How do I win a diplomatic victory?

Solution 1:

When either one civilization has reached the Information era or 50% of civs have reached the Atomic era, the World Congress becomes the United Nations.

In alternating UN sessions, there will be a 'world leader' vote, where civilizations and city states can vote on a single leader to unite the nations of the world under their influence and control (AKA win a diplomatic victory).

Each allied city state contributes one or two delegates (depending on the era) to vote for a civ, and if you have ever liberated a civilization's capital city, that civ's delegates will vote for you. Other than that, the AI will always vote for themselves.

It's not enough to simply have the most delegates. There is a minimum number of delegates required to be in favour of a civ in order for them to win. This means that if someone has gone on a city-state shopping spree there may not be enough delegates left in the world for a player to win a diplomatic victory. The number of votes required is determined by game conditions such as the number of civilizations and city states in the game.

In order to maximize your chances, you need to make sure you control as many delegates as possible. Depending on your era, you get the following delegates by default:

1. Atomic Era: 4 by default, +2 for being the host, and +1 per allied city-state.
2. Information Era: 5 by default, +2 for being the host, and +2 per allied city-state.

Other ways to increase your delegate count:

1. The Forbidden Palace grants two extra delegates.
2. The Globalization technology gives +1 delegate per spy assigned as Diplomat you have in another civilization's capital city.
3. You get two extra delegates for being part of the World Religion, if there is one.
4. You get two extra delegates for being part of the World Ideology, if there is one.
5. If no civ receives enough support to win a World Leader election, and you are among the two civs who received the most support, you permanently get additional delegates to use in future sessions (please note that this was listed on the online Civilopedia but isn't something I can verify as a fact myself.

If you find you are having trouble retaining city-state allies for the vote, a very cunning tactic which I've encountered is to wait until the turn before the vote, then buy out all the city-states to get their vote, then declare war on every AI so your allied city-states also go to war with them, meaning that they cannot be stolen as allies by the AI.