The voters of those left-wing parties identify as "left" so if a Rush Limbaugh encourages people to distrust the "left" then those voters simply distrust Rush Limbaugh instead of altering their vote. Otherwise, if he covers Left-1 party with shit, Left-2 gains voters; if he points out a scandal in Left-2, Left-1 gains voters; if he points out that both Left-1 and Left-2 have a horrible foreign policy, there's likely Left-3 that opposes Left-1 and Left-2 on that policy, but he won't convince them to vote for a Right party if there are reasonable Left options. Unlike the two-party scenario where you might disagree with your "main" party on a single key issue and thus feel forced to vote for "the other" party, in a multi-party environment you generally choose an alternative that's quite close in other aspects as well.
> The voters of those left-wing parties identify as "left" so if a Rush Limbaugh encourages people to distrust the "left" then those voters simply distrust Rush Limbaugh instead of altering their vote.
But what about the center?
> if he points out that both Left-1 and Left-2 have a horrible foreign policy, there's likely Left-3 that opposes Left-1 and Left-2 on that policy
That seems to assume there's a party for every combination of views, but is that realistic? How frequently is there a party that's say, hard right on social policy but very left on economic policy? I get the impression that it usually plays out that you get a few parties that are different "degrees" of left or right (say hard left, left, and center left).
I don't think it is that unrealistic (not every combination, but popular ones). The results from parts of Europe that have many political parties, eg. Germany, show voters being relatively fluid over just a few years [1]. The US, on the other hand, has been consistently split in roughly two for ages. The combination of right on social/left on economics may be somewhat strange in the US now (and perhaps the west in general?), but in China it's the norm.
