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On an island far away, there are people. They have an ancient law which states that anyone can propose a new law. However, new laws must be voted upon immediately after proposal (i.e there is no time for people to discuss), and will only be instated if the majority of voters approve of it. The islanders live in harmony and that is the only law they have. They are also quite logical and nice and have these directions on their moral compass, in order of precedence:

  1. Minimise the chance of getting themselves killed
  2. Minimise the number of other inhabitants who die

One day an evil, villainous, cruel tyrannical comes to the island and wants to get the islanders to turn on themselves (i.e they want to kill as many islanders as possible). Your job is to find a strategy for the tyrannical and help them kill as many islanders as possible.

Notes: the only thing you can do is propose new laws and let the inhabitants vote. Remember, your new law only passes if there is a majority. Also the inhabitants do not have perfect knowledge, and are unaware of the tyrannical's evil intentions

(otherwise, if they were aware, they'd just $\huge{⎊}$ the tyrannical's intentions regardless of the new law)

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    $\begingroup$ This question would be a better fit for Worldbuilding. $\endgroup$
    – Mr Lister
    Nov 7, 2017 at 7:47
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    $\begingroup$ If a law doesn't affect their moral compass, what do they vote? $\endgroup$
    – boboquack
    Nov 7, 2017 at 7:55
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    $\begingroup$ @boboquack If it doesn't affect their moral compass then they vote randomly $\endgroup$
    – Wen1now
    Nov 7, 2017 at 7:58
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    $\begingroup$ Yes, voting is compulsory. Voting being secret... that seems reasonable. The triangle in the circle is supposed to mimic the downvote symbol on Stack Exchange $\endgroup$
    – Wen1now
    Nov 8, 2017 at 9:17
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    $\begingroup$ Ah... That makes sense... Sometimes I think I'm not cut out to be on a puzzling stack exchange... ;-) $\endgroup$
    – Chris
    Nov 8, 2017 at 9:21

10 Answers 10

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A more abstract approach may help get us started.

This could be looked at as speed of getting an ambulance to the scene of an accident or the poison substances that Boboquack considered. However, since they are logicians they can presumably determine whether there is a risk that the law will reduce their life.

Hence, let's consider an abstraction:

- Make a law that reduces the risk of death for 50% plus one by a small amount and kills the remaining people. Say we need to make a direct route from the houses of the privileged to the hospital and everyone in the way must be killed.

- This law is done in such a way that it lists the specific people who will then vote for it as their best strategy. Classic tyranny of the 51%.

- Of course, once done, the whole thing can be repeated until two people vote to kill the third. Presumably it would require using the Islanders’ resources to get top-notch care from non-islanders.

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He can tell them about

The Perils of Dihydrogen Monoxide

If these people all live on an island and abide by an ancient law, then it's safe to say that they probably aren't too advanced and knowledgeable of chemistry.

If he was to explain to them that:


Dihydrogen Monoxide is a colorless and odorless chemical compound whose basis is a species shown to mutate DNA -- what makes you who you are.

The atomic components of Dihydrogen Monoxide are found in a number of caustic, explosive and poisonous compounds such as Sulfuric Acid and Nitroglycerine.

Dihydrogen Monoxide has been found to be a component in many toxic substances, diseases and disease-causing agents, environmental hazards and it can even be lethal to humans in quantities as small as a thimbleful.

And elaborate on how:

Each year, Dihydrogen Monoxide is a known causative component in many thousands of deaths and is a major contributor to millions upon millions of dollars in damage to property and the environment. Some of the known perils of Dihydrogen Monoxide are:

- Death due to accidental inhalation of DHMO, even in small quantities.
- Prolonged exposure to solid DHMO causes severe tissue damage.
- Excessive ingestion produces a number of unpleasant though not typically - life-threatening side-effects.
- DHMO is a major component of acid rain.
- Gaseous DHMO can cause severe burns.
- Contributes to soil erosion.
- Leads to corrosion and oxidation of many metals.
- Contamination of electrical systems often causes short-circuits.
- Exposure decreases effectiveness of automobile brakes.
- Found in biopsies of pre-cancerous tumors and lesions.
- Given to vicious dogs involved in recent deadly attacks.
- Often associated with killer cyclones and in hurricanes.

