By far the two topics with the most votes were the game of Nim and Check Digits. Check Digits are appealing, because they relate to barcode numbers that students see every day. I'm a little surprised that Nim was so popular.
I got several votes for Game Theory. I think students want to count cards and make awesome stock trades. I could definitely look into some game theory topics, but I'm not sure it would be as flashy as all that.
Students also expressed interest in doing an independent research project. This could be a chance for students to write a program relating to one of the topics discussed in class. We already did limited automation of apportionment calculations using computer spreadsheet programs, but ran into some trouble when we needed to "guess and check" a number until we found the correct one. These problems could be resolved through programming.