Fair way to split coins

Question

Alice and Bob went walking in the desert. Alice had two gallons of water and Bob had three gallons. They met Charlie who had no water at all and they all (Alice, Bob, and Charlie) shared the five gallons of water evenly. As a token of his gratitude, Charlie gave them five gold coins. What is the fair way to split these five coins?

Source: Ponder This

score 13 · Accepted Answer · answered Mar 19 '19 at 00:54

13

Alice has 6/3 gallons of water. Bob has 9/3 gallons of water.

After sharing the five gallons of water evenly,

Alice has given Charlie 1/3 gallons of water and Bob has given him 4/3 gallons of water.

As such, I believe Alice should get

1 gold coin

and Bob

the other four - the effective trade is 1 gold coin for 1/3 gallons of water, here.

answered Mar 19 '19 at 00:54

Braegh

2,767
11
19

That's one way of looking at it. Another, from the economists: using logarithmic utility. Alice, who has less water to begin with, is likely to value it more. 'Fair', should reflect that. – Ben S Mar 19 '19 at 05:39

Fair way to split coins

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