After reading and re-reading the Mockingjay ending, I feel conflicted. I'm pretty sure I have the story right though.
I believe that Katniss had the intention of killing Coin. Katniss had a complete distaste for Snow and had every intention of killing him. But it was when she looked into his eyes at the end that gave her a greater realization; Snow is a terrible man, but he's never lied to her.
The exact words of the book are, "I search his eyes for the slightest sign of anything, fear, remorse, anger. But there's only the same look of amusement that ended our last conversation. It's as if he's speaking the words again. " Oh, my dear Miss Everdeen. I thought we had agreed not to lie to each other." He's right. We did."
It was here that confirmed all suspision of Coin, her cold ability to seize power and the killing of Prim to control/stop the Mockingjay. Which made the choice very easy to kill Coin. Also, Snow was medically frail. He was coughing blood; he was going to die soon enough anyway. So she came to terms with the fact that she didn't need to kill him.
I beleive that Katniss voted yes because she beleived that she was still a target. If she didn't play ball with Coin, she would be taken out. Haymitch has always had an complete understanding knowledge of Katniss. His character has always protected her. I think he agreed with Katniss that a yes vote would would take her off of Coin's radar, as well tell Katniss that he understood what she was going to do. Hence him saying, "I'm with the Mockingjay." The Mockingjay wasn't just a symbol to end the oppression of the Capital, she is a symbol to end oppression of all corrupt sources. Something Haymitch, who was probably the smartest person of them all, thoroughly understood and believed in.
If you read the book, Katniss is immediately escorted away, after the vote, for last minute touches and then takes her place to kill Snow. Coin only had time to immediately go to Snow, place the white rose over his heart, and tell him about the final Hunger Games. She wouldn't have had time to announce the vote to her colleagues. Since her death, Coin couldn't relay the vote. In the scramble after Coin's death, Paylor became the new President and a different option to handle the Capital citizens was chosen. Also, since Coin was corrupt, her colleagues probably didn't really have a choice as to what Coin wanted. Paylor would be a much different leader. The final Hunger Games was solely Coin's idea, so with a new President, no games.
This was long, and I'm sorry to drag it out. Please write a rebuttal if you disagree. I relish other's thoughts and ideas.
"We sleep safe in out beds because rough men stand ready, in the night, to visit violence on those who would do us harm." - George Orwell