It seems there're quite a few people who believe that voting eligibility should depend not on your citizenship, but simply on whether or not you pay taxes.
So a country's permanent residents and even those with work visas should be allowed to vote.
Some might even extend this to illegal immigrants - and even illegal immigrants who don't pay income taxes, since sales taxes are also taxes (furthermore, I cannot imagine the young, the unemployed and the elderly, most of whom will not be paying income tax, being denied the right to vote based on their not paying income taxes).
The logic, presumably, is that if you live in a country and contribute to its financial well-being, you deserve to have a say in what your tax dollars are used for - and ultimately the future of the country, since you live in it. This is a further step in the argument that foreigners should get just as many benefits as citizens and permanent residents (see: Citizens and Permanent Residents vs Foreigners for why they shouldn't, even for benefits) and in the end, leaves even less distinction between citizens and non-citizens than ever. Coincidentally (or maybe not), I saw this proposal being floated in relation to the topic of Brexit, and this is by no means a fringe proposition - in the UK the Labour Party tried a version of this, and attempted to allow EU nationals to vote in UK general elections.
Besides the various other problems with this proposal (for one, those proposing it tend to favour open borders, and for another it's pretty easy to see how this is a cynical attempt to flood the electorate with new voters who'll support left-wing policies), without the right to vote, the only reasons one might want to become a citizen, then, are national pride, consular assistance and possibly protection from being deported in extremis. Then again, to liberals, in developed countries nationalism isn't kosher (note that only developed countries would ever consider giving non-citizen the vote), they are against deporting people and for all we know they would want non-citizen residents to benefit from consular assistance too. On reflection, though, if you believe national borders are obsolete, there's no reason you would want any distinction between citizens and non-citizens.
More fundamentally, this proposal devalues voting by tying it purely to economics rather than higher concepts of belonging and nationhood. This is ironic given that the left has traditionally sniffed at arguments predicated on economics.
Someone objected that investor visas are already tied to economics, in the sense that you can "buy" a visa, which a few years later can give you citizenship and thus the right to vote, but at least in theory spending money is not enough - you're supposed to *invest* it. And then, in the UK for example (since this is the country in whose context this objection came up), for the visa to remain effective, you need to show that you have earned income from your investment, which means you're not simply buying it.
Besides which, the citizenship arising from the investment visa is both a second order effect (not a direct consequence of the visa) and time delayed (you can only get citizenship after a few years on the visa), which means one cannot sensibly call investor visas tying the vote to economics. Practically speaking too, investor visas are so hard to get that the effect on the franchise is not going to be significant - even if one waits around to get one's citizenship. This is in contrast to giving all taxpayers voting rights.
Related posts:
Citizens and Permanent Residents vs Foreigners
Why giving the young more votes has implications you will not like