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.
> 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...
> If enough people are participating in a vote, then the cost of voting (e.g., research + going to polling station) outweighs the benefit (possibility of changing the outcome). The cost of voting is roughly fixed, while the benefit decreases rapidly as the number of participants grows.
Does quadratic voting address this, or are there other ideas you've heard of that address that problem?
I just read a big chunk of your paper "Voting Squared: Quadratic Voting in Democratic Politics", and I really enjoyed it. For a long time I've wanted to do an open source project related to characterizing an optimal government, or at least simulating the outcomes you could expect from different types of governments. If you know of a useful way to go about doing this I'd love to hear it.
By the way, I reside in a coliving space with 50+ people, and we've struggled with voting on certain issues that minority groups feel strongly about. I will definitely be suggesting QV!
This isn't a problem if the individuals apportioning their vote budget are similarly-highly-motivated legislators prioritising from a known raft of policies whilst being well informed about which initiatives are most likely to meet with strong opposition (though it significantly advantages parties able to coordinate the efficient distribution of their votes). Probably they can handle the complexities of a voting budget that compensates the losers too.
But for a broader electorate that doesn't excel in performing stochastic optimisation problems, doesn't have good intelligence to help them vote tactically, doesn't know what future votes might be, the quadratic nature of the voting system doesn't deal with the problem of budgeted and secret voting being a game of iterated prisoners' dilemma; it might even intensify the problems.
It's not too difficult to devise a scenario in which it actually makes the "tyranny of the majority" problem worse: a minority of bigots wish very strongly to enact a law against a minority of regular targets. The disinterested majority wishes to avoid diluting their future voting power by participating, whilst the victimised minority wishes to hold back some of their voting power to avoid being disenfranchised when faced with conceivable future bullying initiatives[1]. In a secret ballot, the bigots can conceivably win if the groups are a similar size (even if they can subsequently reverse the decision)
[1]This is mitigated if the losers get their own votes back as compensation, but actually worsened if they get higher compensation, in which case optimum strategy in a iterated electoral battle is to win by the narrowest possible margin, whilst voting for something incredibly unpopular is a practical way to increase your future influence.
Imagine a scenario in which there are N Jews, N neoNazis (for simplicity: example works if the Jews simply believe the number of Nazis is approximately equal) and yN ordinary citizens. Each individual in those groups has an equal budget to distribute between initiatives V(1)...V(X), where X > 2.
neoNazis desire a "yes" vote for both initiatives V(1) and V(2) - let's call them "internment" and "pogroms" - so strongly that they are (or are believed to be) willing to forego all votes on initiatives V(3)...V(X) to pass them
Jews have similarly strong views on not being interned or the victim of pogroms, but in the absence of adequate information on how the neoNazis will use their votes cannot be assured of allocating their voting budget between V(1) and V(2) in a way sufficient to negate the votes of the neoNazis on both issues. (Note also that the existential threat posed by V(1) and V(2) sitting on the [future] referendum list also deters the Jews from using part of their budget to influence votes on V(3)...V(X) in ways which might improve their individual utilities)
If ordinary citizens have a preference for a "no" vote which would be sufficiently strong for them to vote against it in a regular referendum, but insufficiently strong for them to allocate voting budget that could otherwise purchase decisions on initiatives V(3)...V(X) the moderate majority will not provide the same bulwark against extremism as they do under a 1 person 1 vote system. If all or most Jews decide that pogroms are significantly worse than incarceration and are sufficiently risk averse to warrant allocating all their budget to eliminate the possibility of an equal number of Nazis enacting V(2), it's surprisingly easy and inexpensive in terms of voting budget for the Nazis to pass V(1). The only way I can see the Jews avoiding both initiatives being passed is to put the neoNazis on the defensive with an equally vicious anti-Nazi counter-proposal - assuming Nazis can be targeted as effectively as Jews - but I'm not convinced that mutually assured destruction is the ideal way of resolving voting conflicts.
Unfortunately, this also applies to less extreme examples where balloting is secret and intentions uncertain: in order to shift the Nash equilibrium of a particular proposal in your favour you simply raise the spectre of an [additional, and credible] proposal you anticipate your adversaries will like even less.
One question that comes to mind is whether quadratic voting is the best improvement. I look forward to giving this a read.