The mishna in Rosh Hashana says bi-arba prakim haolam
nidon – during four periods the world is judged. On Pesach for the grain, on Shavuos
for the fruits of the trees but then, instead of simply saying that people are judged
on Rosh Hashana, it says "kol bnei haolam ovrim lifanav kivnei marom".
We note the change in language with respect to Rosh Hashana. Also, at the end of
the mishna with respect to Succos it says "nidonin al haayim" – We are
judged [in the plural form] on the water. Why is Succos in the plural form
while the other judgements are framed in the singular form ["haolam nidon"]?
We must say that it is a continuation
of the previous sentence "Bi-Rosh Hashana kol bnei haolam" etc.
referring to the masses, so it continues talking about Succos in the plural.
On Rosh Hashana we are judged
"kivnei maron" meaning as many individuals [see the gemara] and on
Sukkos as well we are judged not communally [which is how we are judged on
Pesach and Shavuos, as indicated by the word "nidon" – everybody
together] but individually [as indicated by the word "nidonin"]. That is
the seder of the mishna.
This is a source for our minhag to continue
saying "Lidovid Hashem" until Shmini Atzeres, as the judgement of
Rosh Hashana continues on the individuals through Sukkos. [Rav Hutner explained
the mayim is called "mayim chaim" so we see that the Succos judgement
on mayim is bound up with the Rosh Hashana judgement on chaim.]
עפ"י הספר מרבה טובה על מס' ביצה פרק שני ממו"ר הרה"ג ר' יעקב דוד המניק