The Day of the Doctor and the Veil of Ignorance (Warning: Spoilers!)

The 50^th Anniversary episode of “Doctor Who” aired this week in theatres throughout the world. There was an interesting scene towards the end of the movie, which I would like to share. Below I give a very simplified version of the scene.

There are two main characters in the scene, a human and a shape-shifting alien refugee that took on the human’s form.

The human and the alien are located in a secret storage facility in London and it has the most dangerous alien weapons on Earth.

The alien wants to take over the earth, and she plans to use the dangerous weapons in the room to do it. The human will do anything to stop them from using the weapons.

The alien has two choices: (1) continue to plan to take over earth, or (2) back down and leave earth with no other reasonable place to go, resulting in certain death of her species.

The human has two choices: (1) she can set off a nuclear warhead that will destroy the weapons facility and all of London, or (2) she can allow the alien to take the weapons, take over the earth, and destroy all humans. She prefers the first option. Even though she expects to destroy London, she believes she can save the rest of the earth.

The two figures below outline the game. There are two Nash equilibriums, {Take Over; Set Off} and {Leave; Set Off}. Since the Alien is indifferent between these two outcomes- she has nothing to lose, as her species would die regardless of what the human did- it is hard to predict what the alien should do. In the scene, the alien chooses to try to take over earth. Then the human starts the timer to set off the bomb, and this results in the {Take Over; Set Off} outcome.

When it seems like London is doomed, a third character, the Doctor, enters the room and tries to convince the characters to come to a peaceful agreement. When neither character backs down, the Doctor comes to an ingenious solution: he puts a veil of ignorance over the human’s and alien’s minds, causing them to forget whether they are human or alien. Immediately both players agree to halt the warhead timer and begin to negotiate an agreement.

Ultimately, the Doctor forces the alien and the human to consider each other’s preferences. The Doctor’s solution is similiar to Rawls’ veil of ignorance solution. According to Rawls, if people are unaware of their own personal characteristics at the negotiating table, they are more likely to come to equitable or fair agreements. Since people under a veil of ignornance are unable to determine if they are rich and powerful, or poor and weak, they will  develop an equitable agreement over the distribution of opportunities and rights.

Not only does the Doctor force the alien and the human to take into account each other’s prefereces, the Doctor also forces the characters to consider a third option: sharing the earth. It is possible that neither the human nor the alien believed they could credibly commit to sharing the earth, and this is why they did not consider it prior to the Doctor’s arrival. However, since the Doctor is forcing them to negotiate, they may be more likely to consider the option.

The two figures below outline the new game. The strategic form game takes into account that neither player knows their own preferences, so there is 50% chance of receiving the human’s payoff and a 50% chance of receiving the alien’s payoff. In addition, I think when both players are individually choosing their optimal strategies, they choose the set of strategies that best work out for both players, instead of just for themselves.

The Nash equilibriums of this new game are {Leave; Set Off} and {Divide Pie; Accept Proposal}. Note that neither of these solutions includes setting off the nuclear warhead, so the Doctor successfully changes the outcome of the game. In addition, since {Divide Pie; Accept Proposal} is a better outcome than {Leave; Set Off} (an expected payoff of 0 for both players is better than an expected payoff of -15), I think both players would end up choosing to {Divide Pie; Accept Proposal} as their final agreement.

The main issue I have with the Doctor’s solution is that there is no suggestion of an enforcement mechanism. Both the human and alien could come to an equitable agreement, but they might intend to renege once they find out who they really are. In the very least, after the agreement is reached, both parties would have to be locked out of the room before the veil is lifted. Otherwise, the alien could try to take over again and the human could set off the nuclear warhead. With respect to sticking to the agreement in the long term, both parties would have to come up with some way to force each other to adhere to the terms.