Using max() to find highest in a list, and if they tie, choose only one

I'm making a voting software, and having some problems. Here is a sample:

import random


One = "Test"
Two = "Testy"
Three = "Testyy"
Four = "Testyyy"
Five = "Testyyyy"
Six = "Testyyyyy"

running = {One: 0, Two: 0, Three: 0, Four: 0, Five: 0, Six: 0}


for voter in running:
    vote = random.choice(running)

    running[vote] += 1

winner = max(running)

I want to make it so if two candidates tie for the win, it will randomly select one of them as the winner. Is there any way to do this?