libertarian and Green parties, claimed their First Amendment rights had been violated, alleging that their participation was denied “because of hostility towards their political viewpoints.”

The U.S. Court of Appeals for the D.C. Circuit rejected their argument, however.

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“Every four years, we suffer through the celebration of democracy (and national nightmare) that is a presidential election. And, in the end, one person is selected to occupy our nation’s highest office,” wrote Judge Janice Rogers Brown, a George W. Bush appointee who announced she would be retiring at the end of August, in the majority decision. “But in every hard-fought presidential election there are losers. And, with quadrennial regularity, those losers turn to the courts.”

The Johnson and Stein campaigns also brought antitrust claims into the mix, saying that the two-party system and overall requirements for participation in presidential and vice presidential debates constituted a political monopoly of sorts.

Among those requirements was garnering at least 15 percent of voter support, as gauged by an average of five recent national public opinion polls. The campaigns of President Barack Obama Barack Hussein ObamaTwitter investigating automated image previews over apparent algorithmic bias Donald Trump delivers promise for less interventions in foreign policy Rush Limbaugh encourages Senate to skip hearings for Trump's SCOTUS nominee MORE and his GOP challenger, Mitt Romney, agreed to that stipulation, which was enforced by the Commission on Presidential Debates.

The Johnson and Stein campaigns, however, called the threshold an “unreasonable burden on free speech or political association in violation of the First Amendment.” The 15 percent requirement, they said, was meant to “boost the political speech of the two major party nominees.”

The rules, the plaintiffs continued, represented an “unlawful agreement to monopolize and restrain competition.”

They also said their campaigns “lost millions of dollars’ worth of publicity, campaign contributions and matching funds that ordinarily would follow participation in the debates, as well as the salaries they would have earned as President and Vice President if they had won” as a result of not being allowed to participate in the debates.

In her decision, Brown slammed the complaints as failing to “articulate a clear legal claim, let alone identify a cognizable injury.”

“To make matters worse,” she adds, "the complaint omits entirely any allegation of government action [to suppress First Amendment rights], focusing entirely on the actions of the nonprofit defendants,” referring to the nonprofit Commission on Presidential Debates.

“The court also found the alleged harm — lack of media coverage that led to low popularity — preceded their exclusion from the debates,” she wrote.

Brown also said that forcing the Commission on Presidential Debates to include particular candidates would infringe on the nonprofit’s First Amendment rights.

The court also rejected alleged violations of antitrust law, specifically the Sherman Antitrust Act.

“To understand the scope of antitrust standing, we focus on the bedrock principle of this field: antitrust laws protect market (i.e. economic) competition,” Brown wrote. "Plaintiffs, however, define their injuries as millions of dollars in free media, campaign donations, and federal matching funds — injuries to them as individual candidates in a political contest for votes.”

Brown then added: “Square peg, meet round hole.”