(or: “Danny and Bethany jump the shark”)
Bethany and I had Ravioli tonight. Afterwards, there was a little left in the pot. Five pieces, to be exact. We usually use yootles for binary decisions (say, which one of gets the last portion of ravioli) but in this case, Bethany wasn’t sure she wanted all of it. What, we wondered, was the socially optimal division of the ravioli?
We decided we wouldn’t be risking much social efficiency by discretizing this decision into 6 options, characterized by how many pieces I (Danny) would get. We submitted our bids at yootopia.org as follows:
Danny: ybid ravsplit r0 0 r1 .2 r2 .4 r3 .6 r4 .8 r5 1 Bethany: ybid ravsplit r0 .67 r1 .67 r2 .5 r3 .33 r4 .23 r5 0
These are graphed below, with my utility as a function of number of pieces graphed in blue, Bethany’s in pink, and the mean utility (i.e., half the aggregate utility) in black.
As you’d expect, the Decision Auction (DAUC) made the socially optimal choice of giving me four pieces of ravioli and Bethany one, charging me Y$0.235.