> They see polls that show strong support for policy X
i would imagine those polls are full of selection bias - even if the poller is trying to be as neutral as possible. People who would agree to participate in polls tend to have strong(er) feelings than those who don't.
> referendum process
instead of referendums, there should be a representative vote by the elected politician, but with an option for the voter to submit their own vote (provided they pass a cursory examination that certifies they have read and understood the bill they're voting for).
E.g., a senator or an elected politician has N number of votes for a bill, where N is the number of people he/she represents. If those people don't want to participate in a bill voting process, the politician will vote on behalf of them (like they do now, supposedly).
However, an individual voter who wishes to, can certify their understanding of said bill, and rescind the representative vote for his electorate and vote himself directly on the bill. The politician will now have N-1 votes on that same bill.
This means for issues of importance, the individual can choose to participate. For issues that they don't care about, but have a vague sense of direction, they have their votes delegated to the politician that they elected once every X years.