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

[Chana Luntz]

RSM writes:
> 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.

This is all true, but why does this not make matters worse, rather than
better?  Given that everyone will have done a mitzvah, either chalitza
or yibum, why not have one person who knows he has done the vadai
mitzvah of yibum, and four who know they have done the vadai mitzvah of
chalitza.  Instead, everybody will have done a safek mitzvah of yibum
and a safek mitzvah of chalitza - ie two sfekos.  Now agreed that one of
those sfekos has to come up trumps, ie if one has done yibum one has not
done chalitza, but if one has not done yibum, one has indeed done
chalitza, meaning everybody gets a mitzvah apiece, but it is equally
true that everybody gets a mitzvah apiece if you go the other way - and
at least that way, everybody knows which mitzvah he has performed.  

 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. 

The many safeks may indeed in the general case wind up doing no mitzvah
at all, but if it were not for the mitzvah of chalitza here, if we
allowed the vadai yibum here, the other four would vadai wind up doing
no mitzvah at all.   Would that not seem to be worse?  At least here,
one could say that the other four would vadai get a "lesser" mitzvah and
the one would get a vadai "greater" mitzvah, so why mess with safekos?
If it is important that each man should get the chance merely to upgrade
his mitzvah from a lesser to a greater one, then one would have thought,
perhaps, how much more so, that each should have the chance of upgrading
his no mitzvah to a real mitzvah.

>Saul Mashbaum

Shabbat Shalom

Chana