ANN ARBOR, Mich. — The quality of refereeing at the World Cup had been a source of relief until June 18, when referee Koman Coulibaly of Mali disallowed a perfectly legitimate goal by the United States that would have given it an all-important win over Slovenia. Worse still, Coulibaly never had to account for his terrible decision, or explain it to anyone — not the players and coaches on the pitch, and not the public at large.

Referee decisions in soccer, no matter how egregiously erroneous, are incontestable and immutable. Soccer fans the world over will always remember the outrageous error that awarded France the decisive goal against Ireland to qualify for the tournament, despite obvious hand-play by the French superstar Thierry Henry.

We believe that a concerted effort to reform soccer refereeing is urgently needed. Refereeing errors increasingly mar the game on all its levels — country and club, major and minor leagues, globally televised tournaments and matches, and local games. Since such errors have major implications for the outcome of key tournaments that define this most global of sports, their ubiquity and frequency jeopardize the game's very integrity — and thus its essential legitimacy. Such episodes, after all, are increasingly part of the public domain, owing to new media that have rendered the game even more global than it was.