I always thought that voter turnout would be huge if you combined voting with the lottery. One vote, one chance to win!
I would be very afraid of an electorate equal to the union of "the set of all people who wish to vote" and "the set of all people who play the lottery".
Yeah, that's all we need. The majority of lottery players are low-income & low-IQ (that's why they call state lotteries "a tax on the poor & the stupid"). So we'd get millions of people from society's bottom-end packing the voter's booths (probably multiple times), not because they understand the issues and want to make positive changes in how we are governed, but for a shot at getting rich quick.
Increasing voter turnout is unimportant. What's important is getting people well-informed and sufficiently involved in our government. Voting should be somewhat difficult, not made less difficult (e.g., Clinton's "Motor Voter" law); it certainly should never be financially rewarded. If people are too complacent to register or make it to the polls once or twice a year (for the right reasons), then they are surely too complacent to spend the time and mental energy understanding the issues.
Or is all that too un-Politically Correct for you?