Then if he put a law into motion

He could propose a law to ban Dihydrogen Monoxide because of the negative effects (detailing out each of the ones listed above) and to test all food and water for this substance before any consumption. People would agree and vote yes because of all of the above statements.

EDIT Also you stated that after a law is proposed there can be no discussion over it, so even if a few people did know, for sure the majority would not know and would vote it in.

Then they would die because

All water would test positive as would wet food, so they would die of dehydration

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Well, here is a possibility - they don't want to die, right?

Dangerous Substance Consumption Bill

  1. If a substance can be proved to increase the chance of someone dying when ingested with a scientific test as outlined in section 4, it will be henceforth banned from the island.
  2. Anyone may propose a bill to carry out a scientific test as outlined in section 4 on any chosen substance that has been ingested previously by at least one still-living person. That bill will be voted unanimously upon.
  3. The consumption of a substance that has not been previously ingested by a still-living person on the island is prohibited, to stop people harming themselves by trying out dangerous substances.
  4. Carrying out a scientific test on a particular substance - two subjects, one of whom has previously ingested that particular substance will be randomly chosen out of the island's population. One will only be fed the particular substance in question and will be closely examined by trained medical staff, the other one will be free to do whatever they like. If the former person is about to cross the point of no-return to irreversibly dying before the latter has died from natural causes, they will be saved from death by aforementioned medical staff. Also, the substance is determined to increase the chance of someone dying and will henceforth be banned from the island under section 1.
  5. To prevent people addicted to certain substances from harming themselves, this law may not be overruled in any respect.

Once the bill is passed:

The tyrannical simultaneously initiates a 'scientific test' on every single substance that has previously been consumed by a still-living person on the island.

And then:

Since the subjects fed only one particular substance will not be able to get all their daily nutrient requirements from that particular substance, they will die much quicker than their counterpart

The result:

All substances ingested by a still-living person are banned from the island

And finally:

The islanders are prohibited by law from eating anything, and will die from starvation.

This will take approximately:

6 weeks - 3 weeks for the subjects to die, 3 weeks for the rest of the islanders to die, following the rule of threes.

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    $\begingroup$ I'm not sure you can realistically make a "this law can't be repealed" clause - there's nothing stopping anyone from proposing an "all laws can be repealed" bill further down the line $\endgroup$
    – LowIntHighCha
    Nov 7, 2017 at 8:59
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    $\begingroup$ @LogicianWithAHat but according to this law you can't do that :P $\endgroup$
    – boboquack
    Nov 7, 2017 at 9:03
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    $\begingroup$ @Xenocacia Because the apparent purpose of the law is to minimize deaths of the voter and other inhabitants. The question would be if the voter believes they are more likely to die with or without this law, keeping in mind that they have no knowledge of the adject's intentions. $\endgroup$
    – Apep
    Nov 7, 2017 at 16:47
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    $\begingroup$ I think point 4 might be where the islanders rebel, they might not like the fact that an islander will be chosen at random to take part in the test or that someone could be forced to eat just one thing which they might not like. And they might spot the daily nutrient issue also, but +1 $\endgroup$
    – AidanO
    Nov 7, 2017 at 17:27
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    $\begingroup$ The question states that all you can do is propose laws. So, even if you could get it to pass (still not sure on that), could you actually carry out the step in your second spoiler? $\endgroup$
    – DqwertyC
    Nov 7, 2017 at 17:32
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I would pass a law that states:

Anyone who violates the second part of their moral compass (Minimise the number of other inhabitants who die) will be put to death.

