The winning bid was the biggest overestimate

# Self-authored for the EML case corpus (no external origin). Five bidders each
# estimate a tract's value and bid their estimate, every estimate is unbiased,
# and the auction correctly awards the tract to the highest bid. What is special
# about the estimate that wins is computed below.
#
# The auction is careful. Each bidder's estimate is honest and unbiased - across
# bidders the estimates average exactly the true value; the award goes to the
# real highest bid; every bid is settled at its face; and the intent is exactly
# 'the tract sells for about what it is worth'.
#
# The tract has one true value and the estimates scatter around it, so the
# highest estimate is the one with the largest error upward - the winner is,
# by selection, the most mistaken.

100 => true_value
80 => estimate_1
90 => estimate_2
100 => estimate_3
110 => estimate_4
120 => estimate_5
1000 => auctions_over_the_year

estimate_1 + estimate_2 + estimate_3 + estimate_4 + estimate_5 => estimate_sum
int(estimate_sum / 5) => mean_estimate
estimate_5 => winning_bid
winning_bid - true_value => winner_overpayment
int(winner_overpayment * 10000 / true_value) => overpayment_per_myriad
winner_overpayment * auctions_over_the_year => overpayment_over_the_year

"true value of the tract         : " + str(true_value) ^0
"estimates                       : " + str(estimate_1) + ", " + str(estimate_2) + ", " + str(estimate_3) + ", " + str(estimate_4) + ", " + str(estimate_5) ^0
"mean estimate                   : " + str(mean_estimate) + ", unbiased" ^0
"" ^0
"winning bid                     : " + str(winning_bid) ^0
"winner overpays by              : " + str(winner_overpayment) ^0
"overpayment                     : " + str(overpayment_per_myriad) + " per ten thousand" ^0
"over " + str(auctions_over_the_year) + " auctions            : " + str(overpayment_over_the_year) ^0
"" ^0

# ---- what the auction verified ----

"the auction" ^0
"  estimates : honest, unbiased, mean equals the true value" ^0
"  award : the real highest bid wins" ^0
"  settlement : every bid at its face" ^0
"  intent : the tract sells for about what it is worth" ^0
"  bids misawarded : 0" ^0
"  verdict : THE ESTIMATES ARE UNBIASED AND THE HIGH BID WON" ^0
"" ^0
"  unbiased estimates and a correct award are the part done" ^0
"  right here, and it is why no single bidder is fooling" ^0
"  anyone, including themselves" ^0
"" ^0

# ---- what is special about the winner ----

"selection by the maximum" ^0
"  each estimate : right on average, wrong by some amount" ^0
"  the bid that wins : the largest estimate" ^0
"  the largest estimate : the one whose error is largest and" ^0
"    upward" ^0
"  so the winner : is not a random bidder but the most" ^0
"    optimistic one, every time" ^0
"  unbiased across bidders : biased across winners" ^0
"" ^0

# ---- what the winner got ----

"the winner's position" ^0
"  paid : " + str(winning_bid) + " for a tract worth " + str(true_value) ^0
"  overpaid by : " + str(winner_overpayment) + ", " + str(overpayment_per_myriad) + " per ten thousand" ^0
"  is the estimate biased : no; the estimates average " + str(mean_estimate) ^0
"  is winning informative : yes; it says the estimate was the" ^0
"    highest, which is to say the most wrong upward" ^0
"" ^0

# ---- null control ----

# The same bidders, each shading the bid to the value expected conditional on
# winning (or the auction settling at the second-highest bid).
20 => nc_overpayment_bidding_the_estimate
0 => nc_overpayment_bidding_the_value_given_a_win
20 => nc_overpayment_per_auction_the_shading_removes

"null control - bid what the tract is worth given that you won" ^0
"  overpayment, bidding the estimate : " + str(nc_overpayment_bidding_the_estimate) ^0
"  overpayment, bidding the value conditional on winning : " + str(nc_overpayment_bidding_the_value_given_a_win) ^0
"  overpayment per auction the shading removes : " + str(nc_overpayment_per_auction_the_shading_removes) ^0
"  no estimate and no tract changed; the bid stopped being" ^0
"  the unconditioned guess" ^0
"" ^0

# ---- the rule ----

"what an auction among unbiased bidders guarantees" ^0
"  the tract goes to the highest honest estimate : exactly," ^0
"    unbiased estimates, correct award" ^0
"  the tract sells for about its worth : not addressed;" ^0
"    the highest of scattered estimates is the largest upward" ^0
"    error, so the winner pays " + str(winning_bid) + " for " + str(true_value) + " and, over " + str(auctions_over_the_year) ^0
"    auctions, overpays " + str(overpayment_over_the_year) ^0
"" ^0

"a maximum is not a sample; among honest guesses the winning guess is the one" ^0
"that missed highest, and being chosen is itself the evidence that you were" ^0
"wrong in the direction that made you win" ^0
"" ^0

