Online elections. Think of how many more people would actually vote in the US if it were online. The 2008 election had 63% voter turnout, which is historically high, but is nothing compared to countries like Italy with 90%.
Obviously, there are huge security concerns and it would be a logistical nightmare, but that's what someone needs to solve.
In Denmark, turnout is consistently 80+%, and we don't have online voting. Clearly, it's not the lack of online voting that's the (sole) problem.
I can see how it's practical, and probably inevitable in the future, but quite frankly, if you can't be bothered to spend an hour every two-three years voting, I really don't need your input on who should be in charge.
Voting should be harder, if anything. Then politicians would have a higher lowest common denominator to speak to.
I don't think low turnouts are the biggest problem with voting as it is done today. No use in having 99% participate if the process remains easily gameable, influenceable and opaque.
If not proper elections at least a whole population simulation before the polls. That way people could express their true preferences without fearing that their vote will not count if it goes to a fringe candidate and would reassure them that they're not as few as regular polls and eventual results usually show.
Surely the issue is voting systems that do not rationally incorporate each voter's preference equally?
Unless you're suggesting iteration as a way to get around Arrow’s paradox? I'm not sure if anyone has tried it - could be interesting? But if not, then ranking candidates get you the same results.
Few voters will express their true preferences and will go instead with 'the lesser evil' when they fear their option will be in a small percentile and discarded. It is not unusual to have systems where 5% is required for a party to get into the parliament, or for a nominee to get into preliminary rounds, etc.
So one cannot expect a voting system to incorporate all voter's preferences if they are very small but a warm-up voting would reveal that the fringes that big media avoids covering can become popular.
By 'online', I assume you mean online from your home/office. There is no way, I can think of, to prevent someone else from watching how you vote in that scenario, which pretty much stops the idea dead in the water.
Canada and Australia at least allow the census to be completed online. There's probably less motivation to rig the census than the election (though there are benefits to both) but it's still an interesting point.
Obviously, there are huge security concerns and it would be a logistical nightmare, but that's what someone needs to solve.