[Avodah] Is it better to have one person do a vadai

[Chana Luntz]

RSM wrote:

> RCL wrote 
> >>>
> 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
> >>
> This statement is true, but does not take into account the 
> *risk* involved in the two cases. As I pointed out, in the 
> yibum case, the risk is relatively small, since even if we 
> "lose our wager" and none of the brothers marries his yevama, 
> each one has nevertheless performed a mitzvah min haTorah, 
> chalitza.  

Thinking about this some more (and doing some research), I now wonder
can we indeed say this at all?  Is not the general principle that - even
though chalitza is a mitzva, b'mkom yibum aino mitzva.  Because if the
yevama is forbidden to the yavam by way of a lav, yibum can still be
performed, on the basis that aseh docheh lo ta'ase, and we do *not* say
that since it is possible to do chalitza and it is not as though he will
not do a mitzvah at all, since he will perform chalitza, and it is
merely not a mitzva min hamuvcha, we should be mevatel the mitzvah of
yibum in favour of the mitzvah of chalitza  (for the sources on all of
this, see the Encyclopedia Talmudit entry on Chalitza first section,
fifth perek).  If in the case of being doche a lav, we cannot say what
you are saying, on what basis can we say it when a mere safek is
involved - or are we not similarly required to treat the case as if
there was no mitzvah of chalitza waiting in the wings? 

>In the "general" case, there is a chance that, 
> according to the procedure which favors the the safek, *no* 
> mitzva will be done at all;  it is possible that this risk is 
> unacceptible, given the alternative which *ensures* that a 
> mitzva will be done. Let's consider the following scenario, 
> which illustrates the general case. On RH, someone with a 
> shofar has a choice of going to one of two places. In place 
> aleph, there is one person who would otherwise not be able to 
> hear shofar; in place bet there are five. However, the person 
> with the shofar can with almost certainty reach place aleph 
> before shkia, but reaching place bet on time is uncertain, 
> although possible. Are we mandated to apply the priciple of 
> yibum, go for the max as RCL puts it, and go to place bet, 
> favoring 5 safek mitzvot over one vadaui one? According to 
> what I wrote, not necessarily. Unlike the yibum case, here 
> there is achance that *no* mitzva will be done if the shofar 
> is brought to place bet. Perhaps, under these circumstances, 
> given that a mitzva in place aleph is vadai, going there is 
> preferable. 

I do like your case here - I was racking my brains to think of such a
case, and really struggling, it is a nice counterpoint.   I guess the
question in essence really boils down to the relationship of chalitza to
yibum and to the extent that it is deemed "counted" as an alternative.
Otherwise, while there may be some scope for my earlier argument, which
is actually a form of kal v'chomer, I tend to agree it doesn't dictate.
It is still interesting though that even if ones says that the risk is
smaller than the normal case, that the pshat of the Mishna would seem to
suggest that the halacha should take this stance.
> Saul Mashbaum

RER writes:

> Others have added to the discussion, prompting me to pull out 
> some notes which I compiled many, many years ago following my 
> amateurish mathematical examination.
> 
> I stand to be corrected if I erred, but my findings were that 
> if each man  performed one Yibum there were 120 possible 
> outcomes as follows:-
> 
> 5     Yibumim      1     possibility
> 3     Yibumim    10     possiblities
> 2     Yibumim    19     possibilites
> 1      Yibum       46     possibilities
> 0     Yibumim     44     possibilities
> 
> We see that out of the 120 there are 76 cases (120-44), i.e a 
> 63%+ possibility that will be at least one Yibum and 30 cases 
> (1 + 10 +19), i.e. a 25% possibilty that there be more than one.

I have now had an opportunity to brush up on my probability theory
(which is a much simpler way of doing this kind of analysis) and which
gives the probability of getting five actual yibums at 1/5 x 1/5 x 1/5 x
1/5 x 1/5 = 0.00032 while of getting five chalitzas at 4/5 x 4/5 x 4/5 x
4/5 x 4/5 = 0.32768.  That means that the probability of getting one or
more cases of yibum (ie of equalling or bettering the situation where
you have one brother marry all the women) is 1 - 0.32768 = 0.67232.

On the other hand, if you run the calculation with six women the
equivalent figures for six chalitzos is: 0.334897 and the chance of
equalling or bettering the situation is: - 0.665102.  

So it would seem that in the case of five, the chances or equallying or
bettering getting one yibum are just over two thirds, and for six, it is
just under two thirds (and reducing, so that seven will be less than 6
etc).  Is that a significant number?

> Elozor Reich, Manchester

Regards

Chana