[Avodah] Is it better to have one person do a vadai mitzvah or a number do a safek mitzvah?

[saul mashbaum]

RCLunz addressed the question in the subject line in the framework of he Mishna on Yevamos 98b, it which five brothers of uncertain parentage, each of whom definitely has a brother, die childless. Each of the 5 y'vamim give 4 chalitzot, and marry one y'vama. Thus for each yavam, there is a 20% chance that he did mitzvat yibum with his y'vama. If one yavam married all 5 y'vamot, although in that case he would vadai be doing mitzvat yibum, none of the other yvamim would be doing mitzvat yibum. So five safek yibubim, which of which real yibumim range from 0-5, are seen to be preferable to one, and only one, vadai yibum. 
It is pertinent to point out that in the mishna's case, each of the 5 brothers has with 100% certainty done a mitzva. This is because chalitza to one's yevama is a mitzvah min haTorah. Thus in the mishna's solution, each brother has with 80% probabilty  performed mitzvat yibum, and with 20% probability performed mitzvat yibum. In the alternate possibility, when one yavam marries all of the y'vamot after each of the other brothers have given chaliza to all of the y'vamot, each of the choltzim has with certainty done mitzvat chalitza, and the the fifth brother has with certainty done mitzvat yibum.
Thus although the presumtion of the g'mara is that yibum is a greater mitzva than chalitza, in any event everyone will have done, with certainty, either yibum or chalitza. Thus the mishna does not allow one to draw a conclusion for the general case of "one vadai vs many safeks", in which the many safeks may wind up doing no mitzva at all.
Saul Mashbaum
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