Is Voting a Commandment or Simply Good Advice? Selected sources from the Moment Magazine May/June 2016 Article (http://www.momentmag.com/ask_the_rabbis_voting/)
(ד) כֹּ֥ה אָמַ֛ר יְהוָ֥ה צְבָא֖וֹת אֱלֹהֵ֣י יִשְׂרָאֵ֑ל לְכָל־הַ֨גּוֹלָ֔ה אֲשֶׁר־הִגְלֵ֥יתִי מִירוּשָׁלִַ֖ם בָּבֶֽלָה׃ (ה) בְּנ֥וּ בָתִּ֖ים וְשֵׁ֑בוּ וְנִטְע֣וּ גַנּ֔וֹת וְאִכְל֖וּ אֶת־פִּרְיָֽן׃ (ו) קְח֣וּ נָשִׁ֗ים וְהוֹלִידוּ֮ בָּנִ֣ים וּבָנוֹת֒ וּקְח֨וּ לִבְנֵיכֶ֜ם נָשִׁ֗ים וְאֶת־בְּנֽוֹתֵיכֶם֙ תְּנ֣וּ לַֽאֲנָשִׁ֔ים וְתֵלַ֖דְנָה בָּנִ֣ים וּבָנ֑וֹת וּרְבוּ־שָׁ֖ם וְאַל־תִּמְעָֽטוּ׃ (ז) וְדִרְשׁ֞וּ אֶת־שְׁל֣וֹם הָעִ֗יר אֲשֶׁ֨ר הִגְלֵ֤יתִי אֶתְכֶם֙ שָׁ֔מָּה וְהִתְפַּֽלְל֥וּ בַעֲדָ֖הּ אֶל־יְהוָ֑ה כִּ֣י בִשְׁלוֹמָ֔הּ יִהְיֶ֥ה לָכֶ֖ם שָׁלֽוֹם׃ (פ)
(4) Thus saith the LORD of hosts, the God of Israel, unto all the captivity, whom I have caused to be carried away captive from Jerusalem unto Babylon: (5) Build ye houses, and dwell in them, and plant gardens, and eat the fruit of them; (6) take ye wives, and beget sons and daughters; and take wives for your sons, and give your daughters to husbands, that they may bear sons and daughters; and multiply ye there, and be not diminished. (7) And seek the peace of the city whither I have caused you to be carried away captive, and pray unto the LORD for it; for in the peace thereof shall ye have peace.

(ב) רַבִּי חֲנִינָא סְגַן הַכֹּהֲנִים אוֹמֵר, הֱוֵי מִתְפַּלֵּל בִּשְׁלוֹמָהּ שֶׁל מַלְכוּת, שֱׁאִלְמָלֵא מוֹרָאָהּ, אִישׁ אֶת רֵעֵהוּ חַיִּים בְּלָעוֹ.

(2) Rabbi Chanina, the Deputy High Priest, says: Pray for the welfare of the government, for were it not for the fear of it, man would swallow his fellow alive.

אמר רבי יצחק אין מעמידין פרנס על הצבור אלא אם כן נמלכים בצבור שנא' (שמות לה, ל) ראו קרא ה' בשם בצלאל אמר לו הקדוש ברוך הוא למשה משה הגון עליך בצלאל אמר לו רבונו של עולם אם לפניך הגון לפני לא כל שכן אמר לו אף על פי כן לך אמור להם הלך ואמר להם לישראל הגון עליכם בצלאל אמרו לו אם לפני הקדוש ברוך הוא ולפניך הוא הגון לפנינו לא כל שכן
R. Isaac said : "We must not appoint a leader over the Community without first consulting them ; as it is said, "See, the Lord hath called by name Besalel, the son of Uri" (ibid. xxxv. 30). The Holy One, blessed be He, asked Moses, "Is Besalel acceptable to thee?" He replied, "Lord of the universe, if he is acceptable to Thee, how much more so to me!" He said to him, "Nevertheless, go and tell the people." He went and asked Israel, "Is Besalel acceptable to you?" They answered, "If he is acceptable to the Holy One, blessed be He, and to thee, how much more so to us ! "

כל צרכי ציבור שאינן יכולין להשוות עצמן יש להושיב כל בע"ב הנותנים מס ויקבלו עליהם שכל אחד יאמר דעתו לשם שמים וילכו אחר הרוב

