@andy-dienes This is very interesting Andy. It is similar to the conclusions we got from the original simulations which did not include strategy. By this I mean that there was a clear trade off between desirable things. We decided that this trade-off would be skewed by the strategic considerations so it was hard to choose which was best without that. We were using the term Pareto Frontier to refer to this set of trade-offs. I suspect that since the set of choices is a small number of models not a continuously variable property there is a solution which is "best".

About the interpretation, the original simulations where a histogram of the number of simulated elections showing each property. Yours show the mean (?) of each property by the % of strategy. The difference in shape of histogram was important. Particularly if you look at things like "fully satisfied voters" for allocation methods. There are a few ways to solve this. The most obvious is a 2d histogram with the axes of percent insincere and the metric in question. This would prohibit the ability to show multiple models at the same time. The other is to show different metrics other than the mean. You could for example show the standard deviation as an error bar on each point. This would also give you an idea of if the differences are "large". Note that this is not the same as if they are "significant".

For that you would need the standard error on the mean. Judging by the fluctuations between bins you seem to have run about the right amount of simulations needed to distinguish so that is likely not an issue.

To see if things like the "fully satisfied voters" goes away with strategy I would just choose a few points on the percent insincere line and make the same plots as in the original simulations. eg 0%, 25%, 50% and 75%. If the histogram shape is the same at each point then you do not need to dig deeper. I hope this makes sense