1. Yamauchi. No doubt he was the guy who made Nintendo the Nintendo we know today. He obviously understood the business and market - and the fact that Nintendo could not keep doing the same things but better. Iwata credited the NDS being Yamauchi's idea, that ended up "rising Nintendo to heaven". Against everyone else, he had faith in Famicom/NES to push it to western markets. It also seems that when trying out new concepts, Yamauchi did not let the old ones die away until the new ones could live on their own.

2. Iwata. Despite the Wii U flop, he did come up with Switch, that seems to sell quite well. Wii was also developed under Iwata's watch. If he had not died so soon, it had been interesting to see what Nintendo had came up with. He was a gamer, which is both a good thing and a bad thing when developing games.

3. Furukawa. So far he has had the privilege to lead the company when it's doing good. His challenges are still ahead, as Nintendo's old guard is retiring and the next console is released.

4. Kimishima. Not much to see here, he did his job as a CEO until Iwata's successor was found.

Yamauchi did turn Nintendo from a game card producing company into a commercial giant. However his antagonism with Sony and the Playstation project opened the door for his greatest competitor and permanently diminished Nintendo's dominant position in the gaming market. His old philosophy of third parties as obedient servants worked in Japan in the 80s but not anymore on a global market with western studios.

Actually, the third party policies were introduced to west with NES. Nintendo faced the same problems with Famicom in Japan as Atari faced in US with having no control over who could release games on the system. It was the NES10 lockout chip that mostly prevented the unlicensed games being released on NES. Nintendo also followed itself the same rules it forced on the 3rd parties.

My exact ranking, I'm surprised to see even one person with the same despite only 4 presidents in the running. 

I truly cannot dissociate Yamauchi's titanic accomplishments with his greed, arrogance, and even some of his failures. Because of that, I can't rank him 1 or 2 like most are doing.

The other 3 presidents we're ranking seem like leaders who steer the ship with the lower ranked leaders and even the employees around the bottom of the totem pole. Yamauchi is the type who cracks a whip while the employees pull him in a chariot. That's again not to discount his accomplishments and some of the leaders he helped mold. It's just my preference and a big reason I rank him last. 

These policies might have worked in the 80s but the moment a bigger fish appeared (Sony) with better services, everyone was eager to jump ship. Konami, Square, Namco etc. moved to the PlayStation asap. Nintendo wanted to push expensive N64 cartridges to 3rd parties when cheap CDs became Nr. 1 medium of storage. Yamauchi overplayed his hands here. Nintendo could win the retail shelf space war against smaller companies like SEGA or ATARI but not against Sony or Microsoft.  Everybody has anti-piracy measures and some form of lock down, that was not the issue here. Even today, Nintendo is developing their hardware foremost with their own games in mind and 3rp parties have to eat what they get.

Well, there already were bigger fish, such as NEC and Philips. Microsoft already had Windows and MSX. Sony was smart enough to do things differently than Nintendo did. Cartriges or discs weren't the issue - GameCube had mini-DVD's and did worse than N64, whereas Gameboy Advance and Nintendo DS had carts, just like Switch. N64 had mainly two problems: N64 was released so late that the competition had a good headstart and Nintendo's "dreamteam" of publishers who were allowed/invited to develop for the system. If Nintendo's policies had not been ok with the publishers, they had not developed for NES or SNES, like some of publishers did not do it. 

Don't know if I'd even count Kimishima in the ranking since his presence was just too short, coupled with the fact he was always meant as an interim after Iwata's passing.

Furukawa has been managing Nintendo's most prosperous period but in the same light as Yamauchi, he's not much versed on the development side of things so he feels quite distant to his customer base unlike Iwata which was the only true CEO of the big 3 having hands down on the development side of things. Guy was a genius of his time despite the managerial blunder of the WiiU/3DS era.

Yamauchi was the first, the most strong-headed of them all but he deserves major props to get all the talent he needed so the company could prosper under the watch of Iwata.

1) Iwata
2) Yamauchi
3) Furukawa
4) Kimishima

There’s only one correct choice for number one: Yamauchi

Yamauchi wins since he hand-picked Iwata as his successor.

I voted for Iwata for the sole fact that he took a paycut during hard times to avoid massive layoffs.

IMO leadership should not only be judged during times of success, but what they do during times of hardship. Iwata did the right thing, IMO, and was a very honorable president.