"Honest" decision systems

Saari at aol.com Saari at aol.com
Thu Apr 10 15:51:42 PDT 1997

Awhile back you asked me for more info on Second Place Auction and on Median
Voting.  Each of these has the desirable property that the exactly "honest"
behaviour is also the most rational behavior.  In other words, there is zero
incentive to exaggerate.

In a standard sealed-bid auction, there is an incentive to try to bid less
than your true value.  For instance, let's say the item is worth spending up
to $100 (to you), and you believe the next higher bidder is unwilling to
spend more than $80.  Then a lower bid of $90 instead of $100 will save you
$10 (assuming your info was accurate).

In "Second Place Auction", the auction rules state that the highest bidder
wins, but only pays the amount of the next highest bid.  Weird, but it has a
desirable result of virtually guaranteeing high but honest bids.  For
instance, let's say again that the item is worth (to you) spending any amount
up to $100 but no more.  Under Second Place Auction, a bid of exactly $100 is
the ONLY rational choice.  Bidding higher can never do any good (and risks
buying the item for more than your upper limit).  But bidding lower can also
never do any good!  It won't save you any money, and it might cost you a
valid opportunity to get the item for $95 or whatever.  

If you're not convinced I can elaborate further, but the final result is
clearly that Second Place Auction practically forces the participants to make
"honest" bids, i.e. the maximum they are willing to pay.

"Median Voting" is a separate situation, but with the similar quality of
more-or-less forcing an honest response.  Let's say a group of people is
trying to choose a number, such as the temperature of the room.  The prior
agreement is that everybody picks a single number, and the "median" value
will be chosen.  (This means that if there are 21 voters, the votes are
ordered and then the number in position number 11 is the winner.)

This method has the desirable quality that the "honest" vote is always the
most rational one.  Even if a person has foreknowledge of the votes of some
or all of the other voters, there is never anything to be gained by
exaggerating in either direction.  (Try it!)
Both of these methods have the desirable property that an "honest" response
is the only rational response.  I haven't figured out how to adapt either of
these to general-purpose voting, but they inspire me to try.

Mike S

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