5 economists, 1 island and a bad of gold?

Question

this is a scenario question i was posted when i attended an interview. hope everyone can contribute to the answer and at the end i well disclose the answer and see if it is a unanimous answer. this is a economic question in a way.

here is a scenario:-
5 economists are stuck in an island. Each older than the next. And there is a bag consist of 100 gold coins. The youngest economist is given a task. To distribute the gold. If the majority of the including him agree with his distribution method, his life will be spared. What does he do?

bag of gold. not bad of gold. sorry for the mistake

somehow, there is a particular theory to the answer. even though i don't agree, i will share with you guys later.

Answer 1

They should use the gold to pay a sailor to take 'em off the island!

(Or share 20 each, though nothing to spend the cash on)

Answer 2

The answer depends on how the 'game' works. If you're allowed to hide the treasure, that's a good incentive for the others to keep you alive. If there's no particular plan for what happens when the youngest dies, I'd split the money evenly -- but 25% to the other four, leaving the youngest out (his skin is worth more than his share of the gold). In my analysis below, I'll label the economists A, B, C, D, and E with A the oldest and E the youngest.

I think the intent is that:
1. The gold coins are indivisible
2. If the majority don't like the distribution the youngest is killed and the process repeats.

If so, there are two possibilities. Consider first that on a tie the youngest is killed. If there are only two left, A will get all the gold, since otherwise he'll have B killed. As such if there are three, the youngest (C) needs only to give B 1 gold coin and keep the rest for himself, since 1 coin is better than the nothing B would otherwise get. With four, D needs three votes to survive. A can be bought for just 1 coin (since otherwise C would cut him out entirely) and B for 2, leaving 97 for D. The final answer, then, is to give A 2 gold coins and C 1, leaving the rest for E.

If a tie results in the survival of the youngest, which is my best guess as to the intent, a similar analysis results. A and C get one coin each, with E taking the remainder.


Hermes suggests an interesting variant, in which each player can make a binding proposal as desired, not just the offer of the current economist. With two economists this changes nothing, of course. Consider the case where at least half the votes are needed. Between A and B, A gets all the gold as usual. C cannot just offer 1 gold coin to B, though, since A could promise B 2 gold coins for his vote. In fact, C cannot even offer B 98 coins, since A would then promise B 99. As a result, C must offer at least 99 coins to B to save his life -- and if either A or B is bloodthirsty (prefers to kill if money is the same), C must offer it all to B. The final result with binding proposals is just as absurd as the current result.

Answer 3

Bury it in a hidden location, only he knows .... then they have to keep him alive to dig it up when they are rescued .... lol

But don't worry. He can give them a line of credit to use until a rescue boat comes. He will be the "bank manager" and finish up bankrupting all those that threatened his life.

GUESS NUMBER 2:
give each 5 gold coins to start a financial based system on the island. The balance of the coins are hidden where only the youngest knows. Each economist has the chance to develop different survival or lifestyle commodities that the others can buy with their other 15 coins each held in the youngest's "bank", with him being the "bank manager".
When rescued, the remaining coins will be unearthed and the final distribution of gold will be made.
This will ensure the youngest will stay alive till rescued. It can also allow him to manipulate the "Credit/Loans" needed to pay the most ruthless economists. This will make the ruthless ones targets of those made bankrupt, and the youngest will save his skin while eliminating those threatening to murder.

Answer 4

The fundamental question is: what can the youngest economist do, such that no 3 people have anything to gain by killing him? Because only then will the majority be satisfied. He himself will agree with his choice, and he's one of the five, so he needs to please 2 others for a majority agreement of 3 people.

So he gives 50 coins each to two of the other guys. They'll each have no reason to expect any better arrangement for themselves; each of them will see that no one else has MORE coins than he does. That makes 3 happy people, who will outvote the two losers. Um, sounds good enough to me.

Answer 5

Well the correct answer would be 100/5=20 gold coins each.
If there is a catch... I do not seem to get it... On an Island, isolated, the gold coins are useless....
If the fact that they are older affects the way it is dristributed... I do not get it... the older gets more? Does not make much sense for an interview minitest.
Weird. Tell me where did you apply so I do not go there. LOL Just kidding

Answer 6

Economists are greedy b*****ds so dividing by 5 would not be the right answer.
First though is 34 to two of them and 32 for his self.
Pick two of the strongest to share with.
With economists I presume it is dog eat dog mentality.
There are possible repercussions with this mathematically sound solution.
Like watch your back.
Me personally. I would set up a Texas Holdem Poker Tournament.
Having 70 first and a 30 gold coins second prize.

