According to Shi'ite view, the holy Prophet Peace be upon him and his household, determined Imam Ali, peace be upon him, from the very beginning of his prophethood, maybe first at the very ceremony in which he invited his closer family and tribe's members, where Kuffar was making joke of Abu-Talib peace be upon him, for he should obey his son due to what the holy prophet said. The last serious determination of Imam Ali Peace be upon him, as his Caliph, was at the last sermon, in Qadeer-e-Khom. The sermon is by itself a long speech, only the most famous sentence from it being "من کنت مولاه، فهذا علی مولاه", and that's after Allah had already stated in his book
النَّبِيُّ أَوْلَىٰ بِالْمُؤْمِنِينَ مِنْ أَنفُسِهِمْ
The Prophet has more authority over the believers than themselves
which yields into
وَمَا كَانَ لِمُؤْمِنٍ وَلَا مُؤْمِنَةٍ إِذَا قَضَى اللَّـهُ
وَرَسُولُهُ أَمْرًا أَن يَكُونَ لَهُمُ الْخِيَرَةُ مِنْ أَمْرِهِمْ ۗ
وَمَن يَعْصِ اللَّـهَ وَرَسُولَهُ فَقَدْ ضَلَّ ضَلَالًا مُّبِينًا
It is not for a believing man or a believing woman, when Allah and His
Messenger have decided a matter, that they should [thereafter] have
any choice about their affair. And whoever disobeys Allah and His
Messenger has certainly strayed into clear error.
But some people disregard this fact and interpret that sentence by merely saying, whoever likes me, should also like this Ali.
Anyway, in Saqifah, when Imam Ali PBUH was engaged in funeral managing of the holy prophet PBUH, Ansar have had gathered in a place called Saqifah Bani Saa`edah, to determine the Caliph after the holy prophet, PBUH. Soon after, Muhajereen joined them, but they were claiming that the Caliph should be selected fro Quraish. Different people from Ansar and Muhajereen were nominating their own candidate, and Abu-bakr was hardly a candidate. People were somewhat aggressive then towards others not thinking like them, and in such a situation Umar asked Abu-Bakr to open his arm. Abu-bakr did and Umar gave priviledge to him, then some others. Some Sahaba denied to accept it, some left the city, some opposed and gathered in the house of Imam Ali and Fatimah, PBUT, the only hoe with still a door open to the mosque of the holy prophet, PBUH.
This is not the case that people were giving their votes with free will (even according to Shi'ite view, any accept Abu-Bakr's ruler ship scaring for their lives, not because of Abu-Bakr, but scaring from Umar) and one was selected, as you concluded it is a normal game in politics. Even, in Ahl-ul-Jamaa`t's one of most authenticated books of Hadeeth, Umar himself has had a sermon at the end of his life, confessing that I did so, because I was afraid The Ummah will loose its integrity, and whoever did what I and Abu-Bakr did on that day, kill both of them immediately!
After Abubakr, no election was done, AbuBakr just seleted Ummar as the Caliph after him.
After Umar, the election was done actually by one person, between 6 candidate who were introduced by Umar, Imam Ali PBUH being one among them, and not the one who had the superior vote. Uthman was elected finally when Imam Ali PBUH refused the conditions put forward in the sitting, enforcing the next Caliph to rule the society by the Sunnah of Sheikhain (Abu-Bakr & Uthman), besides Quran and Sunnah of the holy prophet, PBUH.
Uthman didn't determine the Caliph after himself, and indeed according to Shi'ite view, Uthman was killed by Muslims who were suffering misbehavior of Uthman's government, so even if Uthman has had introduced a Caliph, no one was going to listen to it. It was then the first time after the holy prophet PBUH that people gathered around a person to force him to accept to be a Caliph, and Imam Ali PBUH was elected as Caliph.
These are history. Certainly, many of those who know themselves as Sunni, if understand that AbuBakr and Umar were not sound Muslims, will never continue to like them; and many of those who know themselves as Shia, if understand the those two were righteous and real believers in Islam, will stop hating them. This is because, Allah is the one we like, and we like the holy prophet for Allah like him and like us to like him. The same is true about Imam Ali PBUH for us, and I guess Abu Bakr and Umar for Ahlul-Jamaa`ah.
However, history is also important. History of Islam, specifically, is a rich source of knowledge about Islam and psychology of believers and hypocrites, friends and enemies, so that we can also better understand Quran and Ahadeeth. But I added that much to also mention why we insist on unification of all Muslims, specifically when Islam is continuously under attacks by common enemies.