Into each business life, a little acrimony must fall. That seems to be especially true of the relationships between brokers and their clients. In a pin-stripe version of Murphy's Law, apparently anything that can go wrong in any other line of work has a better chance of going awry in the brokerage business. We cite several examples:

*Dispute No. 1. Client Jones calls broker Smith and says, "I have 1,000 shares of XYZ stock. I'm thinking that if it gets up to $25, I'd like to sell it." Broker Smith says fine and makes a note. Two weeks later, the broker calls the client and says, "I sold your XYZ stock at $25." Client Jones replies, "You did? I didn't really want to sell it. What's the price now?" The broker checks. "It's $27," he says. "Well," replies the client, "You shouldn't have sold it. You were supposed to call me first. You've just cost me $2,000."

Question: Who is responsible?

*Dispute No. 2. Client Brown calls broker Green and says, "I've got 1,000 shares of ZZZ. When it gets to $125, I'd like to sell it." The broker says okay, and puts in an open order, instructing the specialist on the floor of the exchange to sell at $125. The broker sends the client a confirmation.

Three months go by, the price of ZZZ lingers around $110, the client gets tired of waiting, calls broker Green and says, "Sell my 1,000 ZZZ." The client does not mention his previous instructions and the broker, forgetting about the open order, sells the shares at $110. Two more months go by and the price of ZZZ finally reaches $125. The open order is executed, although the client no longer owns 1,000 ZZZ. Broker Green calls his client and tells him that the 1,000 ZZZ has been sold. "Waddaya mean?" the client bellows. "I sold that at $110!"

The broker tries to buy the 1,000 shares back but, by this time, the price is at $130. He has to buy the shares back for $5,000 more than he sold them.

Question: Who is responsible?

*Dispute No. 3. Client White walks into the office of broker Blue and says, "I've inherited 1,000 shares of QRQ from my mother and I would like to sell them." He gives the broker the stock certificate in his mother's name and documents to prove he owns the stock. The broker sells the 1,000 shares at the market price, which is then $10 a share. He sends the certificate to the transfer agent, and two weeks later gets some bad news. Ten years earlier, it appears, the QRQ company had a reverse split and the 1,000 shares became 100 shares. So the broker has sold 900 shares the client didn't really own and has to buy them back. But the price has gone up to $15, so there is a loss of $5 a share, or $4,500.

Question: Who is responsible?

As unlikely as it seems, mind-bending disputes like these take place almost every day. Fortunately, when brokers and their clients can't agree on who is responsible, they can settle their arguments by going to arbitration -- although they do have a right to seek relief in court.

So common are broker-customer disagreements that the securities industry has created a massive arbitration system. The National Association of Securities Dealers (NASD), based in Washington, arbitrates about 1,100 cases a year, of which about 800 involve customers. The New York Stock Exchange handles more than 1,000 cases a year -- many of which are customer-related.

One of the hallmarks of the investment scene in America is the rapid increase in the number of arbitration cases. NASD-arbitrated cases were up 248.4 percent between 1980 and 1984 while those involving NYSE arbitrators were up 174.7 percent.

These cases count both industry disputes -- brokers suing their firms and vice versa -- and battles between customers and brokers. Last year, 74 percent of NASD arbitration cases involved customers. Many complaints arose when customers transferred their accounts from one brokerage firm to another. Others were based on charges of bad investment advice.

For clients who have a dispute with a broker that involves $5,000 or less, the arbitration procedure is easy and inexpensive to use. For a controversy that involves $1,000 or less, the claimant pays a fee of $15. It's $25 for a dispute between $1,000 and $2,500, and $100 for a case involving $2,500 to $5,000. Higher fees apply as the amounts go up, with $750 the top fee.

There are a couple of things customers should know about arbitration, which usually takes place in one's hometown. First, choosing arbitration to solve a dispute generally means giving up your right to pursue the matter through the courts. Second, an arbitrator's award is final. Courts generally will decline to review an arbitrator's decision.

In addition, when clients open new accounts these days, they are likely to be asked to sign an agreement to arbitrate disputes with their broker. Under recent decisions of the U.S. Supreme Court, the power of brokerage firms to compel arbitration appears to be growing stronger.

The size of an arbitration panel depends on the size of the claim. In simple disputes involving less than $5,000, the case will be heard by a single arbitrator. Cases involving more than $5,000 will go before a three-member panel.

Leslie J. Silverstone, senior vice president at Dean Witter Reynolds Inc. and manager of one of the firm's offices in downtown Washington, has been a broker for 25 years and has sat on many arbitration panels. He suggests that customers who have had problems with brokers air their complaints as soon as possible.

He can recall instances in which customers waited for months before airing complaints. When that happens, said Silverstone, the question inevitably arises as to why the customer, if he felt aggrieved, didn't say so at the time. The delay doesn't help the customer's case when it gets to arbitration.

"The longer you wait, the more suspect you are," Silverstone said.

Silverstone said the best way to initiate a complaint is to write to the broker's office manager. Usually a call to the office will give you the manager's name. A letter of complaint generally will get prompt attention from the office manager, because examiners from the Securities and Exchange Commission and his own firm routinely review his complaint file.

"If a firm thinks it's wrong," said Silverstone, "it will try to settle the matter. They don't want to waste time and legal fees if there is a justifiable complaint." On the other hand, he said, if a firm thinks it is right, it will demand arbitration.

From the standpoint of the customer, Silverstone said, arbitration is a good deal on several counts. It is cheaper and faster than court action. Arbitration panelists are likely to have a better understanding of a complex securities case than a jury. A customer does not even need a lawyer, although Silverstone thinks it is wise to consult one. Finally, Silverstone said, in his experience "arbitrators bend over backwards to be fair to the customer."

Not all customers may agree, of course, but with arbitration, a customer at least gets his day in court without going to court.

To contact an arbitrator, write or call the Director of Arbitration at one of the following exchanges: National Association of Securities Dealers, Two World Trade Center, 98th floor, New York, N.Y. 10048 (212-839-6251). New York Stock Exchange, 11 Wall St., New York, N.Y. 10005 (212-623-3000). American Stock Exchange, 86 Trinity Place, New York, N.Y. 10006 (212-306-1000).