I think you can’t really assume “that we (for some reason) can’t convert between and compare those two properties”. Converting space of known important properties of plans into one dimension (utility) to order them and select the top one is how the decision-making works (+/- details, uncertainty, etc. but in general).
If you care about two qualities but really can’t compare, even by proxy “how much I care”, then you will probably map them anyway by any normalization, which seems most sensible. Drawing both on a chart is kind of such normalization—you visually get similar sizes on both axes (even if value ranges are different).
If you really cannot convert, you should not draw them on a chart to decide. Drawing makes a decision about how to compare them as there is a comparable implied scale to both. You can select different ranges for axes and the chart will look different and the conclusion would be different.
However, I agree that fat tail discourages compromise anyway, even without that assumption—at least when your utility function over both is linear or similar. Another thing is that the utility function might not be linear, and even if both properties are not correlated it might make compromises more or less sensible, as applying the non-linear utility function might change the distributions.
Especially if it is not a monotonous function. Like for example you might have some max popularity level that max the utility of your plan choice and anything above you know will make you more uncomfortable or anxious or something (it might be because of other variables that are connected/correlated). This might wipe out fat tail in utility space.
I think you can’t really assume “that we (for some reason) can’t convert between and compare those two properties”. Converting space of known important properties of plans into one dimension (utility) to order them and select the top one is how the decision-making works (+/- details, uncertainty, etc. but in general).
If you care about two qualities but really can’t compare, even by proxy “how much I care”, then you will probably map them anyway by any normalization, which seems most sensible.
Drawing both on a chart is kind of such normalization—you visually get similar sizes on both axes (even if value ranges are different).
If you really cannot convert, you should not draw them on a chart to decide. Drawing makes a decision about how to compare them as there is a comparable implied scale to both. You can select different ranges for axes and the chart will look different and the conclusion would be different.
However, I agree that fat tail discourages compromise anyway, even without that assumption—at least when your utility function over both is linear or similar.
Another thing is that the utility function might not be linear, and even if both properties are not correlated it might make compromises more or less sensible, as applying the non-linear utility function might change the distributions.
Especially if it is not a monotonous function. Like for example you might have some max popularity level that max the utility of your plan choice and anything above you know will make you more uncomfortable or anxious or something (it might be because of other variables that are connected/correlated). This might wipe out fat tail in utility space.