Every time two people who support different parties get into a debate, they each end up convincing the other that their party is terrible and not worth supporting, and both decide to switch their vote to the third party. For instance, a debate between a Left voter and a Right voter will turn both of them into Centre voters. This is the only way anyone's chosen party can change: if more than two people get into a debate, they'll just end up fighting instead.
Is it possible that by the next election, everyone will be agreed on the same party?
For the sake of simplicity, assume a fixed population: the set of voters is exactly the same in the next election as the last one.