Why is "Tzidkas'cha" ordered as it is?

Question

Toward the end of mincha on Shabas, nusach S'farad and S'faradim say Psalms 36:7, 71:19, and 119:142, in that order. However, nusach Ashk'naz says the same verses in the reverse order: 119:142, 71:19, and 36:7. What's the reason for each order?

Answer 1

Justifications for Minhag Sfard:

1. The Tur (OC 292) brings both customs, and writes that the Nusach Sefard is the correct one, as the verses follow the same order which they appear in Tehillim.
2. According to the Zohar (Parshas Terumah 156a), the three verses correspond to three Tzadikim who passed away on Shabbos afternoon - Yosef Hatzadik, Moshe Rabeiynu and Dovid Hamelech. Nusach Sefard recites the verses according to their respective birth order (Siddur Ha'arizal).
3. The Sefer "Tanya", Abudraham and Sefer Hamanhig explain that the three verses are in ascending order of praise for of Hashem. We begin by saying that Hashem's charity is, "like the mighty mountains", then add that it in fact, "up to the heights", and finally conclude that even more so, it is "perpetual".
4. The Sefer "Tanya" there adds that the order of the verses is alluded to in the verse "וה' אלוקים אמת"; we first mention the verse that contains the word "Hashem", next a verse with the word "Elokim" and finally a verse containing the word "Emes"

Justifications for Minhag Ashkenaz:

1. The Levush (OC 292:2) explains that the idea of reciting these verses is considered "Tziduk Hadin", and each verse is considered a stronger form of "Tziduk Hadin" to the previous.

2. The Likkutey Maharich (Seder Tefillas Mincha) brings an explanation that it is in order to conclude with the word "Hashem", and thus connect it to the Kadish we recite immediately thereafter.

3. The Likkutey Maharich there quotes another explanation that the three verses are brought in the order of importance. The first is praise to Hashem for giving us the Torah, the second for the fact that He chose us over the angels, and the third for the respite he gives to those in Gehenom during Shabbos.

4. The Aruch Hashulchan (OC 292:6) suggests that the verse 119:142 corresponds to Moshe Rabbeynu (as it concludes "ותרתך אמת"), and was brought first in his honour.

(See 29-30 of this PDF for more.)

Answer 2

Elya Raba 292:17 in the name of the Avadraham from the Sefer Hamanhig that we increase the greatness of Hashem and therfore we say in this order

1. צִדְקָתְךָ כְּהַרְרֵי אֵל, מִשְׁפָּטֶיךָ תְּהוֹם רַבָּה אָדָם
   וּבְהֵמָה תוֹשִׁיעַ יְהֹוָה (Tehilim 36:7)

2. וְצִדְקָתְךָ אֱלֹהִים עַד מָרוֹם, אֲשֶׁר עָשִׂיתָ גְדֹלוֹת. אֱלֹהִים, מִי כָמוֹךָ (Tehilim 71:19)

3. צִדְקָתְךָ צֶדֶק לְעוֹלָם, וְתוֹרָתךָ אֱמֶת (Tehilim 119:142)

"זה לשון אבודרהם: כשאומרים כסדר הוא נכון להגדיל ולהוסיף בשבח המקום ברוך הוא בתחילה נדמית שגדולה כהרר"י א"ל, ועוד גדולה עד מרום ולעולם צדקתו ותורתו אמתיים, עד כאן. וכן כתב בספר המנהיג.

Tur 292 says that the Nusach Sefard is correct as it follows the order of the verses in Tehilim.

Regarding Nusach Ashkenaz - Minhagei Yeshurin 80 says that based on the Zohar Teruma 278 each verse is for a different Tzadik that passed away at Shabbos Mincha time. Yosef, Moshe, David. First we say the verse that represents David, then the one that represents Moshe, then the one that represents Yosef as the later problem causes us to forget the earlier one.

בזוהר תרומה רע"ח. נאמר בפירוש: תלהא אינון דאיסתלקו מעלמא בהאי זמנא חד משה נביאה, וחד יוסף צדיקא, וחד דוד מלכא, בגין כך תלת צדוקי דינא הכא: צדקתך כהררי אל - דא יוסף, וצדקתך אלוהים עד מרום - דא משה, צדקתך צדק - דא דוד מלכא.

טעם אחר: כי צרות אחרונות משתכחות הראשונות, ומצטערים בראשונה על דוד, ואח"כ על משה ואח"כ על יוסף (מנהגי ישורון סי' פ'). ולפ"ז אמירת צדקתך צדק הוא כמו צדוק הדין על פטירת שלושה גדולי עולם באותה שעה במנחת שבת. משום כבודם אין עוסקים בתורה בין מנחה למעריב (רק אומרים תהלים) לקיים 'נשיא שמת - כל מדרשות בטלין' (לקוטי הפרדס לרש"י).

אף כי לפי סדר עולם מת משה בערב שבת, עם זאת לא נקבר עד שבת במנחה, ואנו אומרים צדוק הדין בשעת הקבורה (עי' הרא"ש וקרבן נתנאל פסחים ק"ה).

Thanks to daat.ac.il for a significant part of this answer.