Answer 7

The preceding anwer is truly insane. It must come from one of those insane economists on the island ...
How can such a ridiculous answers be presented as rational, and rational for economists ?

To understand that we need to look at the conditions of the game. They are not clearly spelled here so we need to guess them.

The logic of the scenario leads us to expect that the 5 economists want to enjoy the maximum of the gold (and in order to do so want to stay alive), do not care about the life of the others. (that is their rationality their preference curbs)
The logic of the scenario leads us also to believe to expect that if the younger is killed, the next younger will be given the same task.
And we can also guess that the youngest can only try once and can not discuss with others.
We must also presuppose that economists can not communicate and make credible engagements (promisses).

Once all those conditions are set, then we end up with the absurd reasonning presented above. So where lies the error ?

The error is of course in the game itself. Who decided the game ?
We face two options here :
A fairy a djinn, God, or natural selection, forced the economists to accept the game as is. May be god came and told them about the rules. Or may be there are thousands of such islands and on each of them games are being played, and replayed. THe rules of the games evolve by spontaneous mutations. And when island communicate with another those islands with the best games rule over the islands with poor games.
Anyway the point remains : humans in general and economist in particular can not choose rules of the game, can not commit to respecting them, the rules are instated from above or below them.
If this is the case, then the answer is logical. But it clearly shows how unintersting the answer is. Indeed we all know that humans can purposively modify the rules of their interaction that different cultures lead to differnt rules etc. So It s not really interesting to learn about what would do people lacking the basic hability to discuss rules, make commitments etc.

The second possible explanation is that economists themselves set up the rules of the game. And here it becomes really strange.
How have they agreed in the first place on who shall make the repartition between them. If rational economist reason in the way presented above, how did they agree to have the yougest make the repartition first, and not the oldest for instance ? Did they not foresee the result ?

Assuming they did adopt such a rule, and commit to respecting it, why make other commitments. Consider two options available to players to increase their gains : propose higher bids assorted by commitments not to vote, make coalition.
Both are interesting to explore.
Consider the solution given above where E offers A 2 and C 1 and keeps 97.
What prevents D to say the following :if you vote to kill E, I propose to offer each of you 10, (indeed he could propose 3 to A and 2 to C). To ensure you that I will give you this and not cheat at the last minute, I promise that those will be taken from my share of the 100 gold coins after the repartition has been voted. This is a legally enforceable promise and you can kill me if I don't respect it.
What prevents him to propose such a deal ? Nothing.
Hence E is forced to raise his offer.
Where will this end ?
Well if only E and D make counter proposals, B is systematically forgotten. He may then try to enter the game.

How ?

And here we have another solution, an alliance to share equally the gains and to vote together. The funny thing is that alliances can be kept secret. For instance B and D could make an alliance to share gains, and not tell others about it. B and D now form F' which has two votes. F' wll vote against E and propose 1 to A to gain support and share the 99 of the rest equally.

of course if E hears of the alliance he may try to form one with A or C ...
etc.

It s easy to see that the solution proposed highlights all the default of mainstream economic theories :economic agents are unable to choose rules, make credible commitments, and this leads to completely counterintuitive results.

I suggest another game. There are 5 economists on an Island, and one bag of gold, how do they agree on a rule that will decide how they split the gold bag ?

I believe that they will vote for someone who makes credible promisses to do a fair distribution. I believe that they will warn him that if he departs from his proposition he will get killed.

The game proposed would never exist among rational economist, because rational economist would immediatly see where its leading to, and hence would refuse to play it and instead create another game.

I think it s a bit like a perfect market. No rational holder of capital would ever accept to play by the rules of the free market if he/she can be a monopolist instead and pocket profits (under perfect competition there is no profit).

So why worry at how rational agents would react in a hypothical situation if no rational agents would agree to institute that situation ?

Put 5 economists on as island and watch how they produce and trade. One thing is sure, they will not create a free market or anything approaching. Yet I bet they ll spend scores of time at wondering how they would trade and produce under free market.

Answer 8

An economist would realize that gold has no value on an island, so he should go catch a fish or do something to help them survive.

Answer 9

Is it bag of gold or bad gold, in either case it is worthless to him since they stucked.

Answer 10

They kill him anyway, and name the nation America