How can we break the Brexit deadlock? Ask ancient Athens (sortition)

Look at the big lottery winners for the past few years, the ones who got pictures in the paper.

Ask yourself will they really be better than the current Governor/ President/ prime minster?

At the very least The process of getting elected does have some selection in it - for all its faults, a 2 year presidential campaign does at least weed out those who could not stand the pressure of the job itself.