The one problem that I had with the previous political implementations was not only that it was "easy" to change the political balance of another country with a few short years of espionage, but also that any changes which did occur either had no real effect, or a radical one. If, for example, the US went from a Democratic party controlled government to a Republican controlled one, there was no real change in policies, and the same ministers remained in place. If FDR lost the election, why would the Republicans leave him in office? Political drift and other effects should be moderated by shifts in the cabinet and in the ruling party: if a left-leaning democratic party is elected, they should be more sympathetic to Communists than Fascists, while if a right-leaning democratic party is chosen, they should view the Communists as a bigger threat than the Fascists. In HOI3, there was no difference.
Go one step toward a Right-wing Republic or Autocratic government in HOI3, and suddenly the Nazis are treated as fine upstanding members of the international community and the Communists are Satan incarnate. The reverse holds for left-wing equivalents. It's "all or nothing".
An election should either result in a cabinet chosen by the newly elected party (with the heads of State and Government being members of the leading party), or consist of a proportional mix of all organized parties which got enough votes to be represented, depending on the type of government. Each minister should contribute a small amount of "drift" in favor of his own faction, so an equally-divided cabinet should exert little influence on the overall country's direction, while a cabinet almost exclusively from one party would cause a stronger effect.
In addition, one should be able to have some effect on the political direction of one's own country, not only by selecting ministers, but by manipulating public sentiment, changing laws, and generally strengthening public support for one or another course of action.
Politics should matter more, but it should be harder to change.