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.

What makes this issue so central to soccer’s future is that these errors do not result from referees’ negligence, inattentiveness or incompetence. Rather, they reflect the game’s speed, its players’ athleticism, the size of the playing surface, and a puzzling resistance by the game’s leading authorities to adapt 19th-century rules to 21st-century resources.

First, there is a need for video evidence. This would literally furnish the game changer in those few key situations that decide a match, such as an unjustifiably denied goal, an erroneous red card, or an egregious offside call.

One could establish a sort of super official who surveys video monitors, immediately overrules blatantly wrong calls, and directly communicates this decision with the referee and linesmen on the field (who are already equipped with earphones). Alternatively, one could give each team the opportunity to challenge up to two referee decisions per game, employing video replays to review rules infractions and settle disputed calls.

This procedure would give the referees on the field the opportunity, if necessary, to overrule their initial decisions. And quick reviews would not waste much time or interrupt the flow of the game. Under current conditions, the berating of the referee by the slighted team’s players consumes more game time than any review ever will.

Second, we need to make use of the perfectly functioning electronic chip already inside the ball to settle decisively whether a ball has crossed the field’s boundaries or its all-important goal lines. Consider how an essentially equivalent technology has successfully reduced line-related controversies in major tennis tournaments.

Third, serious consideration should be given to introducing a second referee, with each given responsibility for one half of the huge playing field. After all, the U.S. National Basketball Association employs three referees on a playing surface one-ninth the size of a soccer field.

Lastly, the culture of secrecy and nonaccountability that permeates soccer’s major governing bodies such as FIFA, UEFA and the various country federations needs to be changed. No other major team sport tolerates the arrogance of governing bodies who feel no responsibility to explain their actions.

These measures — and many others that include the overdue use of available technology — would augment the effectiveness of often-clueless referees, whose authority has declined sharply with the proliferation of decisive mistakes in major games and championships. While none of these measures is new, implementing them would add significant clarity and fairness to soccer, and thus enhance the legitimacy of the game.

Above all, referees must be accountable for their decisions. They must not be permitted to decide games of utmost importance in an arbitrary manner that need never be explained to anyone.

Many of these overdue reforms have long been promoted by leading soccer experts, such as the Dutch world-class striker Marco van Basten and the former FIFA referee Markus Merk of Germany. A majority of soccer fans around the world also supports decisive reforms that easily minimize refereeing errors. Like the Irish, many of them have become increasingly alienated by soccer’s old ruling regime and the conservative authorities that guard it.

Of course, we are fully aware that human error will never be eliminated from affecting outcomes in any sport. Nor should it be. Indeed, we actually believe that the “we wuz robbed” dimension of all sports adds to their lore and legend. But those responsible for a global product on the scale of soccer surely must act boldly to minimize the most egregious and avoidable errors, and thereby preserve the game’s integrity.

Andrei S. Markovits and Lars Rensmann, professors at the University of Michigan, are the authors of “Gaming the World: How Sports Are Reshaping Global Politics and Culture.” © 2010 Project Syndicate

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