The median voter has very little impact on policy.
Gerrymandering has assured most political parties maintain their seat, no matter what the voter does. That is why we have red states and blue states. Bush was unpopular, McCain equally so. Obama was an unknown, hyped by the media, with many Independants, and even some Republicans, voting in his favor, yet 22 states voted for McCain.
The only the way the voter has any impact is when they have power to change things, that requires:
1. The 80/20 districts are redrawn to 50/50.
2. It requires re-writing campaign contribution law, so special interests don't overwhelm the voter with political ads.
3. It requires separating special interests from the media, so they go back to being the watch dog that tracks campaign promises to to results, and follow up on the results of policy, not it's intent.