like when Jack values the renovation at $120 and Jill values it at $200. Jack would vote “no”, even though their total value is $310.
I think there’s an error in the arithmetic here...
That said, great post! The math bits could probably do to be more gentle, mostly just cause you introduce a lot of concepts in a short space. Nevertheless, it seemed fundamentally approachable—I have relatively little math background (high school calculus and some dabbling in elementary game theory) but I feel like I’m I capable of understanding this fairly easily, even if I didn’t actually understand all of it on the first or second go.
I did introduce a lot here. Now that I’ve thrown all the pieces of the model out on the table, I’ll include refreshers as I go along so it can actually sink in.
Oh, and now that I’m going over it more carefully, another nitpick: You don’t seem to actually define the notation Π_i before using it in the definition of a social choice function, and it isn’t clear (to me) from context what it’s supposed to mean.
I think there’s an error in the arithmetic here...
I don’t Jack will vote no because he has to pay 150 but values the renovation at 120 leading to a benefit of −30 for him if he assumes that same for Jill.
I think there’s an error in the arithmetic here...
That said, great post! The math bits could probably do to be more gentle, mostly just cause you introduce a lot of concepts in a short space. Nevertheless, it seemed fundamentally approachable—I have relatively little math background (high school calculus and some dabbling in elementary game theory) but I feel like I’m I capable of understanding this fairly easily, even if I didn’t actually understand all of it on the first or second go.
Thumbs up!
Thanks for catching that!
I did introduce a lot here. Now that I’ve thrown all the pieces of the model out on the table, I’ll include refreshers as I go along so it can actually sink in.
Oh, and now that I’m going over it more carefully, another nitpick: You don’t seem to actually define the notation Π_i before using it in the definition of a social choice function, and it isn’t clear (to me) from context what it’s supposed to mean.
That’s an indexed Cartesian product, analogous to sigma notation for indexed summation, so
Oh, okay. Hah, here I was trying to fight my instinct to automatically interpret capital-pi as a product. Thanks!
I don’t Jack will vote no because he has to pay 150 but values the renovation at 120 leading to a benefit of −30 for him if he assumes that same for Jill.