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The proposal had called for adults to be paid an unconditional monthly income, whether they worked or not.
Supporters said since work was increasingly automated, fewer jobs were available for workers. Switzerland is the first country to hold such a vote.
No figure for the basic income had been set, but those behind the proposal suggested a monthly income of 2,500 Swiss francs (£1,755; $2,555) for adults and SFr625 for each child, reflecting the high cost of living in Switzerland. It is not clear how it would affect people on higher salaries.
There was little support among Swiss politicians for the idea and not a single parliamentary party has come out in favour, but the proposal gathered more than 100,000 signatures and was therefore put to the vote under the Swiss popular initiative system.
Critics of the measure say that disconnecting the link between work done and money earned would be bad for society.
But 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."
The popular initiative system
Allows citizens to suggest changes to the federal constitution
All initiatives that gather 100,000 signatures in 18 months go to a public vote
A constitutional amendment by initiative not only requires a majority public vote but a majority of cantons must also approve it
Differs from the mandatory referendum, which is called by parliament and does not need public signatures
But 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," he says.
"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 wording on the initiative was vague, asking for a constitutional change to "guarantee the introduction of an unconditional basic income" but with no mention of amounts.
And in the Dutch city of Utrecht is also developing a pilot project which will begin in January 2017.
Another four issues were on the Swiss ballot on Sunday.
A proposal to speed up the country's asylum process. The projections suggested 66% in favour.
The Pro Service Public initiative proposing that bosses of big public sector companies should not earn more than government ministers - a reflection of dissatisfaction with railways and telecoms provider Swisscom - is also being rejected by 67%.
A proposal to allow genetic testing of embryos before they are inserted in the uterus in cases of in-vitro fertilisation, where either parent carries a serious hereditary disease, was projected to pass with 61%.
Transport financing: An initiative from the car lobby which wants more investment in roads. The government had urged a "No" vote, and it appears to have been rejected by 70%.