Depending on which issues matter to you, there are a lot more than 4 dimensions.
I'm a fun example. Of the major candidates in the last election, preference list read (best to worst) Ted Cruz, Bernie Sanders, (big gap) John Kasich, Donald Trump, Marco Rubio and Hillary Clinton. This does not fit with ANYONE's idea of the political spectrum.
Why that order, and how do the most oppositely polarized candidates wind up on top? My top issue is NSA surveillance. Ted Cruz opposed NSA surveillance and has publicly voted and taken a stand on it. Sanders has questioned it and been luke-warm against it. Kaisich at least made some comforting noises about controls. The only good thing to hope for about Trump is that he will be incompetent. The remaining two are strongly pro-NSA and bureaucratically competent enough that they would have been able to push the NSA agenda forward.
That said, people like me are weird. As survey data shows, the parties are polarizing along the traditional left/right divide. See https://www.people-press.org/2014/06/12/political-polarizati... for data showing that now over 90% of Democrats/Republicans are farther left/right than the average Republican/Democrat. While back in the mid-90s, there was a much, much larger overlap of views.
It seems like even personally identifying as conservative or liberal is a fairly new (last 30 years) change. Time was it meant "stay the course" vs "shake things up", which are reasonable things the change your mind about from election to election, or federal vs state elections. Now the parties are just sports teams, and you support your side as a matter of personal pride.
Look at Reagan's last election - he was hugely popular, and won by a massive margin in the electoral and popular votes. A big chunk of the country was happy voting for a democrat before Reagan, and went back to voting for one after him. I can't imagine a scenario like that these days.
In the US we have only two political parties that are able to regularly elect people to national offices. So yes, its pretty one-dimensional politicking here.
so peculiar that while existing in a 4d space, we are so prone to believing that politicians only operate on a 1d vector.