Since there is, in principle, no reason why third parties should not pay\nindividuals for the use of their data, we introduce a realistic market that\nwould allow these payments to be made while taking into account the privacy\nattitude of the participants. And since it is usually important to use unbiased\nsamples to obtain credible statistical results, we examine the properties that\nsuch a market should have and suggest a mechanism that compensates those\nindividuals that participate according to their risk attitudes. Equally\nimportant, we show that this mechanism also benefits buyers, as they pay less\nfor the data than they would if they compensated all individuals with the same\nmaximum fee that the most concerned ones expect.\n