Power in games
Look for any kind of real-life examples where some kind of vote takes place. Model and determine the power that each involved party has using the Shapley-Shubik power index. Here are some possibilities.
Find out how much power each state has in the US presidential elections according to the Shapley-Shubik power index.
Are there student elections at your school? Do you vote on certain school decisions? How much power do you have in an election where each department has one vote, but some departments are larger than others? What kind of majority is needed?