                               In the

United States Court of Appeals
               For the Seventh Circuit

Nos. 10-3062, 10-3068

BCS S ERVICES, INC., et al.,
                                             Plaintiffs-Appellants,
                                 v.

H EARTWOOD 88, LLC, et al.,
                                            Defendants-Appellees.


            Appeals from the United States District Court
        for the Northern District of Illinois, Eastern Division.
     Nos. 05 C 4095, 07 C 1367—James F. Holderman, Chief Judge.


    A RGUED F EBRUARY 24, 2011—D ECIDED M ARCH 24, 2011




  Before B AUER, P OSNER, and M ANION, Circuit Judges.
  P OSNER, Circuit Judge. These consolidated appeals are
from judgments in two suits seeking damages under the
Racketeer Influenced and Corrupt Organizations Act
(RICO), 18 U.S.C. §§ 1961 et seq., for mail fraud. (The
suits are materially identical so we’ll pretend that
they’re one case and that the two appeals are also one.)
The district court dismissed the case more than five
years ago on the ground that the plaintiffs lacked
standing to sue because they hadn’t relied on the fraud
2                                     Nos. 10-3062, 10-3068

and therefore “at best were indirect victims of the alleged
fraud.” Phoenix Bond & Indemnity Co. v. Bridge, 2005 WL
3527232, at *5 (N.D. Ill. Dec. 21, 2005). We reversed, 477
F.3d 928 (7th Cir. 2007), and the Supreme Court affirmed
our decision. 553 U.S. 639 (2008). The case returned to
the district court, which has again dismissed, this time
by granting summary judgment for the defendants on
the ground that the plaintiffs can’t prove that the fraud
was a “proximate cause” of their alleged losses. Although
that sounds like a different ground from the first
dismissal, it’s actually pretty close. The district judge’s
second opinion states that “any number of reasons
wholly unrelated to Defendants’ alleged violations of the
SSBR [the rule that the defendants are alleged to have
violated to effectuate the fraud] could impact the value
of Plaintiffs’ lien portfolios: [among others,] the Trea-
surer’s determination of whether to bar Defendants
from the sales, and if so for how long; the actions of third-
party bidders, including how quickly they bid; the auc-
tioneers’ subjective awarding of liens; and the property
owners’ decision to redeem the property.” 2010 WL
3526469, at *14 (N.D. Ill. Sept. 1, 2010). The only sig-
nificant difference between the two opinions is that in
round one the judge dismissed the suit because the plain-
tiffs were (he ruled) only indirect victims of the fraud
and in round two he granted summary judgment for
the defendants because he thought that although we
and the Supreme Court had held that the plaintiffs were
direct victims, they had not been injured directly; the
causal link between the fraud and the injury was “tenu-
ous.” Id. at *13. The case is again before us on appeal by
the plaintiffs.
Nos. 10-3062, 10-3068                                    3

   When an owner of property in Cook County, Illinois,
fails to pay his property tax on time, the amount of tax
that is due (which is to say past due) becomes a lien on
the property. The county sells its tax liens at auctions.
The bids at the auctions are stated as percentages of
the taxes past due. The percentage, multiplied by the
amount of past-due taxes (plus any interest due on
them, which we’ll ignore), is the “penalty” that the bidder
demands from the owner to clear the lien. The winning
bidder is the bidder who bids (that is, is willing to ac-
cept) the lowest penalty—often zero percent of the tax
due, meaning that the bidder is just offering to pay the
County the past-due taxes and receive in exchange the
lien. The taxpayer has two to three years in which to
erase the lien by paying the winner of the auction (and
hence new owner of the lien) the past-due taxes that the
winner had paid the County, plus the penalty (if any). If
the taxpayer fails to redeem by paying what he owes, the
purchaser of the lien can obtain a tax deed to the
property and thus become the property’s owner. In
deciding which tax liens being auctioned to bid for, and
how much to bid (whether a zero-percent penalty, or a
5 percent penalty, or any other percent), the would-be
tax lienor is looking for properties, (1) whose owners are
unlikely to redeem them by paying the past-due taxes
during the redemption period and (2) are worth more
than the past-due taxes on them.
  The auctions are conducted in rapid-fire fashion in a
room in which the bidders bid by raising a card with
their bidder ID number and shouting out their penalty
percentage (usually “zero!”). Almost 85 percent of the
4                                     Nos. 10-3062, 10-3068

