TheStreet (October 8, 2014 5:00 am) -- Did you hear the one about the guy who got on a Finra arbitration panel even though he'd pled no-contest after being indicted for practicing law without a license?

How about the time Finra sent a list of potential panelists to the litigants only to hear back that two of the arbitrators were dead?

Or surely you've caught wind of the tales of elderly panelists who paused for a snooze even as testimony was under way?

If you have ever been fleeced by a broker and tried to get your money back, you already know that your day in court is by a secret tribunal run by Finra, a self-regulatory organization that's funded by the people it polices. You signed away your right to sue your broker in court the day you opened your account, and Finra arbitration is what you get instead.

Finra takes a lot of flack for its arbitration debacles. In fairness, it has successfully fixed some problems. A rule change in 2011 that gave investors the option of having a panel that doesn't include anyone from Wall Street was among several welcome reforms.

But it's still enough of a mess that the keepers of Wall Street's private justice system are launching a new effort to solicit input from all corners of Investment Land as to how they might improve the operation known as Finra Dispute Resolution.

The exercise, which is to last 15 months, begins officially on Oct. 10 when the newly formed Finra Dispute Resolution Task Force of 13 regulators, lawyers, industry types and academics meets in New York City.

As luck would have it, a group of lawyers who represent investors in arbitrations has released a fresh trove of data that makes Finra arbitration look even worse than it already did, just in time for the group's maiden assembly.

The Public Investors Arbitration Bar Association said Tuesday it analyzed the profiles of 5,375 people in Finra's current and past arbitrator pool only to learn that it's a demographically lopsided group. The pool "consists primarily of elderly men who have a socioeconomic status that put them out of touch with the average investor," according to the Piaba report.