Southwest doesn't allow multiple bookings for the same passenger, same day. As a result of the new reservation system, they are now enforcing this policy by automatically cancelling such flights (reports are they cancel the most expensive of the conflicting flights).You won't be able to double-book anymore on Southwest.

This message is shown online when selecting your flights:

Prohibition of Multiple/Conflicting Reservations: To promote seat availability for our Customers, Southwest prohibits multiple reservations for the same Passenger departing from the same city on the same date, or any multiple reservations containing conflicting or overlapping itineraries (such as departures for the same Customer from multiple cities at the same time). Furthermore, without advance notice to the Passenger or purchaser, Southwest may cancel such reservations, or any other reservations that it believes, in its sole discretion, were made without intent to travel. With the exception of Southwest gift cards, funds from proactively cancelled reservations by Southwest will be returned to the original form of payment. Reservations paid for with a Southwest gift card will have the amount applied from the gift card held as travel funds for use by the Customer on a future Southwest Airlines flight.