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        riddles >> easy >> What's fair? What's right?
        
(Message started by: BenVitale on Jul 27^th, 2010, 3:45pm)

Title: What's fair? What's right?
Post by BenVitale on Jul 27^th, 2010, 3:45pm

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?

Title: Re: What's fair? What's right?
Post by ThudanBlunder on Jul 27^th, 2010, 5:09pm

[hide]A offers to pay 60% in case of losing, $3.
(S)he is therefore entitled to 60% in case of winning, $24.[/hide]

Title: Re: What's fair? What's right?
Post by BenVitale on Jul 27^th, 2010, 5:39pm

on 07/27/10 at 17:09:53, ThudanBlunder wrote:

[hide]A offers to pay 60% in case of losing, $3.
(S)he is therefore entitled to 60% in case of winning, $24.[/hide]

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.

Title: Re: What's fair? What's right?
Post by MathsForFun on Jul 28^th, 2010, 12:52am

on 07/27/10 at 15:45:59, BenVitale wrote:

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).

Title: Re: What's fair? What's right?
Post by towr on Jul 28^th, 2010, 12:57am

Like Thud and MathsForFun, I'll go for option 3.

on 07/27/10 at 17:39:07, 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.

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.

Title: Re: What's fair? What's right?
Post by MathsForFun on Jul 28^th, 2010, 1:31am

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?

Title: Re: What's fair? What's right?
Post by Grimbal on Jul 28^th, 2010, 1:55am

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.

Title: Re: What's fair? What's right?
Post by Grimbal on Jul 28^th, 2010, 2:00am

on 07/28/10 at 01:31:23, MathsForFun wrote:

What would you give each person?

That is really a different problem. You should start a new topic.

Title: Re: What's fair? What's right?
Post by BenVitale on Jul 29^th, 2010, 12:20pm

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.

Title: Re: What's fair? What's right?
Post by AndyR2000 on Aug 4^th, 2010, 10:50pm

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

Title: Re: What's fair? What's right?
Post by Grimbal on Aug 5^th, 2010, 3:16am

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.