> I don't think having the vote and having the basic income is compatible with each other. Why aren't people going to vote themselves larger basic incomes every year?

The same reasons that people vote themselves lower taxes every year, though they do vote themselves lower taxes sometimes: 1. We don't have a direct democracy, so people don't vote for policies directly; 2. Quite a lot of people, even if they can't analyze all the implications, can see that voting yourself a lower net contribution to government (either via lower taxes or greater benefits) has consequences that may be undesirable.

> How can you both have the (modern conception of the) vote, and a basic income at the same time?

The same way you can have the modern conception of the vote and have taxes at the same time. Mostly, this involves relying on an electorate that is largely composed of at least modestly responsible adults, rather than infants that gorge themselves on candy without limit given the opportunity without thought of the consequences.