One part of Canada's tax-transfer system increases inequality of wealth. That's not an unfortunate side-effect of the policy; it is deliberately designed that way. It would be very easy to design it differently so that it did not increase inequality.
The policy in question reduces the wealth of many people by a small amount, and makes a very small number of people very wealthy. Those who get wealthy as a result of this policy do so by sheer luck. Nobody argues that those who gain wealth are more morally deserving than those who lose wealth as a result of this policy.
Most government tax-transfer policies try to increase equality, even if there's a cost to doing so. We could scrap some of those tax-transfer schemes easily, and save on those costs, if we wanted to increase inequality. But this particular policy is designed to increase inequality, and has an administrative cost of doing so. By scrapping this particular policy we could increase equality at a negative cost.
The policy in question has cross-party support, at all levels of government. Some parties might want to modify this policy a little, but as far as I know none of the major parties wants to scrap it altogether. And the policy enjoys popular support as well. Anecdotal evidence suggests the poor are especially likely to support this policy.
Any outside observer who looked at this policy alone would conclude that Canadians wanted to increase inequality of wealth. And Canada is not alone.
I'm talking about lotteries. Lotteries redistribute wealth and increase inequality in a way that depends on sheer luck. Lotteries have an administrative cost, and so reduce average wealth. Sure, some part of the revenues are used to fund good things. But a simple lump sum tax on everyone could do the same funding, without increasing inequality at the same time.
A libertarian would find no paradox here. If people voluntarily join a club that increases the inequality of wealth of club members in some morally arbitrary way, the libertarian has no objection. Because it's a voluntary club. A libertarian would also not object to voluntary transfers from rich to poor that reduce inequality. As far as the pure libertarian is concerned, the only thing that matters is that it be voluntary. Whether it increases or reduces inequality is not what matters.
But very few people are libertarian.
Nearly all the rest of us say we value equality, and want the government to use its power to promote equality, providing the cost of doing so is not too great. The benefits of an extra dollar to the poor are greater than the benefits of an extra dollar to the rich. We argue only about which inequalities are morally justified, and how big the costs are of reducing inequality, and whether the costs are worth the benefits.
But when we buy lottery tickets our actions say that we want more inequality. When governments sell lottery tickets their actions say they want more inequality.
We do not begrudge the wealth of lottery winners. Even though we know they are not morally deserving of their wealth, and got it through sheer luck. Perhaps precisely because they got it through sheer luck, and so can't pretend they are more morally deserving than we are (which is what gets us really annoyed at the rich).
There's something paradoxical here. Are we really closet libertarians, despite what we say? Do we really support more inequality, despite what we say? Do we really believe the Utilitarian doctrine that says the poor benefit more from an extra dollar than the rich?
An ultra-quick Google says that one quarter of Canadians buy lottery tickets weekly. That means, at an absolute minimum, one quarter of Canadians want (have a revealed preference for) more inequality. They put themselves behind the Rawlsian Veil of Ignorance, and vote for more inequality.
None of this makes sense to me.