Is there an idiom or saying for someone asking the same question many times in hopes of a more favourable answer?

Solution 1:

The term that fits the case is "opinion-shopping". There are online definitions that seem to restrict the use to audit and accountancy: "Opinion shopping is a dubious practice that involves finding an auditor who will overlook any shortcomings in the company's financial reporting. Opinion shopping is prohibited by the Securities and Exchange Commission (SEC)." (Investopedia). But the term is certainly used in wider contexts within UK government circles.