“There are numerous law of economics which appear to fall into this category; however, so far as I can tell, few of them have been mathematically formalized.”
For better or worse, just about everything in economics has been mathematically formalized. If you are wondering about a specific “law” or concept I can try to dig up examples.
It says that if the voters make the same decisions once the alternative is added, then the voting algorithm does. See Arrow’s definition of IIA on page 27 of the 2nd edition of Social Choice and Individual Values (you can find this part for free on Amazon).
The independence of irrelevant alternatives (“pairwise independence”) can also apply to individuals, it is just that Arrow’s theorem doesn’t directly require it. However, a better statement of the independence of irrelevant alternatives for Arrow is “if all individuals have preferences satisfying pairwise independence, then the group’s decision function should also satisfy it”. So for group IIA to matter we should have individual IIA
It sounds like you rediscovered the “Core”.
This is the evil corollary of the Efficient Markets Hypothesis (that all publicly available information is instantly incorporated into market prices).
Hi. EconPhD student in Philadelphia. Found OB through Marginal Revolution a couple years ago.
I do solemnly swear by the great Wiki that from now until April 1st, I will finish every part of every homework assignment by the midnight before it is due, on pain of food deprivation until the work be complete.
“And this essay does remind me a lot of Paul’s letter to Galatians—in an entirely good way!” I second this.