R. Bachye: Because, based on the Gemara in Rosh Hashanah Rosh Hashanah 15a ?The world is judged four times a year - on Pesach, Shau?os, Rosh Hashanah and Succos ¹ - it transpires that, on Pesach, when all four judgements have still to take place, there is no Simchah, on Pesach, when the judgemen of Pesach (on the produce) has successfully passed, the Torah mentions Simchah once; on Succos, when three judgements have successfully passed - on produce, on fruit and on people - it mentions Simchah three times. ²

Ba'al ha'Turim: It mentions it once on Shavu'os - because the grain has been harvested, twice on Sukos - because everything has been gathered into the house, and not at all on Pesach - since no harvest has yet taken place.

B?chor Shor, Da'as Zekenim and Rosh (both on Pasuk15): Pesach is not a time of Simchah of gathering grain; it is to remember the miracle of Yetzi'as Mitzrayim. Shavu'os is a time of Simchah of the grain harvest, and all the more so Sukos, ³ when everything has been gathered in from the field. ⁴

Oznayim la'Torah: Because on Pesach when the Torah has not yet been given, there is no Simchah because whatever bounty we receive is likely to be used in pursui of our own physical pleasure and not for the sake of Hashem. On Shavu'os, our undertaking to accept the Torah brings with it a measure of Simchah - so the Torah mentions Simchah once; Whereas on Sukos, following the Yamim Noro'im , when we have done Teshuvah and on Sukos itself, when we are busy with actually carrying out the Mitzvos that we accepted on Shavu'os, the Simchah reahes its zenith and the Torah writes it three times.

Yerushalmi Chagigah, 1:2: It teaches us via a Gezeirah Shavah "Vesamachta" "Vesamachta" from Ki Savo, 27:7 in connection with Har Gerizim and Har Eival, that the obligation of Simchah must be performed by eating Shalmei Simchah on Yom-Tov. ¹

R. Bachye: It refers to a Ger Tzedek (who is a ben B?ris - like a Levi).

Rashi and R. Bachye (citing a Midrash Agadah): They correspond to ?Bincha, u?Vitecha ve?Avd?cha va?Amasecha? mentioned earlier in the Pasuk. 'If you will make My four happy - by inviting them to your table to share your Shalmei Simchah and Shalmei Chagigah', says Hashem, 'I will make your four happy!?

Seforno: With reference to answer #1 - If you will make Mine happy - the Ger, the Yasom and the Almanah ¹ with the Leket and Pe'ah that they find during the harvest season.

Ramban #1: To teach us that, once the Beis-Hamikdash has been built, we will not assemble to bring the Korbanos of Yom-Tov anywhere else. ¹

Ramban #2: To exempt from Aliyah le'Regel three times a year until Hashem chooses a place to rest His Shechinah .