This challenge 25 was a lot of fun. I added some additional statistics to the end of the output to make it interesting.

Challenge25.py

# In an election, the person with the majority of the votes is the winner. Sometimes
# due to similar number of votes, there are no winners.
# Your challenge is to write a program that determines the winner of a vote,
# or shows that there are no winners due to a lack of majority.

import random

def vote(team1, team2, times):
    """Takes two strings and an int, randomly votes for each of the strings
    then gives the string that gained the most votes.
    it returns a tally int that indicates which team won over all"""
    tally1 = 0
    tally2 = 0
    for i in range(1, (times + 1)):
        team1vote = random.randint(20, 100)
        team2vote = random.randint(20, 100)
        print "+++++++++++++++++++++++Round %d+++++++++++++++++++++++++++++" % i
        print team1, " scored %d votes." %team1vote
        print team2, " scored %d votes." %team2vote
        if team1vote == team2vote:
            print "There were no winners, try again"
        elif team1vote > team2vote:
            print "%s won the majority of the votes! We have a winner!" % team1
            tally1 += 1
        else:
            print "%s won the majority of the votes! We have a winner!" % team2
            tally2 +=1
    return tally1, tally2

blue = raw_input("Give me a name for the first team: ")
red = raw_input("Give me a name for the second team: ")
elections = input("How many elections do you want to hold? ")
print "Let's get started!"
totalBlue, totalRed = vote(blue, red, elections)

# Evaluate and assign the winner
if totalBlue > totalRed:
    total = totalBlue
    winner = blue
elif totalRed > totalBlue:
    total = totalRed
    winner = red
else:
    winner = "Neutral"
    total = int(elections * .5)

print "The results of %d elections show that over all Team %s was the best!" % (elections, winner)

if elections % 2 == 0:
    halfElect = elections * .5
else:
    halfElect = (elections + 1) * .5
percentage = ((1.0 * total) / elections) * 100
print winner, "won %d percent of the time!" % percentage
print total, "times total!"
if (totalBlue + totalRed) != elections:
    zeroes = elections - (totalBlue + totalRed)
    print "Also there were %d elections that ended in a tie." % zeroes