malchus - Divine right or by consent of the people?

Why is it that מלך שמחל על כבודו אין כבודו מחול (Kes 17a)?  Rashi explains:

שום תשים עליך מלך. ישראל הוזהרו שישימו עליהם שימות הרבה כלומר שתהא אימתו עליהם הלכך אין כבודו מחול שלפיכך ריבה הכתוב שימות הרבה:

In other words, the Torah demands that we give respect to the king; it has nothing to do with his wishes, and so he cannot choose to demur.

Rabeinu Yonah (San 21), however, offers a different explanation. He writes that the honor due to a king is not because of his person, but rather is because he is representative of the nation.   As Tos in Zevachim (16a d"h meyushav) puts it, אין זה שלו אלא של אחרים. Therefore, the honor is not his to dispense with.

These two views may reflect a larger issue, namely, from where does a king derive his authority -- is it a Divine right, or a reflection of the will of the people?  

Radbaz comments on the halacha of moreid b'malchus (Melachim 3:8) that this din applies to 

 והאי מלך היינו שהומלך על פי נביא או שהסכימו עליו כל ישראל

We see two distinct tracks: authority based on appointment by a navi and authority that is vested in the office by the people.

This dichotomy is reflected in different halachos in the Rambam.  In Hil Melachim 1:3 Rambam writes:

אין מעמידין מלך בתחילה אלא על פי בית דין של שבעים זקנים ועל פי נביא. כיהושע שמינהו משה רבינו ובית דינו. וכשאול ודוד שמינם שמואל הרמתי ובית דינו:

You need a prophet and a beis din to appoint a king, which seems to reflect authority being bestowed by G-d.  Yet the Rambam writes with respect to dina d'malchusa (Gezeila 5:18):

במה דברים אמורים במלך שמטבעו יוצא באותן הארצות שהרי הסכימו עליו בני אותה הארץ וסמכה דעתן שהוא אדוניהם והם לו עבדים. אבל אם אין מטבעו יוצא הרי הוא כגזלן בעל זרוע וכמו חבורת ליסטים המזויינין שאין דיניהם דין וכן מלך זה וכל עבדיו גזלנין לכל דבר:

Here the Rambam indicates that it is the consent of the governed which is the ultimate source of authority.

In fact, the Brisker Rav points out that the Mishna in Sanhedrin which lists off the functions of Sanhedrin:

אֵין דָּנִין לֹא אֶת הַשֵּׁבֶט וְלֹא אֶת נְבִיא הַשֶּׁקֶר וְלֹא אֶת כֹּהֵן גָּדוֹל, אֶלָּא עַל פִּי בֵית דִּין שֶׁל שִׁבְעִים וְאֶחָד. וְאֵין מוֹצִיאִין לְמִלְחֶמֶת הָרְשׁוּת, אֶלָּא עַל פִּי בֵית דִּין שֶׁל שִׁבְעִים וְאֶחָד. אֵין מוֹסִיפִין עַל הָעִיר וְעַל הָעֲזָרוֹת, אֶלָּא עַל פִּי בֵית דִּין שֶׁל שִׁבְעִים וְאֶחָד. אֵין עוֹשִׂין סַנְהֶדְרִיּוֹת לַשְּׁבָטִים, אֶלָּא עַל פִּי בֵית דִּין שֶׁל שִׁבְעִים וְאֶחָד. אֵין עוֹשִׂין עִיר הַנִּדַּחַת, אֶלָּא עַל פִּי בֵית דִּין שֶׁל שִׁבְעִים וְאֶחָד. וְאֵין עוֹשִׂין עִיר הַנִּדַּחַת בַּסְּפָר, וְלֹא שְׁלֹשָׁה, אֲבָל עוֹשִׂין אַחַת אוֹ שְׁתָּיִם

omits any mention of their role in appointing a king. GRI"Z explains (the Rav developed this idea as well) that Sanhedrin served a dual role: as the executive branch, and as representatives of the people.  The Mishna in Sanhedrin is an enumeration of the executive branch roles of Sanhedrin.  Appointing a king is a function of their role as representatives of the people, and therefore does not belong on this list.  This is perhaps not just a procedural issue, but is reflective of the source of the king's authority.

