The proposal calls for adults to be paid an unconditional income of 2,500 Swiss francs ($2,555) a month, whether they work or not.
Supporters of the idea say 21st Century work is increasingly automated, with fewer jobs available for workers.
However, polls suggest that only about one quarter of Swiss voters back the idea.
Under the terms of the basic income, workers who already earn more than SFr 2,500 would not get any additional money.
There is little support among Swiss politicians for the idea and not a single parliamentary party has come out in favor.
They say that disconnecting the link between work done and money earned would be bad for society.
Che Wagner, from the campaign group Basic Income Switzerland, says it wouldn’t be money for nothing.
“In Switzerland over 50% of total work that is done is unpaid. It’s care work, it’s at home, it’s in different communities, so that work would be more valued with a basic income.”
Luzi Stamm, who’s a member of parliament for the right-wing Swiss People’s Party, opposes the idea: “Theoretically, if Switzerland were an island, the answer is yes. But with open borders, it’s a total impossibility, especially for Switzerland, with a high living standard.
“If you would offer every individual a Swiss amount of money, you would have billions of people who would try to move into Switzerland.”
The idea is also under consideration elsewhere. In Finland, the government is considering a trial to give basic income to about 8,000 people from low-income groups.
In the Dutch city of Utrecht is also developing a pilot project which will begin in January 2017.
The basic income is one of five issues on the Swiss ballot on June 5, with people also voting on funds for public services and the simplification of the application procedures for asylum-seekers.
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