> QV works best with a large number of voters: the more voters there are, the more accurately the system works. QV’s efficiency relies on all voters perceiving the chance of their changing the outcome with an additional vote as the same. When the number of voters is large, such a perception is (approximately) accurate. If it is small, it is less so. With a small population, it becomes possible for people to have different perceptions about the likelihood that an additional vote will change the outcome (that is, the likelihood that there would otherwise be a tie, in which case an additional vote is pivotal). For example, in a small group that consists of a number of moderate voters on one side of an issue, and an extreme voter on the other side, the extreme voter will believe that a tie is less likely than the moderate voters will believe. The moderate voters assume that all voters are (on average) moderate and so discount the possibility that anyone is extreme, while the extreme voter knows that this is not the case because she knows that she is an outlier. If the extreme voter cares more about the issue than the moderate voters in aggregate, she will buy fewer votes relative to her utility than is socially desirable and QV will suffer the same bias towards the majority that other democratic procedures entail, though in a less severe form. If the situation were reversed and the extreme voter cared less than the three others in total, a reversed failure could occur. The three voters are overconfident and expect to win easily, but the extremist knows that, because of her strong preferences and thus her willingness to buy many votes, a tie is more likely than it appears. In this case, QV could lead to dictatorship in the same manner as standard vote buying. Despite this, simulation evidence indicates that QV almost always outperforms majority rule.
Nice.
Then I wonder why HN sounds like a cult on some subjects...
Another thing to think about is too many small minority groups. So for instance, assume there are N questions to vote for and for each of these questions, we have a significant minority group that deeply cares about specific outcome. At some point, because of required increased expenditure, wouldn't votes for all questions favor minority sentiment?
I think we have to understand that while there is a dark side to "tyranny-of-majority", there is an important bright side too: It shields from scenarios where small group of radicals take over the system because they deeply care about their ideas that are not good for majority.