This question may underpin a machlokes Rav and Shmuel regarding the scope of a king's power.  When Bn"Y demanded that Shmuel haNavi appoint a king, he warned them of the consequences (Sh I:8):

יאוַיֹּ֕אמֶר זֶ֗ה יִֽהְיֶה֙ מִשְׁפַּ֣ט הַמֶּ֔לֶךְ אֲשֶׁ֥ר יִמְלֹ֖ךְ עֲלֵיכֶ֑ם אֶת־בְּנֵיכֶ֣ם יִקָּ֗ח וְשָֹ֥ם לוֹ֙ בְּמֶרְכַּבְתּ֣וֹ וּבְפָרָשָׁ֔יו וְרָצ֖וּ לִפְנֵ֥י מֶרְכַּבְתּֽוֹ:

יבוְלָשֹ֣וּם ל֔וֹ שָׂרֵ֥י אֲלָפִ֖ים וְשָׂרֵ֣י חֲמִשִּׁ֑ים וְלַחֲר֚שׁ חֲרִישׁוֹ֙ וְלִקְצֹ֣ר קְצִיר֔וֹ וְלַעֲשֹ֥וֹת כְּלֵֽי־מִלְחַמְתּ֖וֹ וּכְלֵ֥י רִכְבּֽוֹ:

יגוְאֶת־בְּנוֹתֵיכֶ֖ם יִקָּ֑ח לְרַקָּח֥וֹת וּלְטַבָּח֖וֹת וּלְאֹפֽוֹת:

ידוְאֶת־שְֹ֠דֽוֹתֵיכֶם וְאֶת־כַּרְמֵיכֶ֧ם וְזֵיתֵיכֶ֛ם הַטּוֹבִ֖ים יִקָּ֑ח וְנָתַ֖ן לַעֲבָדָֽיו:

טווְזַרְעֵיכֶ֥ם וְכַרְמֵיכֶ֖ם יַעְשֹ֑ר וְנָתַ֥ן לְסָרִיסָ֖יו וְלַעֲבָדָֽיו:

טזוְאֶת־עַבְדֵיכֶם֩ וְֽאֶת־שִׁפְח֨וֹתֵיכֶ֜ם וְאֶת־בַּחוּרֵיכֶ֧ם הַטּוֹבִ֛ים וְאֶת־חֲמוֹרֵיכֶ֖ם יִקָּ֑ח וְעָשָֹ֖ה לִמְלַאכְתּֽוֹ:

יזצֹאנְכֶ֖ם יַעְשֹ֑ר וְאַתֶּ֖ם תִּֽהְיוּ־ל֥וֹ לַעֲבָדִֽים:

יחוּזְעַקְתֶּם֙ בַּיּ֣וֹם הַה֔וּא מִלִּפְנֵ֣י מַלְכְּכֶ֔ם אֲשֶׁ֥ר בְּחַרְתֶּ֖ם לָכֶ֑ם וְלֹֽא־יַעֲנֶ֧ה יְהֹוָ֛ה אֶתְכֶ֖ם בַּיּ֥וֹם הַהֽוּא:

Was Shmuel haNavi just making a threat as to what might happen should the king abuse his power, or does this list accurately reflect what a king is empowered to do?  The gemara (San 20b) writes:

אמר רב יהודה אמר שמואל כל האמור בפרשת מלך מלך מותר בו רב אמר לא נאמרה פרשה זו אלא לאיים עליהם שנאמר שום תשים עליך מלך שתהא אימתו עליך

Rav Yaakov Ariel suggests that Rav does not necessarily hold that a king is just a figurehead with no real power.  That would not seem to fit with many examples in Tanach.  Rather, the machlokes Rav and Shmuel revolves around this question of whether power is Divinely granted to the king and therefore there is little limit on its scope, or whether it depends on the consent of the goverened, and therefore has a more narrow scope and can be reined in.  

This whole discussion brought to my mind a famous vort of the Gaon m'Vilna on the pasuk in Teh (22:29)  כִּי לַה׳ הַמְּלוּכָה וּמֹשֵׁל בַּגּוֹיִם.  The Gaon explains (see Ibn Erza to Braishis 37:8) that there is a difference between a malchus and memshala.  Memshala means ruling by coercion; malchus is with the consent of those ruled.  When it comes to Bn"Y, כִּי לַה׳ הַמְּלוּכָה because we willingly accept Hashem as our king.  When it comes to the other nations, וּמֹשֵׁל בַּגּוֹיִם, they willy-nilly accept Hashem as king, only against their will.

I think there is a parallel between the malchusa d'arah and the malchusa d'rekiya, and these two terms reflect the issue we have been discussing.  Memshala is not just malchus with an arm twist.  It's a different animal entirely, both in the scope and source of the authority it defines.  It is authority that is imposed form without, as opposed to authority that is a reflection of the will of the people.  The idea of tekiyas shofar, of malchiyos on Rosh haShana, of our acceptance of Hashem as our ruler, is what differentiates us from the aku"m in that it reflects a relationship of malchus and not memshala, authority that comes from isarusa d'litata, bottom up, from the people, as opposed to one of isarusa d'leila, top down, imposed from without, based in fear instead of love.

The truth is that these two tracks, malchus as a function of tzav Hashem and malchus as a  function of consent of the people, are intertwined, as the Shem m'Shmuel points out.  How can you ever arrive at consent of the masses when every person has their own agenda, their own ideas about what should be done and who should do it?  The path to common consensus is only through the common denominator of acceptance of ratzon Hashem.