How did Pharaoh know the interpretations of the dreams he had given by everyone else was wrong but Yosef was right? The Or Hachaim asks the word פרעה in the possuk ואין פותר אותם לפרעה seem extra, we are talking about the dreams of Pharaoh, of course they were interpreting the dreams to him? The Or Hachaim explains the word Pharaoh is not the name of the King but is a reference to the kingship of the Egyptians. He explains that a king has dreams that are about the entirety of the kingdom, not personal dreams. The interpreters said the dreams were about Pharaoh himself but Pharaoh understood his dreams, the dreams of a king, are about what effects the entirety of the nation. Why does a king dream about the nation?
Why was Yehuda specifically set to set up the Jewish settlement in Goshen? Rav Chayim Shmulevitz explains that a king has to take responsibility for the nation. Yehuda took achrayut for Binyamin, he guaranteed his safety and that is the main attribute of a king. He explains with this the idea the Gemarah Yoma (22b) that Shaul lost the kingship because of one sin and Dovid did two sins and was forgiven. What was the difference? Shaul's sin was that he could not stand up to the demands of the people that wanted to spare the property of Amalek an Agag. He did not stay the buck stops here, I need to ensure the commandment of Hashem is fulfilled. That is a lack in the necessary middah for malchus and it was stripped from him. Dovid sinned but those were sins that didn't contradict the middah of a melech and that could be forgiven.
The Alter from Kelm (second maamer) asks why is it that Dovid, Shlomo, Yosef wanted malchus, were they people that wanted honor and recognition? He explains that the melech has the ability to have a greater effect on the world. The king has the power to fix people's problems. This, he says, is the greatest demonstration of נושא בעול אם חבירו. It was to fulfill this middah that the greatest of people desired kingship. Not for greatness but to be great for others.
The Rambam (Chanukah 3:1) says וְגָבְרוּ בְּנֵי חַשְׁמוֹנַאי הַכֹּהֲנִים הַגְּדוֹלִים וַהֲרָגוּם וְהוֹשִׁיעוּ יִשְׂרָאֵל מִיָּדָם וְהֶעֱמִידוּ מֶלֶךְ מִן הַכֹּהֲנִים וְחָזְרָה מַלְכוּת לְיִשְׂרָאֵל יֶתֶר עַל מָאתַיִם שָׁנָה עַד הַחֻרְבָּן הַשֵּׁנִי. It appears from the Rambam that the rulership of the Bais Chashmonei was a continuation of the story of the nes Chanukah. What is the connection between their malchus and their repelling of the Greek decrees? Rav Yeruchem Olshin explains with this idea of the Alter. Since the Chashmoneim stood up for Klal Yisrael , were moser nefesh, they demonstrated the greatest act of נושא בעול and that is what gave the Chasmoneim the ability to be kings. This is why a a melech must feel the sense of responsibility for others for the whole yesod of malchus it to affect a positive change in the lives of others.
What is it about being a king that must contain this middah, is it just due to proper circumstances because they are in control? It is not just circumstance that a king has a big heart that goes out for others but it is part of the essence of his job. The Sfas Emes Vayigash (5648) says ומדת יהודה מלכות בית דוד דלית לי' מגרמי' כלום. וכל כחו הוא מה שהוא כלי לקבל ומוכן תמיד בהכנעתו אל האדון ית"ש. The middah of melucha is the king has on self identity, he is battal to where the ultimate king, Hashem. The king realizes that his power is a mere reflection of this and hence feels only for others not for himself. The Sfas Emes continues ,this is indicated in the names of Yehuda and Dovid themselves, ומדה זו הוא בחי' יהודה ודוד כמ"ש מו"ז ז"ל יהודה ה' כלול בו. ואות דל"ת שהוא מלא הכנעה בהיותו יודע שהשם בו. וכן אותיות דוד. הד' שפלות. וזכה אח"כ להמשכת הקדושה שע"ז רומז אות ו'. ומ"מ נשאר אח"כ ד' כמקודם. Despite all the gedulah, they recognize that it is not due to their own merits and have a sense of complete nullification to put everyone before themselves.
Says Rav Chayim Shmulevitz, that is what Pharoh saw is Yosef to make him second in command. Just because he can interpret a dream does not make him worthy of being the prime minister, so why did he get the job? Because he said אלקים יענה את שלום פרעה. He did not take credit for himself but recognized that he was a mere reflection of a higher power. That is the middah of malchus and when Pharoah heard that he knew this was his man.