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He is to stand as the Scottish Socialist Party candidate in Liberton/Gilmerton ward.
Mr Fox, who was a Lothian list MSP from 2003 until 2007, has lived in the Inch for 25 years.
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At the last council elections in 2017 the ward elected two SNP councillors, one Labour and one Tory. This time Labour is fielding two candidates and the SNP is expected to do the same.
Liberton/Gilmerton is the only ward the SSP is fighting in the Capital, and Mr Fox said the party’s activists would be be busy canvassing, leafleting and holding street meetings between now and polling day on May 5.
He said people were worried about fuel poverty and the cost of living crisis.
In a leaflet being delivered to homes across the ward over the next few days, he says Liberton/Gilmerton has one of the highest rates of poverty in the city.
“Most people who are struggling to make ends meet and are working for poverty wages. We will put an end to that by demanding all employers (including Edinburgh City Council) pay at least £12/hour as a National Living Wage. That’s what the Government say you need to earn to pay your own way.”
The leaflet also calls for “an end to profiteering from public services and common spaces in this city” and a free care service "paid for out of general taxation, publicly-owned and run and with quality of care that befits the 21st century”.