raisinbrahms

Google is your best friend.
But to give you a head start, there are quite a few social psychologists who study the questions you're interested in. Most of them are in psychology departments, some of them are in business schools, a handful are in political science departments, and a few are in communication. There are also political scientists and probably others scattered through different fields who do this sort of research, though the predominant methods are likely to be fairly or very different across disciplines.
Here is a very partial list of (mostly social psych) researchers you might want to look up:
Dan Kahan (Yale)
Linda Skitka (UIC)
Jesse Graham (USC)
John Jost (NYU)
Peter Ditto (UC-Irvine)
Aaron Kay (Duke biz school)
Leonie Huddy (SUNY-Stonybrook - political science)
Jaime Napier (NYU-Abu Dhabi)
Richard Petty (OSU)
Ingrid Haas (Nebraska)
Jarret Crawford (College of New Jersey)
Matt Motyl (UIC)
Christopher Federico (UMN)
Jonathan Haidt (NYU biz school)
Brian Nosek (UVA)
Kurt Gray (UNC)
Ariel Malka (Yeshiva University)
Curtis Hardin (CUNY Grad Center)
Jon Krosnick (Stanford communication)
John Bullock (UT-Austin political science)

Start with the first 5 and see what jumps out at you.
I'm entering a social psych PhD program this fall to study (in part) political psych-related things. My BA is in history and as of 2 years ago I had basically no psych research experience. If you're interested in doing a PhD, here's what I suggest you do:
- read some papers by researchers whose work interests you
- Google PhD programs where the researchers you're interested in are on faculty
- check out http://www.ispp.org/ 
- study for and take the GRE well enough in advance that you can take it a second time without feeling pressured
- get a copy (you can rent to save money) of the Oxford Handbook of Political Psychology (Huddy/Sears/Levy), read the table of contents closely, flip through it, read the sections that seem important/interesting/relevant
- find a way to take a few psych classes at the undergrad level - especially intro to statistics (the more stats the better), and research methods 
- volunteer in a research lab (it's not that important that the topic be what you're interested in long-term) - those undergrad classes will be a good way to connect with a prof for this purpose, but you can try just emailing local faculty if necessary
- make a good impression on your profs and research supervisors/mentors so you can ask 3 of them for letters of recommendation when the time comes
- several months before applications are due, email faculty you want to apply to work with
This is all probably a 2 year investment minimum.
Your undergrad major won't hurt you. Neither will your lack of a writing sample, unless you decide to go the polisci route (social psych programs don't require one). You will need research experience, a decent GRE score, strong letters of recommendation, and probably some coursework.
Send me a PM if you want to follow up. Good luck.