Well, here in Canada...except maybe in Quebec...it is actually often a negative benefit to be in a marriage situation. I am not sure how students could benefit from it at all, as they already get substantial benefits. They usually have negligable income & taxes anyway.
There is currently no income splitting in Canada (the Conservatives are promising this in 2015 - yeah right). Also on Federal taxes you only get one full-value dependant (though the others count for social benefits & social assistance).
Most government social benefits & assistance are already based on household income (not even just spouses), so unless they commit outright fraud and do not disclose the other spouses' incomes, the low income wives would lose their benefits by joining such a union. However, anyone willing to do that is likely doing it already, and just not gotten caught.
Where there could be exploitation is in things like where one person works and gets family benefits - such as dental care. These policies would likely change in the face of polygamy legislation, or one working person could claim dental benefits for themselves, all the spouses, and all the children. If 2 or 3 did, then the plans can double-up to the point of the ridiculous.
Now, as opposed to students, if a group of single mothers got together with a man...with an intent to commit fraud, it is still not clear that they would benefit. They would lose any social assistance if any members of the family were working, if the working members incomes were high enough, there could be tax savings from additional dependants, but would it be enough to offset the low-income benefits that would have come to the non-working ones? I strongly doubt it.
I know a woman with 3 kids who made close to $1000 a month in social assistance plus another $1000 a month in child-tax benefits (total of provincial and federal), those amounts both tax free. The tax benefits to a high-income earner would not come close to that.
So, actually, I think the fears of fraud - in Canada - are somewhat limited.
In the US, where the tax advantages are potentially high, and social benefits are lower...it would likely be a different matter.
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