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Topic: What's fair? What's right? (Read 1544 times) |
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Benny
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What's fair? What's right?
« on: Jul 27th, 2010, 3:45pm » |
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A solution to proportionate sharing may feel fair, but not right.
Consider the following:
Two friends, A and B, bought a $5 lottery ticket together.
A paid $3 and B paid $2. Their ticket won $40.
How should A and B share the money?
(1) A gets $20, B gets $20
(2) A gets $21, B gets $19
(3) A gets $24, B gets $16
Which option do you favor? Why?
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ThudnBlunder
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Re: What's fair? What's right?
« Reply #1 on: Jul 27th, 2010, 5:09pm » |
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A offers to pay 60% in case of losing, $3.
(S)he is therefore entitled to 60% in case of winning, $24.
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Benny
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Re: What's fair? What's right?
« Reply #2 on: Jul 27th, 2010, 5:39pm » |
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on Jul 27th, 2010, 5:09pm, ThudanBlunder wrote:A offers to pay 60% in case of losing, $3.
(S)he is therefore entitled to 60% in case of winning, $24. |
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Okay. What if the winning ticket is worth $1 million?
Would that change how we share the money?
The problem does not describe an understanding or agreement where one will receive money according to one's investment ratio.
So it's possible to go with equal sharing.
What if I tell you that you could not have bought the ticket without my contribution.
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MathsForFun
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Re: What's fair? What's right?
« Reply #3 on: Jul 28th, 2010, 12:52am » |
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on Jul 27th, 2010, 3:45pm, BenVitale wrote:A solution to proportionate sharing may feel fair, but not right.
Consider the following:
Two friends, A and B, bought a $5 lottery ticket together.
A paid $3 and B paid $2. Their ticket won $40.
How should A and B share the money?
(1) A gets $20, B gets $20
(2) A gets $21, B gets $19
(3) A gets $24, B gets $16
Which option do you favor? Why? |
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Option 3 - paying in proportion to the investment. The investment should be treated like a unit trust (see http://en.wikipedia.org/wiki/Unit_trust).
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towr
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Re: What's fair? What's right?
« Reply #4 on: Jul 28th, 2010, 12:57am » |
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Like Thud and MathsForFun, I'll go for option 3.
on Jul 27th, 2010, 5:39pm, BenVitale wrote:Okay. What if the winning ticket is worth $1 million?
[...]
What if I tell you that you could not have bought the ticket without my contribution. |
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Then you should not make a claim on the prize, since you had no interest in the lottery, and I should give you 400.000 anyway, since I wouldn't have won without your help. 
Only at your insistence should I keep more.
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| « Last Edit: Jul 28th, 2010, 1:00am by towr » |
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MathsForFun
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Re: What's fair? What's right?
« Reply #5 on: Jul 28th, 2010, 1:31am » |
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Here's a sharing puzzle that actually occurred in my previous job. There were hundreds of customers who had to be shared fairly (by both number and value of their turnover in the previous 12 months) between telephone reps. It was the most interesting work I have ever been paid to do!
Anyway - here's my simplified version of it: a legacy has to be shared between 4 people. Each should get the same number of items, and the value of each share should be as close as possible (measured by the difference in value between the best and the worst shares). Here are the values of the items:
£150, £200, £212, £215, £251, £277, £315, £370, £400, £414, £450, £477, £581, £697, £841, £888, £999, £1000, £1059, £1137, £1214, £1315, £1423, £1433
What would you give each person?
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| « Last Edit: Jul 28th, 2010, 1:32am by MathsForFun » |
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Grimbal
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Re: What's fair? What's right?
« Reply #6 on: Jul 28th, 2010, 1:55am » |
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To the original problem, I'd also give 60% to A and 40% to B.
Suppose A represents 3 people contributing $1 each, B represents 2 people contributing $1 each.
Now everybody contributed $1, so everybody should receive 1/5 of the prize.
Epilog.
A receives $24 which he redistributes, giving $7 to each person he represents and keeping $3 commission.
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Grimbal
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Re: What's fair? What's right?
« Reply #7 on: Jul 28th, 2010, 2:00am » |
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on Jul 28th, 2010, 1:31am, MathsForFun wrote:| What would you give each person? |
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That is really a different problem. You should start a new topic.
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Benny
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Re: What's fair? What's right?
« Reply #8 on: Jul 29th, 2010, 12:20pm » |
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Thanks to all of you for your contribution.
Yes, the correct answer is option #3. We know it, it's just basic algebra. I was trying to use game theory, and I've conducted a survey with non-math students, and in that survey I included another option:
(1) A gets $20, B gets $20
(2) A gets $21, B gets $19
(3) A gets $24, B gets $16
(4) A gets $20.50, B gets $19.50
since the difference in purchasing the tickets is $1 ($3.00 - $2.00), then I suggested the following split : $20.50 and $19.50)
Sharing profits is one thing, but sharing costs or expenditures is a different matter, and can be trickier.
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AndyR2000
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Re: What's fair? What's right?
« Reply #9 on: Aug 4th, 2010, 10:50pm » |
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Option (3) A gets $24, B gets 16.
It's proportionate to what they originally put it...it is the fairest of them all and most logical.
Not sure I agree with your 'difference in ticket price' rationale.
Person A should be rewarded for taking the greater risk and contributing more towards the ticket. We don't penalise winners, we reward them.
My two cents worth......good thread
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| « Last Edit: Aug 4th, 2010, 10:50pm by AndyR2000 » |
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Grimbal
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Re: What's fair? What's right?
« Reply #10 on: Aug 5th, 2010, 3:16am » |
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BenVitale's (4) would mean that A and B contribute the same, but B borrowed $.50 from A. The split would be as he proposes, but then, in the case of a loss, B should also return $.50 to A.
You could also propose
(5) A gets $38, B gets $2. The logic being that A borrowed $2 from B, so he returns it.
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