To win the Mayoral Election in The Legend of Zelda: Tears of the Kingdom, you need to complete a series of side quests and then participate in the final election. Here are the detailed steps:

1. Complete Pre-Requisite Quests
Before you can start the Mayoral Election, you need to complete four specific side quests:
– Team Cece or Team Reede?: Hand out mushrooms to eight individuals around Hateno Village.
– Cece’s Secret: Complete this quest to learn more about Cece’s motivations.
– A New Signature Food: This quest involves helping Koyin with a new food item.
– Reede’s Secret: Complete this quest to understand Reede’s perspective.

These quests will provide you with the necessary information to proceed with the Mayoral Election.

2. Start the Mayoral Election
After completing the pre-requisite quests, you can start the Mayoral Election by speaking to Sophie, who should be standing outside Cece’s shop. This will initiate the final sequence of events leading up to the election.

3. Participate in the Election
During the election, both Cece and Reede will give their final pitches. However, both characters’ secrets will be revealed, and Cece will decide to drop out of the race. The two will then decide to work together to ensure Hateno Village’s prosperity.

4. Accept Your Reward
After the election, speak with Cece again. She will thank Link for helping out and call the election a success. As a reward, she will give you the Cece Hat. Additionally, Cece’s shop will now sell one-of-a-kind armor pieces that you’ve already obtained in the past, allowing you to have multiple copies of the same armor set in different colors using the dye shop in Hateno.

By following these steps, you will successfully complete the Mayoral Election side adventure in The Legend of Zelda: Tears of the Kingdom.