The society of Muslims needs to be guided by caliph after prophet Mohammad (PBUH). Hence, after the death of holy prophet (PBUH), a caliph was assigned to guide and rule the Muslims. According to my findings in noble Qur'an, God has assigned the caliph. For example, Moses the prophet (PBUH) didn't ask people to form a Shura for choosing a successor when he left for Miqat.
Moses said: "O’ Allah) assign me a vizier from my family, (that is) my brother Aaron (Haroon) ...,”(Allah) said: "We granted your requests, O’ Moses.”(20:29-36).
Or in another verse, Allah the exalted, directly mentions the word "Caliph":
يَا دَاوُودُ إِنَّا جَعَلْنَاكَ خَلِيفَةً فِي الْأَرْضِ فَاحْكُم بَيْنَ النَّاسِ بِالْحَقِّ وَلَا تَتَّبِعِ الْهَوَىٰ فَيُضِلَّكَ عَن سَبِيلِ اللَّـهِ ۚ إِنَّ الَّذِينَ يَضِلُّونَ عَن سَبِيلِ اللَّـهِ لَهُمْ عَذَابٌ شَدِيدٌ بِمَا نَسُوا يَوْمَ الْحِسَابِ
[We said], "O David, indeed We have made you a successor upon the earth, so judge between the people in truth and do not follow [your own] desire, as it will lead you astray from the way of Allah." Indeed, those who go astray from the way of Allah will have a severe punishment for having forgotten the Day of Account.(38:26)
But I didn't find other clues mentioning the authority of the prophet or people. Please let me know if others except God has such an authority. Support your answer using Qur'an and Hadith.