Who elected Khalifah in Rashidun Chalipate?

I asked in history stackexchange. Sunni source is that the first four Chaliphs are "properly" elected. However, some Syiah disagree. This one says, for example, https://history.stackexchange.com/questions/58430/did-ali-say-that-only-muhammads-descendants-can-rule?noredirect=1#comment176183_58430 > In reference to comments, the idea that the first three caliphs were > "elected" is also contested. **If the electoral excludes some of the > most prominent companions of the Prophet and involves coercion, it > can't be called an "election"** and this was the case for Saqifa the > first "election" which was more like a factional coup d'état. The > second caliph was also appointed not elected. You may want to post a > separate question on this but you can also consult Madelung's > comprehensive account of post-prophetic politics. So in case of Abu Bakr, it seems that some prominent companions are not excluded. Is there a reasoanable reason why they're not included? What coercion he's talking about? The reason I asked this is because in politic, this is a very normal game. Suharto, for example, is always "elected". By who? By MPR. Who elect members of MPR? About 50% is chosen by Suharto. So in a very good sense, the whole thing is just a show. Suharto isn't really elected. He just elect himself by electing those who will elect him in MPR. So who elect Abu Bakr? Same trick? He's elected by consensus among those who like him?