I hadn't realized this, and your comment is too late to gain many upvotes, but yes - very good point.
Couldn't you solve this by requiring any randomly-elected candidate to have at least, say, 1% of the popular vote, though? (This means that you don't entirely eliminate strategic voting, unless people can specify a fallback option; but it reduces it by a lot.)
Couldn't you solve this by requiring any randomly-elected candidate to have at least, say, 1% of the popular vote, though? (This means that you don't entirely eliminate strategic voting, unless people can specify a fallback option; but it reduces it by a lot.)