There is an old idea of mine that has been sitting there for over eight years unattended, and I think it could be used with good effects now to increase the awareness of laypersons on basic science. The basic idea is to use the events collected by CMS and ATLAS as lottery tickets: we could sell the run and event number of proton-proton collisions before we collect them, at a 1000-events-per-dollar price (say), and pay large sums to those who own an event ending up as a golden H->ZZ-> four lepton candidate in the correct mass range. That would correspond to, say, the 115-135 GeV region of the histogram below - about 40 events for CMS in 25/fb of collisions.
The CERN experiments have collected of the order of ten billion collisions each in the last couple of years of data taking, and within these samples each has identified two dozen Higgs decays to ZZ pairs in the four-lepton mode. This process has a large signal-to-noise ratio, so it makes sense to choose it as a prize-winning one. Given the above numbers, a reasonable payoff would end up being in the 200,000$-500,000$ range.
The randomness of the quantum processes involved is a perfect guarantee that the selection of winners would be really unbiased. We would just have to ensure that we "sell" run and event ranges which end up corresponding to data-taking periods when the detectors are fully operational; or create a suitable mapping mechanism between actual run/event numbers to ticket numbers, also to account for the actual number of sold tickets.
The benefits of such a lottery would be potentially very large, if the distribution of lottery tickets were handled carefully. People love lotteries, so they would be drawn to this new game and they would learn particle physics without realizing it -since it would be a game! Plus, we could finance some good science project with the money we make.
I can imagine people at the bar boasting about a win over printouts of event displays, or visiting CERN web sites to learn more about their chances to get a Higgs candidate as the experiments change their selection strategy... It could be really fun !
Of course, one could object that it is unethical to encourage gambling. I agree to that, in principle. So maybe instead of offering large sums of money to winning ticket holders, we could give them a paid visit to CERN. I know schools that collect funds for such visits every year, and I see no reason why it would be wrong to finance these visits with a Higgs lottery...