First of all, this is primarily intended to be a simulation game, but I think it's possible for people to actually have fun playing it rather than just learning something. You'll need a large number of people: my guess is at least 20 for it be at all effective. I suppose the ideal setting would actually be a classroom or, perhaps, some sort of seminar. The game would take a little over an hour to play: six rounds of 10 minutes each plus some time for voter tabulation.
Each player is given a card with randomized issues on it. Each issue has a comment as to whether the player is for or against it, but no two players' cards are identical. The number of issues can be expanded to include as many players as decided simply by using the formula 2^x. For example, if there are 32 players, there would be 5 issues. The winner is the person who can elect leaders who most agree with his or her issues.
Each round starts with a 10 minute discussion period which can happen in any manner the players see fit. After the discussion period, the Game Master calls for nominations. Anyone can nominate anyone (including him or herself), but to be a valid candidate, they need a second. There is no limit to nominations (in theory, every player could be a candidate). When all nominations are gathered, everyone votes for one candidate to be president (ballots can be secret or public; I don't think it matters that much). The person with a plurality of votes becomes president (in case of a tie, the winner is decided randomly from the leading candidates). Each player then adds up their personal score based upon how many issues they agree with the president on. For instance, at the end of a round with 5 issues, each player has accumulated between 0-5 points, with the president being the only person to get the full 5 points.
A president can only be elected twice. The game is played in six rounds and the winner is the person who has accumulated the most points at the end of the final round.
I suspect that if this game were actually played, the first couple of rounds would be rather chaotic with a large number of candidates. Pretty soon, though, I'm guessing a few clever people will realize that by forming tight alliances, they can pass their personal agenda more effectively. Everyone else will then latch onto that strategy as well and soon only two broad coalitions will emerge by the end of the game. However, I don't know for sure and would love to see it played out.