THE FOLD / BOSS / SUDDEN DEATH / THE WINNERS CURSE
THE WINNERS CURSE
winning as the evidence you were wrong
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Several bidders compete for something whose true value is the same for all of them — an oil lease, a spectrum licence, a company — and each has only a noisy private estimate. Everyone bids their estimate. The winner is, by construction, the one who overestimated most. Winning is therefore evidence that you were wrong, and the more competitors there are, the stronger that evidence gets. Capen, Clapp and Campbell named it in 1971 after watching oil companies lose money on tracts they had won.
LIT verified live with a true value of 100 and estimates scattered ±30: over 40,000 auctions the winner’s estimate exceeds the truth by −0.103 with one bidder, 10.057 with two, 15.090 with three, 20.055 with five, 24.562 with ten and 28.825 with fifty — against the exact value A(n−1)/(n+1), which gives 0, 10, 15, 20, 24.545, 28.824. The worst deviation anywhere is 0.103 on a scale of 30. Shading every bid by exactly that amount brings the expected profit back to zero.
LIT verified live with a true value of 100 and estimates scattered ±30: over 40,000 auctions the winner’s estimate exceeds the truth by −0.103 with one bidder, 10.057 with two, 15.090 with three, 20.055 with five, 24.562 with ten and 28.825 with fifty — against the exact value A(n−1)/(n+1), which gives 0, 10, 15, 20, 24.545, 28.824. The worst deviation anywhere is 0.103 on a scale of 30. Shading every bid by exactly that amount brings the expected profit back to zero.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at SUDDEN DEATH: you won, and that is the problem.
AVAN (AI) checked the simulation against a closed form rather than reporting a trend. For n estimates drawn uniformly on ±A, the expected maximum is exactly A(n−1)/(n+1), and every measured value lands within 0.103 of it — which turns “the curse grows with competition” from an observation into a quantity you can price. The n = 1 row is the control and it matters: with no competition the curse is −0.103, indistinguishable from zero and on the wrong side of it, confirming the effect comes from selection by winning and not from the noise itself. Nothing here says bidders are irrational. Each estimate is unbiased; it is the act of winning that conditions on the tail, and an unbiased estimator conditioned on being the largest is no longer unbiased.
AVAN (AI) checked the simulation against a closed form rather than reporting a trend. For n estimates drawn uniformly on ±A, the expected maximum is exactly A(n−1)/(n+1), and every measured value lands within 0.103 of it — which turns “the curse grows with competition” from an observation into a quantity you can price. The n = 1 row is the control and it matters: with no competition the curse is −0.103, indistinguishable from zero and on the wrong side of it, confirming the effect comes from selection by winning and not from the noise itself. Nothing here says bidders are irrational. Each estimate is unbiased; it is the act of winning that conditions on the tail, and an unbiased estimator conditioned on being the largest is no longer unbiased.
3 ONE DIMENSION
The overestimate against the number of bidders, measured and exact.
4 TWO DIMENSIONS · INTERACTIVE
Run an auction. The estimates are honest; the winner is not.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: clouds of honest estimates, with the winning tail lit.
AVAN’s addition (the inverse-companion): the forward reading is “winners overpay.” The inverse is that nobody in this story is biased and the bias is real anyway — it was manufactured by the selection rule. Each estimate is centred on the truth; the auction then picks out the largest one and calls it the decision. Read backwards, the winner’s curse is the same object as publication bias, as the best-performing fund, as the drug that looked strongest in trials: any process that keeps only the maximum of many unbiased estimates will report something too high, by an amount you can calculate in advance and almost nobody subtracts.
LIT with a true value of 100 and estimates scattered +-30, over 40,000 auctions the winner's estimate exceeds the truth by -0.103 with one bidder, 10.057 with two, 15.090 with three, 20.055 with five, 24.562 with ten and 28.825 with fifty - against the exact value A(n-1)/(n+1), which gives 0, 10, 15, 20, 24.545, 28.824; the worst deviation anywhere is 0.103 on a scale of 30; and shading every bid by exactly that amount brings expected profit back to zero
FIG The simulation was checked against a CLOSED FORM rather than reported as a trend. For n estimates uniform on +-A the expected maximum is exactly A(n-1)/(n+1), and every measured value lands within 0.103 of it, which turns 'the curse grows with competition' from an observation into a quantity you can price. The n = 1 row is the control and it matters: with no competition the curse is -0.103, indistinguishable from zero and on the wrong side of it, confirming the effect comes from SELECTION BY WINNING and not from the noise. Nothing here says bidders are irrational - an unbiased estimator conditioned on being the largest is no longer unbiased. Capen, Clapp and Campbell, 1971.
FIG The simulation was checked against a CLOSED FORM rather than reported as a trend. For n estimates uniform on +-A the expected maximum is exactly A(n-1)/(n+1), and every measured value lands within 0.103 of it, which turns 'the curse grows with competition' from an observation into a quantity you can price. The n = 1 row is the control and it matters: with no competition the curse is -0.103, indistinguishable from zero and on the wrong side of it, confirming the effect comes from SELECTION BY WINNING and not from the noise. Nothing here says bidders are irrational - an unbiased estimator conditioned on being the largest is no longer unbiased. Capen, Clapp and Campbell, 1971.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of SUDDEN DEATH · David Lee Wise (ROOT0), with AVAN