Each item is a set of “aspect.” Aspect \(\alpha\) has weight \(w\qty(\alpha) > 0\). And the way to get probability distribution of which items to pick:

given menu \(S\), discard aspects shared by every item in \(S\). then:

• choose an aspects with probability \(\propto w\qty(\alpha)\)
• keep only the items that remain, repeat until the list is broken down

Insight: “similar thing being added increasingly should not as much more decision share. Red bus + green ice cream adds more decision share than Red bus + blue bus + green ice cream which adds more than Red + Blue + green …. + purple bus + green ice cream”

Notice: the probability of each underlying selection is a kind of random utility model