What is pure democracy? A Thought Experiment

It’s election season, and as we get closer to establishing a Republican and a Democratic nominee, there are a number of people who are complaining that our process for selecting a president in the United States is “undemocratic”. The electoral college, through which we make these decisions, seems to be unnecessarily complex and gives too much power to the establishment. In my mind, that's a fair argument. But then many such people go on to say, “If only we had a direct democracy, in which each vote counted equally and they were all cast at the same time, this would resolve the problem.” I don’t think so. In my opinion, voting (by itself) is never a clear way to determine the will of any group of people.

To illustrate this, I’ve created a thought experiment: Imagine that someone is planning to cook dinner, and so they send out a blind email asking a group of 24 people what they would prefer to eat: beef, chicken, fish, or tofu. Everyone responds to the email individually, and then the cook replies to the whole group with the results: 8 people had selected beef, 6 people had selected chicken, 6 people had selected fish, and 4 people had selected tofu. So, he announces that he will be cooking beef, since that is what the group selected democratically.

The people who selected tofu were horrified. They would not, under any circumstances, eat beef. Had they known that the vote would go this way, they would have voted for something else. So they got together and sent a follow-up email to the group, responding that they had all decided to change their votes from tofu to fish. According to them, this created a new result: 8 people for beef, 6 people for chicken, 10 people for fish, and 0 people for tofu. They argued that the cook should therefore make fish, according to a democratic process.

But in response to this, several people from the beef group say that they would like to change their vote too. If they knew that people were changed their vote to sway the results, then they too might have voted differently. They couldn’t convince all of their fellow beef-lovers to agree, but they did get five people to sign their names on a third email, requesting that their votes be changed from beef to chicken. This makes the new count 3 for beef, 11 for chicken, 10 for fish, and 0 for tofu. Thus, they argue, the cook should make chicken, according to a democratic process.

Well, the cook doesn’t know what to do, so he calls a friend of his who is a mathematician to tabulate the total results. In the original email, he had actually sent out a survey that required people to rate their preferences from their first choice to their fourth choice. The mathematician assigned a value of 4 for each top choice, 3 for each second choice, 2 for each third choice, and 1 for each fourth choice. Using that system, beef got 58 points, chicken got 58 points, fish got 58 points, and tofu got 66 points. Of course, these rankings were created before anyone had knowledge of how anyone else would vote. Furthermore several people mentioned in their responses to the cook's survey that beyond the first choice, they really didn’t care what was served. So they just picked the rest at random. Even so, the mathematician concluded that tofu was what the cook should serve.

 
What do you think? Based on these results and the “democratic” voting process that everyone consented to implicitly by answering the survey, do you think the group should eat beef, chicken, fish, or tofu?

For anyone who is interested in debating this in details, here are the full results of the cook’s survey, as they were tabulated by the mathematician:

Adam: Beef (4), Chicken (3), Fish (2), and Tofu (1)
Brett: Beef (4), Chicken (3), Fish (2), and Tofu (1)

Christine: Beef (4), Chicken (3), Tofu (2), and Fish (1)
Demarcus: Beef (4), Chicken (3), Tofu (2), and Fish (1)
Ellen: Beef (4), Chicken (3), Tofu (2), and Fish (1)
Frank: Beef (4), Fish (3), Tofu (2) and Chicken (1)
Guadalupe: Beef (4), Tofu (3), Fish (2), and Chicken (1)
Hui: Beef (4), Tofu (3), Fish (2), and Chicken (1)
Isabelle: Chicken (4), Beef (3), Fish (2), and Tofu (1)
Juan: Chicken (4), Tofu (3), Beef (2), and Fish (1)
Karl: Chicken (4), Tofu (3), Beef (2), and Fish (1)
Lee-Ron: Chicken (4), Tofu (3), Beef (2), and Fish (1)
Mark: Chicken (4), Tofu (3), Beef (2), and Fish (1)
Nancy: Chicken (4), Tofu (3), Fish (2), and Beef (1)
Oliver: Fish (4), Tofu (3), Chicken (2), Beef (1)

Pam: Fish (4), Tofu (3), Chicken (2), Beef (1)

Quincy: Fish (4), Tofu (3), Beef (2), Chicken (1)

Rolando: Fish (4), Tofu (3), Beef (2), Chicken (1)

Susan: Fish (4), Tofu (3), Beef (2), Chicken (1)

Teresa: Fish (4), Tofu (3), Beef (2), Chicken (1)

Ushi: Tofu (4), Fish (3), Chicken (2), Beef (1)
Vanessa: Tofu (4), Fish (3), Chicken (2), Beef (1)

Wanda: Tofu (4), Fish (3), Chicken (2), Beef (1)

Xavier: Tofu (4), Fish (3), Chicken (2), Beef (1)