Bribery is a huge problem in many countries. India, the world's largest democracy has a particular problem with this form of corruption. Many studies show that Indians routinely face bribe requests for services they are legally entitled to.
Former chief economic adviser of India and now chief economist of the World Bank, Kaushik Basu, has suggested a radical proposal. Make paying bribes legal, while maintaining the illegality of requesting bribes.
He argues that criminalizing both sides of the transaction aligns the interests of the corrupt official and bribe payer. Neither one wants to report the transaction because they would both suffer. In fact Basu goes further and suggests returning the bribe to the bribe payer in the event that they report that the bribe took place.
This final detail is important for incentivizing bribe givers to go to the trouble of reporting the bribe takers. However, as Basu notes, it does create a new set of incentives to falsely report bribes and this could just create a whole new problem of public official harassment and a court system too overloaded to actually deal with the real claims of bribery.
I think there might be a potential fix to this proposal that would get round these problems. The answer is that we don't return the bribes but we do make not reporting a bribe an illegal act. In this way we create the heavily divergent interests between bribe payer and bribe taker but don't create the perverse incentive to falsely report bribes.
The power of the "duty to report" law will depend partially on the likelihood of being caught. To increase this probability I would suggest running a small number of high publicised sting operations where well audited and video recorded officials request bribes from the public. These bribes are returned in full with a reward in the event of the person reporting the mock bribe and the person is prosecuted if they fail to report it.
The fear that a bribe requester could be a sting operation will heavily skew incentives to report any bribe requesters in fear of being prosecuted if you do not do so.
See here for the Planet Money write up
http://www.npr.org/blogs/money/2011/04/01/135011027/why-paying-bribes-should-be-legal
and here for Kaushik Basu's paper
http://finmin.nic.in/workingpaper/act_giving_bribe_legal.pdf