[Question] When would an agent do something different as a result of believing the many worlds theory?

One of the things im­ped­ing the many wor­lds vs wave­func­tion-col­lapse di­alogue is that no­body seems to be able to point to a situ­a­tion in which the differ­ence clearly mat­ters, where we would make a differ­ent de­ci­sion de­pend­ing on which the­ory we be­lieve. If there aren’t any, prag­ma­tism would in­struct us to write the ques­tion off as mean­ingless.

Has any­one tried to pose a com­pel­ling thought ex­per­i­ment in which the differ­ence mat­ters?