Sheldon Adelson, chairman and chief executive officer of Las Vegas Sands Corp., center left, and wife Miriam Adelson pose for photographs as they leave a news conference during the opening of the Sands Cotai Central resort in Macau, China, in 2012. (Jerome Favre/Bloomberg)

Several prospective Republican presidential candidates have gathered in Las Vegas for the opening round of what has been dubbed “the Sheldon Primary,” an event emblematic of how warped the system for financing presidential elections has become.

The Sheldon Primary is named for Sheldon Adelson, the wealthy casino owner who, with his wife, poured more than $92 million into the 2012 elections. Despite all that money, Adelson made some bad bets in the last election, first on former House speaker Newt Gingrich to win the Republican nomination and then on Mitt Romney to defeat President Obama in the general election.

He is now looking toward 2016 with a fresh eye, determined, according to The Post’s Matea Gold and Philip Rucker, to find a non-extremist candidate who can actually win the presidency. Those who are looking at running would be happy to have that kind of financial support. Some of them have come to Las Vegas on Friday for a meeting of the Republican Jewish Coalition, but also to meet privately with Adelson.

Adelson has become a symbol of the new system of financing presidential elections. He and others play under legal rules. But this new financing structure has had a corrosive effect on public confidence in government and politicians. It is why so many Americans feel shut out of the process.

Many people have had a role in bringing the system to this point — the courts, special interests, incredibly wealthy individuals with their own agendas and candidates seeking to gain political advantage in the fierce competition that is presidential politics.

A series of court decisions, the most prominent being the Supreme Court’s 2010 ruling in Citizens United v. Federal Election Commission, has hastened the rise of super PACs. These political action committees are the new behemoths in political campaigns. They are allowed to take unlimited contributions from corporations, unions and individuals. They can openly advocate for individual candidates, and candidates can help raise money for them. But they are supposed to operate independent of those candidates.

Court decisions also helped usher in a new era of shadowy financing of political activity by so-called “social welfare” groups. Like super PACs, these groups also take huge individual donations — $10 million, $20 million, $30 million — but they are not required to disclose their contributions. They can engage in political activity within limits, but those limits have done little to slow their growth.

Meanwhile, the system of public financing for presidential candidates that came into being after the Watergate scandal and that once was universally accepted and respected by those seeking the presidency has been systematically shredded over the course of the last four presidential campaigns.

In 2000, George W. Bush opted out of public financing in his nomination campaign because money was flowing so freely into his campaign war chest and he was worried about rival Steve Forbes’s ability to fund his own campaign out of his private fortune. John F. Kerry and Howard Dean followed suit four years later in their nomination battle. That effectively destroyed the use of public money in pursuit of the nomination.

Then in 2008, Obama took it a step further. Fueled by nearly half a billion dollars in online donations alone, candidate Obama decided to forgo public financing in the general election after suggesting that he would stay within the system if his Republican rival did, too. His opponent, Sen. John McCain, was one of the most ardent advocates of campaign finance reform who was left to chastise Obama for turning his back on a general election public financing structure designed to level the playing field. Having seen what happened in 2008, Romney in 2012 followed Obama out the door of public financing.

All of these candidates who pulled out of public financing put political need ahead of public interest. They chose to quit the system because by doing so they could spend well beyond the limits of what the law allowed if they accepted federal matching funds. Meanwhile, some of their rivals were constrained by the limits imposed by the acceptance of public money.

What is left now is an arms race in presidential campaign fundraising by the candidates and a new power base, the quasi-independent force of the super PACs, which have eclipsed the political parties as powerbrokers in the campaign process.

Courting wealthy people will always be an essential part of running for president. But the outsize influences of people who are prepared to give tens of millions to a super PAC or the contributor who can bundle hundreds of thousands of dollars in donations have changed the game.

The ability to raise huge amounts of money has become an even more important attribute for those seeking the presidency, a yardstick to stratify the field of candidates long before the voters have taken a serious look at the field.

Dark horse candidates still can break through in one of the early states, as former senator Rick Santorum did in 2012. But anyone thinking of running for president today would be urged by those who shape this inside game not even to think about taking public funds to help finance their campaign and to build a financial foundation designed to go the distance.

Obama was initially critical of super PACs, but there is no longer any hesitation among Democrats to play in this new world. Hillary Rodham Clinton already has a super PAC organizing on her behalf, though she is far from making an announcement about whether she will run in 2016. Priorities USA, which supported Obama in 2012, has reconstituted itself more aggressively than ever in preparation of her candidacy.

Republican politicians know that whomever Adelson and his wife decide to support in 2016 will have what is now a required asset of any campaign—a well-funded super PAC that can provide additional armor against the inevitable attacks from opponents and which can lead the attacks against rivals who threaten their path to victory. Those who lose the Sheldon Primary will look to other rich people to fund other super PACs dedicated solely to the promotion and protection of their candidacies.

Super PACs have yet to prove they can decide the outcome of elections. Romney lost the general election despite having a clear advantage in the amount of outside money on his side. But the super PACs’ role in the GOP nominating process was more significant. Without Adelson at his side, Gingrich might not have lasted as long as he did. Without the support of his own super PAC, Romney might have had a more difficult time fending off Gingrich and later Santorum. That knowledge is what has brought several prospective candidates to Las Vegas.

When W. Clement Stone, an insurance magnate and philanthropist, gave $2 million to Richard M. Nixon’s 1972 campaign, it caused public outrage and contributed to a movement that produced the post-Watergate reforms in campaign financing. Accounting for inflation, that $2 million would equal about $11 million in today’s dollars. If not exactly commonplace, contributions of that size or larger are now an accepted part of the presidential campaign process, in some cases without real transparency. Is it any wonder that the public has a cynical view of how the system works?