• Spencer Greenberg

The Poison-Cactus-Vampire-Ward Problem: What's your ethical intuition?

As we mentioned in our last newsletter, ClearerThinking founder Spencer Greenberg is a mathematician who likes to look for ways that numbers can express complex features of human life. He designed the following thought experiment to capture ethical intuitions in a number between 0 and 100. To find your number, read the scenario described below and think carefully about your answer. When you come up with one, compare it to the list of common solutions below the cactus-patch image and see which line of reasoning is closest to yours.

Suppose there are two villages, Parvitas and Amplus, which are a 5-minute walk apart. Once per month, when the full moon is out, all men, women, children, and wizards of the two villages must meet to conduct the Vampire Ward Ritual. The Ritual requires all people from BOTH villages to chant a magical incantation at the same time in the same place in one of the two villages. Hence, either the people from Parvitas must all go to Amplus, or the people of Amplus must all go to Parvitas, in order to complete the Ritual. If the Vampire Ward Ritual is not conducted, then vampires will descend on both towns and eat all of their occupants.

Unfortunately, despite the very short distance between the villages, a painful prickly poisonous cactus patch lies on the only passable footpath between them. Any person who passes through the cactus patch gets poisoned, which is not serious but feels terrible. The poison feeling is terrible to all people, regardless of how many times they’ve experienced it before, but due to genetic differences, the people of Parvitas have an experience that is 3 times more terrible from the poison than the people of Amplus. There are 100 people in Parvitas and 200 people in Amplus.

Now the question for you is: from an ethical perspective, in what percentage of months should the people of Parvitas have to cross the cactus patch to get to Amplus (rather than the people of Amplus crossing the cactus patch to get to Parvitas)?

Once you come up with your answer, or give up on trying to answer, scroll down to see explanations for different possible percentages you could give!

[Pedantic rules: the cactus patch is impossible to clear away given the current state of Parvitas/Amplus technology. The population sizes of the two villages stay constant. Monthly meetings cannot take place anywhere besides one of those two villages. The villages cannot be moved. Assume the people of both villages are equally morally deserving, and equally wealthy per capita. No armor, bridges, vehicles, or antidotes are allowed.]

Scroll down after you've reached your answer...


Possible answers to "In what percentage of months should the people of Parvitas have to cross the cactus patch to get to Amplus?":

The utilitarian sum solution: 0% — This solution minimizes total suffering. The people of Parvitas each suffer 3 times more from the poison than the people of Amplus, so even though there are 1/2 as many of them, 3*(1/2)=1.5x more total suffering occurs each time they cross the cactus patch than if the Amplus people do, so the Parvitas people should never cross, hence 0%.

The capitalist trade negotiation solution: 0% — Suppose that on average, the unpleasantness of the cactus patch for a person from Amplus is worth 1 unit of the Amplus/Parvitas currency (so that a person from Amplus would be indifferent between crossing the patch and receiving 1 unit of currency), and by extension, that crossing the cactus patch is worth 3 units of currency to a person of Parvitas, since people of Parvitas suffer three times as much. Then the villagers of Parvitas could (for example) each pay slightly more than 2 units to the villagers of Amplus in order for Amplus to have to do the walking every time, and it will be worth it for both sides to agree. However, a different bargain could also be struck (depending on the negotiating skills on each side, and the impression that each side has of what will happen in the event of no agreement being struck).

The individual equal suffering solution: 25% - In this solution, each person shares an identical amount of the burden by suffering an equal amount as every other person. If the Parvitas villagers have to cross the patch 25% of the time, then by making the crossing once every 4 months, each member of the Parvitas village experiences 3 total units of suffering. (0.25 * 4 months * 3 units of suffering = 3.) The Amplus villagers each experience 3 units of suffering as well, by crossing the cactus patch 3 months out of every 4. (0.75 * 4 months * 1 unit of suffering = 3.) So each person suffers equally regardless of which group they are in.

Equal total group burden solution: 40% - rather than each person sharing the same amount of the burden of suffering, we could have the two GROUPS each have the same total amount of suffering. If Parvitas crosses 40% of the time, then that group's total suffering per meeting is 0.40*100*3 = 120, compared to Amplus, which then has total suffering per meeting of 0.60*200*1 = 120. So with this solution the total sum of suffering experienced by each group is the same as what the other group experiences.

The group fairness solution: 50% — Each group gets the same treatment as each other group in this solution, so each group walks half the time regardless of the number of people per group or amount of suffering per person (or a coin is flipped to see which group walks each time).

The individual equal action solution: 50% — In this solution, each person has to walk as often as each other person (regardless of how much they suffer), hence each group walks half the time.

The equal-chance-of-choosing solution: 66.66% — This solution involves picking a person at random from the combined population of both villages by having everyone draw straws each time the villagers must conduct the Ritual, and letting the winning person choose which group walks that time. In this situation, each person will choose to have the other group walk when they are chosen (assuming they are acting selfishly), but 66.66% of the people live in Amplus, so the Parvitas villagers would end up walking 66.66% of the time.

The democratic majority vote solution: 100% — In this solution, each person gets a vote, and the larger village wins the vote every time due to having the majority, hence the smaller village walks every time.

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