winning bids are at the zero-percent penalty level, which
implies that most bids are identical bids (identical zero-
percent bids). How is the auctioneer to pick the winner
in such a case? It’s difficult! Suppose fifteen bidders
bid zero percent on a particular lien being auctioned. The
bids being identical, the auctioneer will try to award the
lien to the bidder who raised his hand first. But if many
bidders raised their hands as soon as the bidding began,
the auctioneer may find it impossible to determine
who raised his hand first, in which event he’ll probably
pick one of the zero bidders at random.
   Bidders use a variety of tactics to attract the auc-
tioneer’s attention, such as by lobbying to be given a seat
closer to the auctioneer so that the bidder’s raised hand
is more likely to be noticed first. A few of the auctioneers
claim improbably that they can always tell who raised
his or her hand first, no matter how many hands shoot
up all over the room, while others say that when there
are multiple identical bidders they try to allocate the
awards “fairly,” whatever that means—probably it just
means not awarding too many liens to the same bidder
at the same auction. So on the one hand liens are not
awarded on a strict rotational basis but on the other
hand a jury could find that most zero-percent awards
are the random product of guesswork.
  The County’s rules permit only one agent of a potential
buyer, or of a group of cooperating buyers (“related
entities”), to bid. Otherwise a potential buyer could
increase the likelihood of winning by packing the room.
Suppose that a potential buyer, call him “BidCo,” was
Nos. 10-3062, 10-3068                                     5

represented by 10 persons—but the auctioneer thought
they were 10 different bidders—and all the other
potential buyers were represented by one person each,
as they’re supposed to be. BidCo would have a big ad-
vantage. If for example there were 21 potential buyers
and all bid zero percent for a particular tax lien,
30 hands would be shooting up but 10 of them would
belong to one buyer. Whether the auctioneer was able
to pick the bidder who raised his hand first, or as is
more likely there was simply a distribution of hand-
raising speeds and well-sited seats, the buyer who had
10 hands in the room would have an advantage over
each of the other 20 potential buyers. He would be
likelier to have some fast hands and some ringside seats,
as well as having an advantage just by virtue of the
number of hands, when the auctioneer threw up his
hands and awarded liens randomly among the zero-
percent bidders, or tried to rotate them among the
bidders in the interest of “fairness.” If BidCo’s violation
of the prohibition against related entities’ multiple
bidding were concealed, so that his scheme operated as
a fraud on the one-armed bidders, BidCo would have
engaged in a pattern of mail fraud in violation of RICO
because, as we explained in our first opinion, “the tax-sale
process employs the mail—perhaps to send affidavits, and
certainly to send notices to owners that the liens have
been sold and the taxes must be paid or the property
forfeited,” and “any fraud that affects which bidders
obtain how many liens is ‘mail fraud.’ ” 477 F.3d at 930.
  The case is a little more complicated than we’ve let on
so far because three separate groups (whose members
6                                   Nos. 10-3062, 10-3068

are the defendants) of allegedly related entities are
accused of the fraud. As a result, instead of having just
three arms the defendants had between 11 and 39, with
up to 13 being used in a given auction session during
the six years in which the conspiracies are alleged to
have been operating. In each of the three conspiracies
a kingpin financed the bidding activity of the group’s
members and when the kingpin agent’s bidder would
win a lien the kingpin would buy it from him.
  For purposes of this appeal (only), the defendants
concede that they committed a fraud actionable under
RICO if the plaintiffs can prove both proximate cause
and damages. The district judge granted summary judg-
ment for the defendants because he thought that the
plaintiffs—two of the one-armed bidders at the auc-
tions—had failed to produce evidence that the fraud
was a proximate cause of their losing any of the bidding
rounds.
   The injection of the term “proximate cause” into this
litigation has muddied the waters. It was injected for
no better reason—and it is not a good reason—than that
it has figured in several RICO cases decided recently
by the Supreme Court, none comparable to this case.
  You cannot obtain damages for fraud or any other
tort, whether you are litigating under common law or
the RICO statute, without proving that the fraud caused
a loss to you, such as a financial loss, for which
damages can be awarded. The problem is that there may
be multiple causes of your loss, obscuring the effect of
the defendant’s wrongful act. Sometimes the causes are
Nos. 10-3062, 10-3068                                       7

joint. For example, a passerby drops a match in a puddle
of oil created by a leak from a tanker truck, and the oil
explodes. HK Systems, Inc. v. Eaton Corp., 553 F.3d 1086,
1090 (7th Cir. 2009); Leposki v. Railway Express Agency, Inc.,
297 F.2d 849 (3d Cir. 1962); Overseas Tankship Ltd. v. Miller
Steamship Co., [1967] 1 A.C. 617 (P.C.) (The Wagon Mound
No. 2). Without both match and leak—hazards created
by separate persons—there would be no explosion and
so no harm. Who should be liable?
   Sometimes causes are alternative: a person is stabbed
by two knife-wielding assailants, and either stab wound
would have been fatal. Should both be excused from
liability because neither was necessary for the injury
to occur? United States v. Johnson, 380 F.3d 1013, 1016
(7th Cir. 2004). And likewise when each of two wrong-
doers could have caused the plaintiff’s injury and it is
unclear which did and each points at the other and says
let me off because the other guy may have done it.
Summers v. Tice, 199 P.2d 1 (Cal. 1948).
  Or sometimes—and here is where the doctrine of proxi-
mate cause does its work—too many unexpected things
had to happen between the defendant’s wrongdoing
and the plaintiff’s injury, in order for the injury to
occur—so many unexpected things that the defendant
couldn’t have foreseen the effect of his wrongdoing and
therefore couldn’t have been influenced, in deciding
how much care to employ in the activity that produced
the wrongful act, by the prospect of inflicting such an
injury as occurred. See, e.g., Gallick v. Baltimore & Ohio
R.R., 372 U.S. 108, 118 and n. 7 (1963); HK Systems, Inc. v.
8                                     Nos. 10-3062, 10-3068