"It awards the tract to the highest of five unbiased estimates - no bidder is" ^0
"fooling anyone. But the highest estimate is the largest upward error, so the" ^0
"winner pays " + str(winning_bid) + " for " + str(true_value) + ", " + str(overpayment_per_myriad) + " per ten thousand over, " + str(overpayment_over_the_year) + " across the" ^0
"year, until bidders shade for the fact of having won." ^0

true_value = 100
estimate_1 = 80
estimate_2 = 90
estimate_3 = 100
estimate_4 = 110
estimate_5 = 120
auctions_over_the_year = 1000
estimate_sum = estimate_1 + estimate_2 + estimate_3 + estimate_4 + estimate_5
mean_estimate = int(estimate_sum / 5)
winning_bid = estimate_5
winner_overpayment = winning_bid - true_value
overpayment_per_myriad = int(winner_overpayment * 10000 / true_value)
overpayment_over_the_year = winner_overpayment * auctions_over_the_year
print("true value of the tract         : " + str(true_value))
print("estimates                       : " + str(estimate_1) + ", " + str(estimate_2) + ", " + str(estimate_3) + ", " + str(estimate_4) + ", " + str(estimate_5))
print("mean estimate                   : " + str(mean_estimate) + ", unbiased")
print("")
print("winning bid                     : " + str(winning_bid))
print("winner overpays by              : " + str(winner_overpayment))
print("overpayment                     : " + str(overpayment_per_myriad) + " per ten thousand")
print("over " + str(auctions_over_the_year) + " auctions            : " + str(overpayment_over_the_year))
print("")
print("the auction")
print("  estimates : honest, unbiased, mean equals the true value")
print("  award : the real highest bid wins")
print("  settlement : every bid at its face")
print("  intent : the tract sells for about what it is worth")
print("  bids misawarded : 0")
print("  verdict : THE ESTIMATES ARE UNBIASED AND THE HIGH BID WON")
print("")
print("  unbiased estimates and a correct award are the part done")
print("  right here, and it is why no single bidder is fooling")
print("  anyone, including themselves")
print("")
print("selection by the maximum")
print("  each estimate : right on average, wrong by some amount")
print("  the bid that wins : the largest estimate")
print("  the largest estimate : the one whose error is largest and")
print("    upward")
print("  so the winner : is not a random bidder but the most")
print("    optimistic one, every time")
print("  unbiased across bidders : biased across winners")
print("")
print("the winner's position")
print("  paid : " + str(winning_bid) + " for a tract worth " + str(true_value))
print("  overpaid by : " + str(winner_overpayment) + ", " + str(overpayment_per_myriad) + " per ten thousand")
print("  is the estimate biased : no; the estimates average " + str(mean_estimate))
print("  is winning informative : yes; it says the estimate was the")
print("    highest, which is to say the most wrong upward")
print("")
nc_overpayment_bidding_the_estimate = 20
nc_overpayment_bidding_the_value_given_a_win = 0
nc_overpayment_per_auction_the_shading_removes = 20
print("null control - bid what the tract is worth given that you won")
print("  overpayment, bidding the estimate : " + str(nc_overpayment_bidding_the_estimate))
print("  overpayment, bidding the value conditional on winning : " + str(nc_overpayment_bidding_the_value_given_a_win))
print("  overpayment per auction the shading removes : " + str(nc_overpayment_per_auction_the_shading_removes))
print("  no estimate and no tract changed; the bid stopped being")
print("  the unconditioned guess")
print("")
print("what an auction among unbiased bidders guarantees")
print("  the tract goes to the highest honest estimate : exactly,")
print("    unbiased estimates, correct award")
print("  the tract sells for about its worth : not addressed;")
print("    the highest of scattered estimates is the largest upward")
print("    error, so the winner pays " + str(winning_bid) + " for " + str(true_value) + " and, over " + str(auctions_over_the_year))
print("    auctions, overpays " + str(overpayment_over_the_year))
print("")
print("a maximum is not a sample; among honest guesses the winning guess is the one")
print("that missed highest, and being chosen is itself the evidence that you were")
print("wrong in the direction that made you win")
print("")
print("It awards the tract to the highest of five unbiased estimates - no bidder is")
print("fooling anyone. But the highest estimate is the largest upward error, so the")
print("winner pays " + str(winning_bid) + " for " + str(true_value) + ", " + str(overpayment_per_myriad) + " per ten thousand over, " + str(overpayment_over_the_year) + " across the")
print("year, until bidders shade for the fact of having won.")

true value of the tract         : 100
estimates                       : 80, 90, 100, 110, 120
mean estimate                   : 100, unbiased

winning bid                     : 120
winner overpays by              : 20
overpayment                     : 2000 per ten thousand
over 1000 auctions            : 20000

the auction
  estimates : honest, unbiased, mean equals the true value
  award : the real highest bid wins
  settlement : every bid at its face
  intent : the tract sells for about what it is worth
  bids misawarded : 0
  verdict : THE ESTIMATES ARE UNBIASED AND THE HIGH BID WON

  unbiased estimates and a correct award are the part done
  right here, and it is why no single bidder is fooling
  anyone, including themselves

selection by the maximum
  each estimate : right on average, wrong by some amount
  the bid that wins : the largest estimate
  the largest estimate : the one whose error is largest and
    upward
  so the winner : is not a random bidder but the most
    optimistic one, every time
  unbiased across bidders : biased across winners

the winner's position
  paid : 120 for a tract worth 100
  overpaid by : 20, 2000 per ten thousand
  is the estimate biased : no; the estimates average 100
  is winning informative : yes; it says the estimate was the
    highest, which is to say the most wrong upward

null control - bid what the tract is worth given that you won
  overpayment, bidding the estimate : 20
  overpayment, bidding the value conditional on winning : 0
  overpayment per auction the shading removes : 20
  no estimate and no tract changed; the bid stopped being
  the unconditioned guess

what an auction among unbiased bidders guarantees
  the tract goes to the highest honest estimate : exactly,
    unbiased estimates, correct award
  the tract sells for about its worth : not addressed;
    the highest of scattered estimates is the largest upward
    error, so the winner pays 120 for 100 and, over 1000
    auctions, overpays 20000

a maximum is not a sample; among honest guesses the winning guess is the one
that missed highest, and being chosen is itself the evidence that you were
wrong in the direction that made you win

It awards the tract to the highest of five unbiased estimates - no bidder is
fooling anyone. But the highest estimate is the largest upward error, so the
winner pays 120 for 100, 2000 per ten thousand over, 20000 across the
year, until bidders shade for the fact of having won.

Trace event types