According to Game Theory, it'll work regardless. The
Prisoner's Dilemma is the simplest illustration of Game Theory and how it works. As you say, it only works if you have enough people thinking that way, but it works one way or the other precisely because you have a certain number of people thinking a certain way. All you have to do is convince enough people that enough people are thinking a little differently.
As the first video that I posted shows, it's not as much about how people think as it is the voting method. The current two-party system ends up being minority rule. Instead of first-past-the-post voting like we have, where it always ends up with two choices, and thus the winner usually not being the first choice of the majority, another voting method is probably called for. The winner of an election needs to have a pure majority in order to be truly representative of the people. Jesse Ventura's 37% win won him the election, but 63% of the people didn't want him to represent them. In 2012 Obama won with 50.9% of the popular vote, and as that first video shows, his true conscience vote was probably about one-third, because of the same tactical voting that many people espouse, and the reality is that the-thirds of the country don't want him in office. There are a lot of people who voted for Obama who would have voted for someone else, if they thought someone else could win. End result, he wins the majority, but it's a minority who want him in office, thus minority rule.
No voting system is perfect, but there are plenty of others, or combinations thereof, which may work better.
Single transferable vote, like NCAA brackets, until you finally get down to two is one way. As is the
Borda count method where you cast a vote that ranks all of the choices in order of preference, with each voting rank is assigned a point value (with 4 candidates, 1st place would be 4 points, 2nd place 3, 3rd place 2, 4th place 1, and whoever ends up with the most points wins). Another is the
Instant-runoff voting where you rank by preference each candidate and then you follow that up with a single-transferable vote if a particular candidate doesn't get the required number of votes. I think a Borda Count followed up with one or the other would word best overall. Not that this country is going to change the voting system any time soon, because every alternative method won't favor those parties already in power. But these are all voting system that are in use around the world.
