I don't think you want to pick the executive using sortition. I think a better system would be to pick the House of Commons using sortition and then have the Ho

I don't think you want to pick the executive using sortition. I think a better system would be to pick the House of Commons using sortition and then have the House interview candidates for President/Prime Minister. In this scenario the President would be directly accountable to the House and would be required to answer to them. The House would have the right to investigate and replace the President at any time for any reason, which should keep them honest and focused on the job.