Allow me to clarify. The best policy I ever saw was at my former employer (a fortune 500).
1. Coworkers are not allowed to date without a dating contract, dating without informing your line manager is grounds for termination.
2. IF both people desire to date (you have to follow the sex harassment policy here, asking once is fine, more than that and you cross the boundary to harassment), they must go to their line managers and put in motion the following steps:
A. Both parties sign dating contracts with their managers explaining the rules about supervision and such and that if things do not work out what will happen and what the consequences will be if it turns bad.
B. While dating, both parties are bared from being in a supervisory role of each other and preference will be given to working on separate teams (even if that impacts career opportunity). If that interferes with promotions that is the cost of the relationship. If one party is promoted to a role that would require supervising the other party said party will be moved to another department or position.
C. If the dating does not work out there will be a very strict line about harassment. This means is one party has hurt feelings and begins to bring up personal information at work to harass the other person they will be warned and if it continues they will be fired. Any ongoing harassment or unwanted non-work related attention will result in the same consequences.
D. If either party is cannot work with the person they were dating (where there isn't harassment, they just won't work with them) the company will try to make arrangement for a transfer but if there is no opening or equivalent position then it may be grounds for termination.
Almost everyone thinks dating should be fine, that is until they start thinking about what happens if it works out or what happens if it doesn't work out and one of the parties starts acting like a child. Dating should be absolutely prohibited without a contract explaining the terms if for no other reason than to protect people from the nasty career consequences. Keep in mind when the dating goes bad its quite common for one party to start harassing the other party in way that quickly creates the legal definition of a hostile workplace.
People also tend to forget the impact on other coworkers and how disruptive dating is to the work atmosphere. Two people giving each other googly eye's disrupts the other workers and hurts productivity and when it goes bad it makes the atmosphere so uncomfortable productivity drops and the best people will start looking for other jobs. Any interoffice dating is very disruptive and it should be heavily discouraged.