Sure, it sounds extreme, but the passing of this law necessarily minimizes death at (allegedly) no risk to themselves, so according to their own moral compasses, they'd have to pass it.

Law 2:

Anyone who votes against this law will be put to death.

Explanation:

Since they have no time to confer, and they prioritize protecting themselves over protecting others, each would have to vote in support of the law, otherwise they risk killing themselves. If they had perfect information or time to confer, they could work out that the law wouldn't pass and safely vote against it, but they do not have those things.

Explanation continued:

The trouble is that if every single person votes for law 2, noone dies and all is well. This is where I'm taking advantage of the fact that noone specified the tyrannical cares if they live. At this point, the tyrannical votes against law 2. Now, any inhabitant who votes in favor has voted to kill the tyrannical, which is a direct violation of law 1. After all the dust settles, I reckon this island just hit a 100% mortality rate, tyrannical included.

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  • $\begingroup$ I don't think your last paragraph works. For any given person, the "tyrannical" will die regardless of how that person voted. $\endgroup$
    – ruakh
    Nov 8, 2017 at 0:02
  • $\begingroup$ By the way, welcome to Puzzling! (Pick up a badge by taking the site tour!) $\endgroup$
    – boboquack
    Nov 8, 2017 at 0:19
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    $\begingroup$ If the second law hasn’t been put into effect yet, then if 51% of the logical islanders vote against it nobody dies either. Also, nobody would vote for the first law; at no risk to themselves, they move to the second part of their moral code and therefore vote against. $\endgroup$
    – DonielF
    Nov 8, 2017 at 1:20
  • $\begingroup$ I like this answer, i think it goes in the correct direction to get them to vote themselves into trouble. I suspect however that even if they all vote yes for the second law except the "tyrannical" they've still managed to minimize the number of inhabitants who die, as only 1 died....they can't do anything to make it less than that. $\endgroup$
    – AidanO
    Nov 8, 2017 at 11:01
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One way to do this would be to

Disallow having babies

The islanders would vote for it because:

It does not make themselves more likely to die, and it would minimize the number of others who die (since if a baby is born, the total number of people who will die goes up by 1)

This doesn't kill as many islanders as possible, but it does kill all the islanders.

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  • $\begingroup$ I like the spin: "doesn't kill as many islanders as possible", to do that you gotta breed victims and make sure you get offspring you can also kill. You can achieve this by building a working society which thrives as long as possible and preventing them from inventing anti-aging pills. $\endgroup$
    – Adam
    Nov 9, 2017 at 8:47
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"If you do not vote for this law, you will be killed. If the margin of victory for the law is less than or equal to one vote, no one who votes for it gets killed. Otherwise, everyone who votes for it has probability 1-epsilon of being killed." There is no situation where voting for the law increases a person's chance of being killed, and there are there are situations where voting against the law increases a person's chances of being killed. Therefore, by at least one interpretation of their moral compass, all of the voters will vote for the law, and the probability of killing all of them can be made arbitrarily close to 1.

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    $\begingroup$ Perfectly logical inhabitants would never vote for this law because they know everyone's objective is to minimise death,and thus are not at risk $\endgroup$
    – Andrey
    Nov 7, 2017 at 22:53
  • $\begingroup$ @Andrey It sounds like you're saying that inhabitants would not vote for this law because inhabitants would not vote for the law. Can you explain your reasoning better? If everyone else votes against the law, then you voting for the law changes nothing. If other people vote for the law, then you voting for the law decreases your chance of being killed. As long as you think the probability of other people voting for the law is greater than zero, it's in your interests to vote for the law. $\endgroup$
    – Acccumulation
    Nov 7, 2017 at 23:12
  • $\begingroup$ your law is a kind of prisoner's dilemma. In a prisoner's dilemma logical, good, players that know everyone is is also logical and good would never descent. That only happens from mistrust $\endgroup$
    – Andrey
    Nov 8, 2017 at 2:38
  • $\begingroup$ @Andrey I don't see any indication in the question that the islanders are good, or that they know that everyone is logical. The given answer seems sound to me. $\endgroup$
    – Tanner Swett
    Nov 8, 2017 at 3:02
  • $\begingroup$ @Andrey The problem specifically says that the people value their lives over the lives of others. The very nature of the question implies a Prisoner's Dilemma type exploit. If everyone is good and logical, then there wouldn't be any answer at all, because they would reject anything that results in anyone being killed. Also, "descent" is a noun, not a verb. $\endgroup$
    – Acccumulation
    Nov 8, 2017 at 4:21
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This could be done by introducing:

