LEXINGTON, Ky. – Officials of the National Horsemen’s Benevolent Protective Association and the British-based exchange-wagering company Betfair met on Wednesday in Lexington in what a horsemen’s representative called an “ongoing dialogue” on the company’s future plans in the United States. During the meeting, Betfair representatives presented the national horsemen’s association with a proposal on how horsemen might be compensated if Betfair launched a betting exchange in the United States, according to Joe Santanna, the president and chairman of the horsemen’s group. Santanna would not provide specifics about the compensation model. “They proposed some numbers, a glimpse at a first attempt to quantify it,” Santanna said. “It wasn’t quite as precise as we would want it. But it was a good way to keep the discussion going.” Betfair officials did not respond to a request for comment on Thursday. In large part because of lobbying by Betfair, legislatures in California and New Jersey last year passed bills authorizing betting exchanges. Both bills made the operation of betting exchanges contingent on agreements between the operator, racetracks, and horsemen. Betfair operates betting exchanges in the United Kingdom and Australia. Under agreements with the racing industries there, the company contributes approximately 10 percent of its revenue from horse race wagering to tracks and horsemen. Officials in the United States have said the model provides less than one percent of the betting to the racing industry, compared with 20 percent in the United States. Santanna said that the model presented to the horsemen on Thursday was a departure from the Australian and U.K. business models. “They are slowly realizing that the model has to be different, because this is a different market,” Santanna said.