I'd already said in a previous answer that I always vote in all elections, so I couldn't say that any of those would make me more likely to vote, but I hardly wanted to anyway. What a dreadful set of options! Thankfully, they offered a box underneath so that I could explain my answers:
The people administering this questionnaire are Electoral Reform Services, whose business is precisely this - to provide the voting apparatus for surveys and elections. They happen to be partially-owned by the Electoral Reform Society, who know all about STV as their primary purpose is to campaign for it, and indeed share my concerns with online voting and voter ID too - but they won't have had any input into the questions for this. Rather, the questions seem to have come from the Electoral Commission, who are responsible for running and ensuring the fair conduct of public elections in this county, and have here employed Electoral Reform Services to conduct the survey. Since some of the questions referenced types of elections which don't apply in Leeds (e.g. mayoral contests), I assume the same survey is being offered to people confirming their electoral eligibility online all over the country.
Given all that, it worries me a lot to see these questions, as it suggests a very real risk of the methods listed being introduced (or extended, in the case of voter ID which has already been piloted to poor effect) in this country. And yet still no prospect of any actual improvements to our electoral system, such as STV. :-( I only hope they get a lot of responses along the same lines as mine, basically saying "All these ideas are rubbish - STV NOW!"
If you share my concerns and get the chance to fill in this questionnaire yourself, please feel very free to use my answers as inspiration.