I created a poll on a sports forum asking people how they think their favorite NBA team did this off-season. The poll options were: Top 10, Middle 10, Bottom 10. I expect dozens of people to respond, which isn't a huge sample.
The hypothesis I'm testing (unbeknownst to the voters) is that there will be a "homerism" bias which makes the "Top 10" vote more likely. In terms of Bayesian methodology, I would like to compare two models, one has preference weighted uniformly across all three poll choices, and the other has the weight heavily biased towards the "Top 10" choice.
So, my question is how to create the prior and the likelihood functions for this type of problem. I don't need full details, but if you could point me in the right direction, I'd appreciate it.