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The Lib Dems are confident Alex Cole-Hamilton will be re-elected as MSP for Edinburgh Western, but hope they could also win enough votes to get a list seat as well, which would mean lawyer and former city councillor Fred Mackintosh getting into Holyrood.
Mr Rennie, who visited the Edinburgh Dog and Cat Home yesterday, said he had spoken to many people who backed independence in the 2014 referendum and had repeatedly voted SNP but who were unhappy about Nicola Sturgeon wanting to pursue indyref2 while people were still worried about the aftermath of the pandemic.
And he claimed these voters were switching to the Lib Dems where the party was a credible contender.
"We have a message which reaches out to SNP supporters who are not sure about pushing independence now.
"We're saying whatever your views on independence – and we don't want it but other people do and we respect that – they've got to agree now is not the moment to pursue independence when we need to focus on recovery. We're not arguing with them about independence, we're saying let's come together because we'll need the skills and talents of everyone in the country to get through this recovery.
“We're not being like the Tories who are ramming it down your throat, we're trying to reach out and attract people to focus on the recovery for now ."
The Lib Dems did not do particularly well in the list vote in Lothian last time, but Mr Rennie points to the party's strong showing in the 2019 European elections in Edinburgh, when it took 23 per cent of the vote. "It shows the potential," he says.
"We're feeling quite good about the Lothians – in part because of that but also because Douglas Ross is not Ruth Davidson, which is a big factor.
"The Tory campaign this time is darker and they've not got the bubbliness of Ruth which was quite an appeal last time and attracted a lot of our people over to them."
The Lib Dems are also asking those opting to vote Tory or Labour as a way of stopping the SNP winning constituencies to vote Lib Dem on the list.
"We're appealing directly to people who feel they need to vote Conservative in Central or for Daniel Johnson in Edinburgh Southern that they should vote for us on the peach ballot paper.”
Mr Rennie says Edinburgh’s crucial culture and arts sector would benefit from the Lib Dem plans for a £50 million “Show Must Go On” fund which would create graduate internships in the arts, pay for theatre seats so there doesn’t have to be a full house to be viable and also set up a government-backed cancellation insurance scheme.
"If get pandemic planning right that insurance would never be required, so hopefully it will be a cost-free option, but it’s about giving the sector the confidence to plan events without the fear of losing all their money on cancellations.”
Less popular – especially in Edinburgh Western, which includes Edinburgh Airport – may be the party’s proposal to “limit air transport” with a frequent-flyer levy.
Mr Rennie says the policy is to encourage responsible flying. “Getting foreign travel back up and running again will be important for the future of the industry but we need to get it to a state where it’s sustainable for the environment. This proposal allows that to happen – people are discouraged from going on frequent, particularly short, flights. It won’t affect the holidaymaker who is going once a year, but has an impact on people who are frequently flying shorter distances.
“It’s about gradually changing behaviours over time. We think its important in order to tackle the climate emergency. We'll do it in tandem with the airport to make sure the airport is sustainable but the airport equally needs to be environmentally sustainable too.”