The leaders of the three major stock exchanges plan to meet next month to try to resolve a conflict over differences in listing standards that affect shareholder voting rights.

Last week John J. Phelan Jr., chairman of the New York Stock Exchange, and Arthur Levitt Jr., chairman of the American Stock Exchange, told a House subcommittee that instead of the NYSE lowering its listing standards to permit companies to have two classes of common stock with unequal voting rights, the Amex and the over-the-counter market ought to raise their standards to require listed companies to have only one class of common stock.

Phelan and Levitt said this would eliminate the competitive pressure on the NYSE to lower its listing standards and would preserve the nation's traditional "one share, one vote" system of corporate governance. But Gordon S. Macklin, president of the National Association of Securities Dealers, refused last week to go along with Phelan and Levitt, saying that he was still studying the issue and would not be ready to discuss substantive changes for several months.

Earlier this week, Macklin changed his mind. He wrote letters to Phelan and Levitt inviting them to meet on June 14 to seek solutions to the conflict. Rep. Timothy Wirth (D-Colo.), in a letter to Macklin, said he was pleased that Macklin was seeking the meeting, a first step in "self-regulation."

"Many have suggested that self-regulation in the securities industry may be undermined by increasing competitive pressures among the dominant markets," Wirth said. "While it is true that self-regulation cannot solve all of our problems we must make every effort to see that it deals with those problems that can be solved through industry efforts. I am hopeful that, instead of a 'race to the bottom,' as some have suggested, the stock exchanges will 'race to the top,' in an effort to demonstrate to shareholders that your respective markets truly protect their interests."

Macklin said he decided to try and seek a resolution of the conflict privately, instead of through government regulation, after testifying at a hearing on the topic last week before Wirth. Macklin said there was significant enough interest in the issue among the members of Wirth's subcommitte to "justify accelerating my timetable."

While current NYSE rules specify that all of the common stock of companies listed on the Big Board must have equal voting rights, the Amex and the over-the-counter market allow their listed companies to have different classes of common stock with disproportionate voting rights.

The creation of two classes of common stock -- with a new class controlling a majority of votes placed in friendly hands -- has become increasingly popular in an era when corporate management is trying to find ways to prevent hostile takeover attempts.

Switching to two classes of stock and putting a safe majority of votes in friendly hands enables a corporation to block an unwanted takeover. Several NYSE companies interested in discouraging hostile takeover bids, including Dow Jones & Co., publisher of The Wall Street Journal, and Hershey Foods Corp., have adopted a second class of common stock and could be forced to leave the NYSE.