Creating a very simple 'evolutionary' algorithm in python

What is wrong with looping?

for person in starting_population:
    person.fitness = person.a1*person.a2/person.a3*person.a4 #Add fitness to object

Also note, the order of operations is:

((a1*a2)/a3)*a4)

in case you meant something different. You may consider making fitness a method of an individual:

class Individual(object):
    def __init__(self, a1, a2, a3, a4):
        self.a1 = a1
        self.a2 = a2
        self.a3 = a3
        self.a4 = a4

    def fitness(self,x):
        fitness = self.a1*self.a2/self.a3*self.a4
        return fitness

starting_population = list()   
for i in range (population):
    a1 = random.randint(1,10)
    a2 = random.randint(1,10)
    a3 = random.randint(1,10)
    a4 = random.randint(1,10)
    starting_population.append(Individual(a1,a2,a3,a4))

so you immediately can call starting_population[i].fitness(), or calculate the value in __init__ and make it a field.

Another solution, dropping the object clarity of code in favor of a numpy array for speed:

import numpy.random as rnd
rnd.seed(78943598743)
starting_population=rnd.randint(1,10,size=100*4).reshape(100,4) #100 rows, 4 columns, each row a person
fitness_vector = starting_population[:,0]*starting_population[:,1]/starting_population[:,2]*starting_population[:,3]

First, you should make fitness a method of Individual:

import random
population = 100

class Individual(object):
    def __init__(self, a1, a2, a3, a4):
        self.a1 = a1
        self.a2 = a2
        self.a3 = a3
        self.a4 = a4

    def fitness(self):
        fitness = self.a1*self.a2/self.a3*self.a4
        return fitness

starting_population = list()

for i in range (population):
    a1 = random.randint(1,10)
    a2 = random.randint(1,10)
    a3 = random.randint(1,10)
    a4 = random.randint(1,10)
    starting_population.append(Individual(a1,a2,a3,a4))

If you want to remove the 20 least scoring ones, first sort them by fitness, then take a slice of the list:

sorted_people = sorted(starting_population, key=lambda i:i.fitness())
fit_people = sorted_people[20:]

You could also filter them according to the value of their fitness, like that, using a list comprehension:

fit_people = [i for i in starting_population if i.fitness() > 0.5]