[PokrLikeItsProse]

This may be outside your area of interest, but I see problems in the area of political legitimacy.

Democracy isn't about maximizing fairness, it's about maximizing legitimacy while maintaining a satisficing condition of perceived fairness.

Consider case 1, where you suggest letting people vote on a fraction of all possible candidates/issues. What happens if you give a person n votes, and he has equally strong opinions on n+1 issues? Will repeated iterations of this situation cause a sufficient number of people to question the legitimacy of the system and ultimately lead to its abolishment?

Consider case 2, where 49% strongly oppose something, 41% weakly support it, and 10% rabidly support it. I don't know if this is sufficiently similar to your proposed case to be relevant, but I suspect that it is, since it is more probable than the entire majority having weak support for a position. How often will someone be in that 10% who get overruled by the minority's strongly held beliefs before they start questioning the system?

You would see the same question of legitimacy pop up if you proposed the solution of creating a barrier to voting so that people with weakly held opinions are less inclined to vote, a situation which some argue exists today.