"Why should we be skeptical of my simplified puppies/kittens example?"
Great post. So the utility function assumes there is no value in voting your preference. There is value assigned to the payout and the outcome, but what about the act of voting your conscious. I'd propose that in addition to your vi (value if your preference wins) and p (payout), there is additional value to your voter or "agent" in simply having voted their preference. This is why people vote for third party candidates in US presidential races, right? If we introduce another variable, say "ci" for how much the voter values voting there conscious, I think you potentially end up with multiple Nash Equilibrium, particularly where ci is greater than p.
DING DING DING!!! Everybody upvote this guy! Yep, that's the answer I was hoping somebody would give. Ignoring your "conscience-value" ci is the trick that lets us claim uniqueness of Nash Equilibria, which makes the result sound much more convincing than it should be.
I don't have time to think about it now, but it might be interesting to see if including ci could lead to anything weird, unexpected, or perverse. I'm fairly certain that in the simple two-choice model, ci would only make our equilibria look better, but sometimes these things can surprise.
Thanks! We could call "ci" the integrity variable.
@biophil thoughts?