Flood the primary with votes for the underdog candidate. Thats your best bet. In order for there to be a viable third party the system, as it exists, has to be destroyed. You would hopefully do that via a program of voting for a progressive set of candidates. Failing that, you have to wait for the system to die naturally and overthrow it.
The existing system will not tolerate a third party or willingly change. It has to be forced.
Its possible if the right fails in this next election they could fall apart. That might, conceivably, create two new right wing parties: a moderate and extreme right wing. But there is no way for the common voter to make that happen.
Latest Answers