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March 10th, 2010, 08:32 AM   #21
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Re: Fair Division

Quote:
 “I don't agree with that (even if I might be convinced to pick 'your' auction vs. 'their' auction). That division may result in the players being strictly less well-off than a different method; I think we should remain open to other possibilities.”
It’s not the auction strategy I’m troubled with. I recognize all auctions have pros and cons. My issue is with the splits being based on different sized pies/shares.

Quote:
 “If the bids are honest, this may be a desirable principle (though I'm not convinced; see above). But when the votes are known to be dishonest, there's no reason to stick to that. Say the estate has just one item. A values it at $90, B at$600, and C at $1200. First of all, it's not obvious that the Vickrey price of$600 is the right one -- any price from $600 to$1200 might lay claim to that. But what if B dishonestly bids $900? He knows that this will increase his share of the estate by$100, so it's in his interests. So just because we *want* to give everyone $200 doesn't mean that we should actually give everyone one-third of the second-highest bid, because that might not reflect reality.” I disagree with your conclusions as it relates to a dishonest bid. Assume for a moment we’re talking about an open auction amongst the three heirs. If B thinks C will bid more than$600 he should continue bidding beyond his target value of $600. Doing that does not make his bids dishonest, he’s just trying to make sure the items are sold at market value. Remember, he takes great risk as he bids beyond his target value because he has no idea when C will stop bidding. The same logic applies to a Vickrey structured auction. So what you are calling dishonest, I call an attempt to establish market value. Again, I'm not all that worried about the auction structure, its the splitting of the proceeds once the auction has been concluded that has me questioning Fair Division. March 10th, 2010, 09:53 AM #22 Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Fair Division Quote: Originally Posted by fever Quote:  “I don't agree with that (even if I might be convinced to pick 'your' auction vs. 'their' auction). That division may result in the players being strictly less well-off than a different method; I think we should remain open to other possibilities.” It’s not the auction strategy I’m troubled with. I recognize all auctions have pros and cons. My issue is with the splits being based on different sized pies/shares. You misread what I wrote. Quote:  Originally Posted by fever I disagree with your conclusions as it relates to a dishonest bid. Assume for a moment we’re talking about an open auction amongst the three heirs. If B thinks C will bid more than$600 he should continue bidding beyond his target value of \$600. Doing that does not make his bids dishonest, he’s just trying to make sure the items are sold at market value. Remember, he takes great risk as he bids beyond his target value because he has no idea when C will stop bidding. The same logic applies to a Vickrey structured auction. So what you are calling dishonest, I call an attempt to establish market value.
You misunderstand the auction, then -- or at least the meaning of dishonest/sophisticated/tactical.

I can't fathom how you can say, for a fixed set of players and items, "X is a fair split because each person has an equal share of the auction values of the items, and Z is a fair split because each person has an equal share of the auction value of the items, but Y is not a fair split" when Z could be strictly between X and Y for each player. If the system can be gamed so that the final bids do not reflect the values (neither to the market nor to the players), then by what right can you call a distribution unfair if a player has a share not equal to the (false) values of the items?

Quote:
 Originally Posted by fever Again, I'm not all that worried about the auction structure, its the splitting of the proceeds once the auction has been concluded that has me questioning Fair Division.
They are inexorably tied. The way the proceedings are divided determined how the auction will proceed; the type of auction determines how much there is to divide. You can't just ignore one if you want the other to be sensible. You're assuming monotonicity in a highly non-monotonic system.

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