Question regarding diplomatic elections.

This occured to me at the end of my most recent game (coincidentally, my first monarch victory! beat out cathy's cultural by just ONE turn)
I decided to pursue diplomatic in the early 1800s when I realized I could quickly beeline to Mass Media and build the UN in just 10 turns. I had Asoka (the tech leader), Roosevelt (power leader) and Cathy all at Friendly, and had DPs with all three of them. The first election came up in 1860 or so and I fell 3 votes short, that number increased with the next election so I knew I needed more votes. I declared on my nearest neighbor, Mao, quickly took 2 cities and capitulated him.
Now in this case it didn't matter (Mao was pleased with everyone, so I took the -1 hit but remained friendly with my buddies), but does the AI take into consideration your their relations with your vassals when deciding to vote for you?

Congrats on the first Monarch win!!

I'm not sure what factors go into making an AI vote for you, although I'm sure others will be along to fill in that knowledge gap. When I go for diplo win I generally still want huge population/land mass myself and then just concentrate on having 1-2 decent allies. The key to success for me is to ensure that the world hates my main competitor. This will increase the likelihood that they will vote for me. I usually guage my chances off of the voting for secretary. If I get an overwhelming vote vs. my opponent then I figure I've got a good shot. If it's close or there are a lot of abstainers, I focus on a different victory condition.

but does the AI take into consideration your their relations with your vassals when deciding to vote for you?

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Yes.

It averages all the relationship tiers, round down and applies the result to both you and your vassals. For example, anyone who was pleased towards Mao and friendly towards you would average pleased and freindly, end up between the two, round down to pleased, and apply that to both you and Mao. You'd get the same result if they were cautious towards Mao, only Mao would basically be "upgraded" to pleased.

schwartz said:

I declared on my nearest neighbor, Mao, quickly took 2 cities and capitulated him.

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You have to be careful when you do this.

In one game I was a few votes short so worked out that if I took 2 cities from my rival that would be enough to win it comfortably. I did this and sat back to wait the next election.

The problem was that I had taken my rival out of second place and my new opponent was my best supporter.