For any community matter on which they cannot find common ground, they should convene all taxpayers, and they should agree that each will voice his view altruistically, and they will follow the majority

(ב) לֹֽא־תִהְיֶ֥ה אַחֲרֵֽי־רַבִּ֖ים לְרָעֹ֑ת וְלֹא־תַעֲנֶ֣ה עַל־רִ֗ב לִנְטֹ֛ת אַחֲרֵ֥י רַבִּ֖ים לְהַטֹּֽת׃
(2) Thou shalt not follow a multitude to do evil; neither shalt thou bear witness in a cause to turn aside after a multitude to pervert justice;

(ב) לא תהיה אחרי רבים לרעות - אם הם דנים שלא כדין לפי דעתך ואף על פי שלא יאמינו לך כי אם למרובים.

(2) לא תהיה אחרי רבים לרעות, if, in your opinion, the majority are about to commit an error in judgment, do not remain silent because they are the majority, but state your view. This applies even if you know beforehand that they will not accept your viewpoint but that of the majority.

Rav Moshe Feinstein Letter, October 3, 1984

On reaching the shores of the United States, Jews found a safe haven. The rights guaranteed by the United States Constitution and theBill of Rights have allowed us the freedom to practice our religion without interference and to live in this republic in safety.

A fundamental principle of Judaism is hakaras hatov -- recognizing benefits afforded us and giving expression to our appreciation. Therefore, it is incumbent upon each Jewish citizen to participate in the democratic system which guards the freedoms we enjoy. The most fundamental responsibility of each individual is to register and to vote.

Therefore, I urge all members of the Jewish community to fulfill their obligations by registering as soon as possible, and by voting. By this, we can express our appreciation and contribute to the continued security of our community.

[signed] M. Feinstein

עַל כֵּן נְקַוֶּה לְּךָ ה' אֱלהֵינוּ לִרְאות מְהֵרָה בְּתִפְאֶרֶת עֻזֶּךָ. לְהַעֲבִיר גִּלּוּלִים מִן הָאָרֶץ. וְהָאֱלִילִים כָּרות יִכָּרֵתוּן. לְתַקֵּן עולָם בְּמַלְכוּת שַׁדַּי. וְכָל בְּנֵי בָשר יִקְרְאוּ בִשְׁמֶךָ לְהַפְנות אֵלֶיךָ כָּל רִשְׁעֵי אָרֶץ. יַכִּירוּ וְיֵדְעוּ כָּל יושְׁבֵי תֵבֵל. כִּי לְךָ תִּכְרַע כָּל בֶּרֶךְ. תִּשָּׁבַע כָּל לָשׁון. לְפָנֶיךָ ה' אֱלהֵינוּ יִכְרְעוּ וְיִפּלוּ. וְלִכְבוד שִׁמְךָ יְקָר יִתֵּנוּ. וִיקַבְּלוּ כֻלָּם אֶת על מַלְכוּתֶךָ. וְתִמְלךְ עֲלֵיהֶם מְהֵרָה לְעולָם וָעֶד. כִּי הַמַּלְכוּת שֶׁלְּךָ הִיא וּלְעולְמֵי עַד תִּמְלךְ בְּכָבוד. כַּכָּתוּב בְּתורָתֶךָ. ה' יִמְלךְ לְעולָם וָעֶד: וְנֶאֱמַר. וְהָיָה ה' לְמֶלֶךְ עַל כָּל הָאָרֶץ. בַּיּום הַהוּא יִהְיֶה ה' אֶחָד וּשְׁמו אֶחָד:

We hope therefore, Lord our God, soon to behold thy majestic glory, when the abominations shall be removed from the earth, and the false gods exterminated; when the world shall be perfected under the reign of the Almighty, and all [humankind] will call upon thy name, and all the wicked of the earth will be turned to thee. May all the inhabitants of the world realize and know that to thee every knee must bend, every tongue must vow allegiance. May they bend the knee and prostrate themselves before thee, Lord our God, and give honor to they glorious name; may they all accept the yoke of thy kingdom, and do thou reign over them speedily forever and ever. For the kingdom is thine, and to all eternity thou wilt reign in glory, as it is written in thy Torah: "The Lord shall be King over all the earth; on that day the Lord shall be One, and his name One." (transl. Birnbaum)