A formal coalition refers to a group of people or organizations working together officially and following specific guidelines or agreements. Full definition
The former SNP leader said he had «no idea» whether a Labour government emerging from such a process would have Mr Miliband as its leader, and suggested that he was wrong to have ruled out formal coalition with the SNP so firmly (dailymail.co.uk)
Labour has had two experiences of formal coalition. (leftfutures.org)
A full and formal coalition agreement to cover the less contentious areas will be published before the Queen's speech on 25 May. (theguardian.com)