Edinburgh Tory councillor on course for Holyrood after winning top-three place in party rankings
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A ballot of Conservative members and supporters gave sitting MSP Miles Briggs the top slot with Cllr Webber number two and sitting MSP Jeremy Balfour number three.
The third current Lothian Tory MSP, Gordon Lindhurst - who did not receive an endorsement from the leadership - was placed seventh, giving him no chance of re-election.
Sources said Scottish Conservative Central Office were confident the party would get three MSPs in Lothian and possibly a fourth on a good day.
The number four slot has gone to Rebecca Fraser, who fought Midlothian at the 2019 Westminster election.
Mr Lindhurst was one of ony three sitting Tory MSPs across Scotland not to be endorsed by a specially-appointed selection committee chaired by the party's Holyrood leader Ruth Davidson.
The committee's list of endorsements were sent out along with the ballot papers for the ranking exercise. It was the first time such a system had been used and prompted accusations of cronyism and stitch-ups.
In Lothian the committee endorsed Mr Briggs, Cllr Webber, Mr Balfour, Ms Fraser and businessman Malcolm Offord, who won the fifth slot.
Around 4,000 members and supporters took part in the process.
A party insider said: "The endorsement system has determined how the vast majority of members and supporters have voted all across Scotland. Basically they have done what the party centrally wanted.
"Gordon is simply a victim of the endorsement system, which massively influenced how people voted."