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

[Chana Luntz]

There is a fascinating (well to me, anyway) piece of gemora in the daf
yomi of a couple of weeks ago that I thought I would send in, as it
seemed to me that it has very interesting philosophical implications.

The Mishna there (Yevamos 98b) is discussing a case where five women
give birth to sons together in one place and the sons all get mixed up,
so nobody knows which son belongs to which mother (and hence to which
father) but where each of the mothers also have a vadai son of the same
father as the one that got mixed up.  And the five mixed up sons grow up
and marry and each die childless.  So what the Mishna prescribes if that
for the first woman, four of the vadai sons give her chalitza, and the
last of the sons marries her - on the basis that, if she is in fact his
brother's wife, he will be doing yibum, and if not, well her real yavam
gave her chalitza as one of the four, and she is free to marry.  And
then the same procedure is repeated for the second woman, with a
different one of the vadai sons taking her in marriage, and so for all
five.

Now the gemora there comments on the fact that the Mishna makes it clear
that the man who takes the second woman in yibum is different from the
man who takes the first woman in yibum, and so too for the third, fourth
and fifth, so that each man ends up with one wife each.  And it states
that the Mishna teaches this so you should not think to say that one man
should do yibum with all of them but that each one should do yibum with
one because maybe he will each get his own [yevama].

Now a straight reading of the gemora provides us with a very interesting
conclusion.  Because if one man married all five (after all the others
had done chalitza of course, so there is no problem), then we know that
he will definitely have done the mitzvah of yibum once, ie a vadai
mitzva (but no more).  Whereas if each of the five takes one woman each,
there is the chance that all five will end up doing the mitzvah of
yibum, but there is equally a chance that none of them will end up doing
the mitzva.   And the gemora appears to be coming down on the side of
"let's gamble and go for the max" rather than go for certainty.

Now the Aruch L'Ner appears bothered by this and seems to suggest that
it is not true, and that in general it would be better to have the
certainty of one mitzvah, rather than the gamble of more.  However, he
says that the Mishna says this because of the fact that, following the
gemora on Yevamos 44a, a man is not permitted to take more than four
women in yibum (even if he has five vadai yevamas falling to him, eg he
has five different brothers who all die childless) because he is require
to give them a minimum of one onah a month, and there are not enough
weeks in a month to cater for five women.  And since, because one of
them would not be allowed to marry five of the women, and if one married
four and another married one, then you still would not have the
certainty that a definite yibum mitzvah would have been performed,
therefore it is better for each to marry one.  But that this is why the
Mishna davka brought the case of five intermixed sons, and not four,
because if it had brought the case of four, and hence one of the
brothers could have married all four, as per the gemora on 44a, then it
would have been preferable to do that.  That is, it is better to go for
the certainty of one mitzvah, rather than the gamble of more, and the
only reason that this is not applied here is because there are other
reasons why one man cannot marry all five.

Now even according to the Aruch L'Ner this is interesting.  Because,
while having one man marry four and one marry one does not give
certainty - presumably one would be able to make a determination as to
which of the men was the greatest tzaddik, and that would allow us to
give that man the greatest chance of performing the mitzvah (as per our
discussion regarding giving up a mitzvah to allow a gadol to do it on
this list previously) - by having him marry four of the women, and then
the second greatest tzaddik the one remaining woman, and the rest all
doing chalitza.  But it seems that even according to the Aruch L'Ner
that is not the case, and we do not weigh the situation in favour of the
greatest tzaddik, but give each of the men an equal chance of performing
the mitzvah (note this is even more pointed given that the reason that
yibum is not generally permitted today is because people are not
considered on the level to do it properly, so if there was any mitzvah
where one would have thought such a determination should have been made,
it would be this one).

But the Aruch L'Ner, while in some ways very satisfying, as he explains
why it is that the Mishna teaches davka about a case of five, and not
fewer, does seem a distinct divergence from the gemora text.  Because
the gemora clearly asks the question as to why we do not say that one
should marry all five women, and could so easily have said - because one
cannot give each of them the necessary onah, oh and why then do we not
say that one marries four etc ... But it chooses not to do so, and
rather seems to stress that the "dilma" of a number takes precedence
over the "vadai" of one.

And I did wonder whether you could not explain the number five in the
Mishna differently.  Because presumably at some point the chance of each
man getting his own yevama must go too low to be considered significant
- for five it is one fifth, but presumably if we were talking about a
hundred sons getting mixed up, we would not say that a 100th chance was
significant.  So maybe it is teaching that one fifth is still a
reasonable risk - but perhaps one sixth is not.  And I was wondering
whether a 20% chance versus a 16 2/3 % chances plays out anywhere else
in halacha - or maybe it is a 20% chance versus something like a less
than 10% chance (ie could you apply some of the statistics that are used
in things like bittel and miut that is or is not matzui)?

Anyhow, wondered what the chevra out in Avodah land thought and whether
they knew of anybody else who commented on this and the philosophical
implications.

Regards

Chana