What about deciding who sits on the Troll Throne by:
1- a vote by nobles, bribes allowed
2- a game of skill, weighted by the amount wagered by each candidate
3- a game of chance, weighted by the amount wagered by each candidate

Give a third weighting to each component, the winner takes 50% of the pot from 2- & 3-, the remainder goes to the town coffers.

Either have challengers pay a fee to challenge, or have a periodic selection at regular intervals.

Always the option of fighting battles to decide who is King, but a formal process could work too.