THE MAJORITY of Sunnis today are the Ash'arites. They, as well as the Mu'tazilites, believe that the institution ofImamate/Caliphate is necessary, and it is incumbent (wajib) on men to appoint a caliph. The Mu'tazilites hold that it is incumbent according to reason; the Ash'arites believe it is incumbent according to tradition.
an-Nasaf; writes in his al-Aqai'id, "The Muslims cannot do without an Imam who shall occupy himself with the enforcing of their decisions, and in implementing their hudud (penal code) and guarding their frontiers, and equipping their armies, and receiving their alms, and putting down robberies and thieving and highwayman, and maintaining the Friday and 'id prayers, and removing quarrels that fall between people, and receiving evidence bearing on legal claims, and marrying minors who have no guardians and dividing booty." 
"The Sunnites want an earthly ruler.... while the Shi'ites look for one who can establish the Kingdom of Heaven on earth and bring an end to all the evils of the world." 
Accordingly, the Sunnis recognize four principles for appointing a caliph.
a) Ijma'; that is, consensus of men of power and position on a certain point. The agreement of all the followers of the Prophet is not necessary, nor is it essential to secure the consent of all the persons of power and position in the ummah.
b) Nomination by the previous caliph.
c) Shura; that is, selection by a committee.
d) Military power; that is, if anyone acquires power by military force he will become a caliph.
The author of Sharhu 'l-maqasid has explained that when an Imam dies and a person possessing the requisite qualifications claims that office (without the oath of allegiance-bay'ah-having been taken for him and without his having been nominated to succeed), his claim to caliphate will be recognized provided his power subdues the people; and apparently the same will be the case when the new caliph happens to be ignorant or immoral. And similarly when a caliph has thus established himself by superior force but is afterwards subdued by another person, he will be deposed and the conqueror will be recognized as Imam or caliph