@toby-pereira yes monotonicity fails, but I think pairwise probability margins are apparently monotonic.

I think maximal lotteries are interesting too, and I wonder if it makes sense to compensate the dissatisfied majorities with electoral credit to spend in subsequent election(s).

For example, say the maximal lottery (or maybe any other Condorcet method) elects A when there is no Condorcet winner. Let beat(X) be the set of candidates that beat X in a head-to-head majority.

Then for each B in beat(A), it seems like the majority preferring B to A should be compensated in some way. My thinking is that in aggregate, that majority should be compensated by something like the smallest extra weight they would have needed to secure B as the (Condorcet) winner against each C in beat(B). This might get complicated, and there may already be literature on this kind of thing.

@kaptain5 said in Professional Politicians skew towards altrusism? [study to read]:

In this study an interesting finding was that on average politicians we behaving altruistically (giving more to the other party than they would receive). On average over all sampled politicians were giving 49% of the prize to political opponents and giving 57% to in-group members. Compared to most other studies of the ultimatum game this is far above most people and very far above the rational expectation. The result is also remarkably consistent between countries. When the out-group and in-group results are combined this gives the result that the politicians surveyed are slightly altruistic in the game.
This one surprised me, I expected the politicians surveyed to be much more greedy.

I haven't properly read the paper but this bit is interesting, and I've been considering whether we should be surprised or not. Politicians certainly have a reputation for being greedy and corruptible. But a lot of people who go into politics probably do so for the right reasons - that they actually want to make things better for people and remove unfairness etc.

I think there is more corruption at the top, but this isn't most politicians. Plus I also think that higher-up politicians might still have some good principles, but these conflict with other things that get in the way of that - wanting to get in with the right people, make the right deals etc. So removed from politics, they still might make fair decisions. They just happen to be morally weak in certain ways.

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.