u/Jack_Faller

It's kinda annoying how the game makes you build that tiny little square. Increasing the bookshelf radius would be really easy and allow more interesting designs to be created. They already let you make Nether portals any shape so this is a similar idea.

Glad they put that warning there.

For background, I was trying to work out expected returns on that red/blue Twitter button thing, and I found something rather peculiar.

Suppose you have an election among N people with two outcomes. For the sake of simplification, we'll say the they vote randomly with equal probability for both options. Where other people vote for either option by a margin greater than one, your vote is meaningless, so the only case we need consider is when the vote is split 50/50 and you have the deciding vote.

To create a tie, you can choose N/2 people which gives N!/(N/2)!(N-N/2)! = N!/(N/2)!² possible ties out of 2^(N) outcomes.

So if the utility for a policy being implemented on one person is X, then NX is the utility of it being implemented on N people. The final expected utility for voting in the election is N! * NX / (2^(N) * (N/2)!²), which when I graph it for X = 1, I get the attached image which looks roughly logarithmic but seems to grow faster than any logarithm. The implication is that there is greater utility in voting in larger elections, which I suppose lines up practically when you look at participation rates for elections.

Is this logic sound, and does anyone have any idea what the final function is?