@toby-pereira Thanks for the feedback!

National elections generally take place several years apart and a lot can change in between, and so voters wouldn't be able to apply game theory in the same way as they would with multiple elections close together under the same conditions. And also I imagine people in the study are more likely to be "clued up" than the average member of the public.

One of my goals is looking towards what the long-run equalibria might be after people have figured out the system. So in this way I see that as a plus.

So that raises a question - with multiple elections, will it just be the same conditions each time just to see how the methods behave in these ideal conditions, or will certain variables change to make it more "realistic", or possibly you'd model both? Both would be interesting in their own ways.

In trying to set up the models one of my conclusions is that a "correct" set of parameters doesn't exist. I think instead of trying to make a study "correct" or "accurate" it would be more useful to search for robustness. A common result of repeated games is multiple Nash Equalibria. Another common result is sensitive Nash Equalibria. So if one number changes slightly a whole new set of equalibria might be optimal now. So I think it is important to vary conditions to see if an equilibrium is stable.

Reading on different strategies and failure conditions of voting systems you come across some really weird ones where it is technically optimal to do make some really weird decision. But that often requires very specific information. An important concept I came across while brushing up on my game theory is imperfect and incomplete information. When you change the information available it can sometimes change what the Nash Equilibrium strategy is. There's also an idea that a strategy might not be optimal over any specific set of game parameters but is optimal when you are unsure of the exact parameters. The more limited the information the simpler a game sometimes becomes.

If you have an allocation game dividing a budget, a pizza, etc... this game is zero-sum in the sense that a you getting a slice of pizza is a slice that isn't going to me.

If you are negotiating with an agent who you are unsure is altruistic, rational, or spiteful there is a strategic incentive to misrepresent as a spiteful agent. An altruistic agent gets less than their fair share and a spiteful agent gets more than the rational agent if they can credibly convince other agents they are spiteful. It is worth it to pay off a spiteful agent rather than provoke it.

So if you are trying to optimize for the social choice there's a big problem with spiteful agents. With limited information all agents are incentivized to misrepresent as spiteful and over-represent how much they care about minor concerns. And for making social choice with limited resources there is a genuine zero-sum nature to the problem. Rational agents operating in a zero-sum environment will behave spitefully (you having it is negatively correlated with me having it.)

So with that irrationality baked in, if we could magically find what the social choice was, with spiteful agents the social choice isn't very sociable. And spiteful agents should be common under resource constraints. This correlation between individual's utility functions will also heavily restrain the types of group choice sets which exist.