Thanks for the shout out on my reply on part three. Two comments: One, I may create a post on working out the "vote-your-conscious" impact as I can't stop thinking about it. And two, on your question: Did I "rig the game" and set up my level-k model in some way that guaranteed I'd get the same result?

I started to write a comment questioning Type-1 being overly pessimistic about the preferences of future voters. I was still thinking puppies and kittens. If Type-1 voters believe that preferences over any significant amount of time are 50/50, then a rational Type-1 player is almost always incented to vote their preference. (50% of vi + P is more than 50% of P if we are calculating potential payouts at the time of voting). However, I realize your example here is much more complicated in that there are multiple choices (or posts) to chose from, so the pessimism of the Type-1 voter is warranted.

I think your analysis further supports (if we are to believe we are rational actors to any degree) the idea that there is a value to the voter in voter their preference. Otherwise the first post to gain any advantage would always skyrocket to the top. I'd love to see some empirical analysis on Steem data on whether such a tipping point exists!!!