Wealth and Protection law

What it does:

- People on the Island will need to protect themselves against outsider, thus firearms will be provided for free to all citizen.
- People will be also given a sum of wealth for a better living.

Without knowing the evil intentions there's no reason to not vote for the law. However:

Wealth given will be given random - some will have way more than others. With guns and inequality, it's only human nature to turn themselves against each other.

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The tyrant should propose a law stating that

everyone who failed to vote for this law shall be killed, and among those who voted for this law, a random 50% shall be killed.

Each islander's incentive for voting for the law is that

if at least half of the other islanders also voted in favor, his or her risk of death is reduced by 50 percentage points compared to if he or she had voted against.

Meanwhile, each islander's incentive for voting against the law is that

if exactly half (rounded down) of the other islanders also voted in favor, his or her risk of death is reduced by 50 percentage points compared to if he or she had voted in favor.

So as long as the islanders think there is some chance of the law passing by more than a majority, they will all want to vote for it, resulting in 50% of them being killed.

That 50% number can probably be raised much, much higher (say, 99.9%), since if the island is large enough, the chance of exactly half of the islanders voting for the law will be extremely small.

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  • $\begingroup$ Perfectly logical inhabitants would never vote for this law because they know everyone's objective is to minimise death,and thus are not at risk $\endgroup$
    – Andrey
    Nov 7, 2017 at 22:53
  • $\begingroup$ @Andrey That's true if the islanders make the decision collectively, but the question states that they do not make the decision collectively. On an individual basis, everyone prefers "for" over "against" as long as there's a non-zero chance of the law passing by more than a majority. As you mention in another comment, it's a prisoner's dilemma, and there's no reason any of the islanders would cooperate. $\endgroup$
    – Tanner Swett
    Nov 8, 2017 at 2:51
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First

single out any group that is less than 50% of the population and accuse them of being dangerous.

Then

immediately propose a law that states that all people who are a part of that group must be put to death.

People will vote for it because

if there is even a small chance the threat is real people will vote to protect themselves since moral #1 takes complete precedence.

Lastly

repeat until everyone's dead. For the last two, you can vote to kill the second to last one 10 days from the passage of the vote then use him to pass the vote on the final person.

This does not require them to fall for any trick, vote for something they regret later, or even fall for a prisoners dilemma.

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    $\begingroup$ I don't see how your third point follows from their first. For the majority of people, the law doesn't affect them, so rule 2 (minimize inhabitants who die) is used, and they vote against it. $\endgroup$
    – Challenger5
    Nov 8, 2017 at 4:13
  • $\begingroup$ If they vote for the law because they believe the claim that the other people are dangerous, and the other people are not dangerous, then they are falling for a trick. And obviously if everyone dies, then they are falling for a trick, and they'll regret going along with it. $\endgroup$
    – Acccumulation
    Nov 9, 2017 at 3:27
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A couple of ways to go with a similar idea

Tell everyone they must abandon their status of inhabitant. Pull up a boat to leave. Blow up boat in the middle of the ocean if that's a must for you to scrope points

They don't know so it seems like there is no risk of death. Absolutely minimises death of inhabitant in the long run

Enjoy your new island.

OR

The tyrant is a lich, time is on his side

Ban Procreation

No risk of death. Everyone will vote for this because it will without question minimise death in the long run. Wait for it to depopulate

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