Eaton Corp., supra, 553 F.3d at 1090. And then holding
him liable would have little effect in deterring wrongful
conduct.
  A better name for the application of the doctrine of
proximate cause in such a case would be “for want of a
nail the kingdom was lost”:
            For want of a nail the shoe was lost.
           For want of a shoe the horse was lost.
           For want of a horse the rider was lost.
           For want of a rider the battle was lost.
         For want of a battle the kingdom was lost.
          And all for the want of a horseshoe nail.
Suppose the blacksmith had been negligent in failing
to fasten the horseshoe to the horse’s hoof with enough
nails to hold it securely. His negligence was therefore
a cause of the loss of the kingdom because it led to the
loss of one of the riders, which led in turn to the defeat
of the king’s army. (And not just any rider: Shakespeare
in Richard III attributed Richard’s loss of the Battle of
Bosworth Field, and thus of his life and his crown, to
his falling off his horse because the horse was not
properly shod; in fact the horse had gotten mired in
the mud of the field, for reasons unrelated to his shoe.)
But had the blacksmith been told ahead of time that if
he didn’t fasten the shoe properly he could be re-
sponsible for the end of the York dynasty, the warning
would not have induced him to use additional care
in fastening the shoe to the hoof because the probability
that his negligence would have such a consequence
would have seemed slight. An injury will sometimes
Nos. 10-3062, 10-3068                                        9

have a cascading effect that no potential injurer could
calculate in deciding how carefully to act. The effect is
clear in hindsight—but only in hindsight.
   A more realistic modern example would be a suit
against the defendants in our case by someone who lost
his job because the one-armed bidder who employed
him didn’t win enough tax liens at the auctions to be
able to afford to keep him on its payroll. The employee
would have suffered a loss caused by the defendants
(assuming their fraud was indeed what impelled the one-
armed bidder to reduce his staff), but as in a literal want-
of-a-nail case their conduct would not be deemed a
“proximate cause” of the employee’s loss of his job, and
so his suit would fail. Evans v. City of Chicago, 434 F.3d
916, 926-29 (7th Cir. 2006); Mid-State Fertilizer Co. v. Ex-
change Nat’l Bank, 877 F.2d 1333, 1335-36 (7th Cir. 1989);
Frank v. D’Ambrosi, 4 F.3d 1378, 1385 (6th Cir. 1993);
Hecht v. Commerce Clearing House, Inc., 897 F.2d 21, 23-24
(2d Cir. 1990). Similarly, a creditor who suffers a
default because his debtor was injured by a tort cannot
sue the tortfeasor for the damages resulting from the
default. In re Teknek, LLC, 563 F.3d 639, 645-50 (7th Cir.
2009); Koch Refining v. Farmers Union Central Exchange,
Inc., 831 F.2d 1339 (7th Cir. 1987). If the creditor could sue,
why not the creditor’s son who had to borrow for his
tuition because his father could no longer afford to pay
it? Or the college, if the son was turned down for a
loan and had to withdraw? Or the bookstore at which the
son would have bought the books for his courses had he
remained a student? Or the publisher of the books sold
10                                  Nos. 10-3062, 10-3068

by the bookstore? Or the companies that sold paper to
the publishers? Or the authors?
  Notice how allowing any of those secondary or tertiary
or even more remote tort victims to obtain a judgment
would dim the primary victim’s prospects of obtaining
redress for his injury. Any tortfeasor’s resources are
limited. The more plaintiffs there are clamoring for
relief, the less in damages each one may be able to re-
cover. That is a further reason, along with a desire
to limit the amount of litigation arising from a single
wrongful act and to confine tort liability to foreseeable
(as distinct from so improbable as to be unforeseeable)
consequences, for limiting the right to relief to the
initial victims of the wrong, as in James Cape & Sons Co.
v. PCC Construction Co., 453 F.3d 396 (7th Cir. 2006),
on which our defendants rely. The plaintiff, a com-
peting bidder as in this case (hence the defendants’
reliance), sued the winning bidders on the ground
that they had agreed among themselves not to bid
less on state construction contracts than an agreed
amount, so as to maximize their profits from a
winning bid. (Probably they also agreed to rotate sub-
mission of the winning bid among the members of the
group, so that each would share in the profit oppor-
tunity that the conspiracy created.) The primary victim
was the State of Wisconsin, which had solicited the
bids; it had paid more for the construction contracts
obtained by the winning bidders than if there had been
no conspiracy. The plaintiff, in contrast, probably hadn’t
been injured at all and might well have benefited from
the conspiracy because the higher his competitors’ bids
Nos. 10-3062, 10-3068                                    11

the likelier he was to be the low bidder and win the
contract. See Phoenix Bond & Indemnity Co. v. Bridge, supra,
477 F.3d at 932.
  There is still another reason for worrying about
imposing liability when the defendant’s conduct and the
plaintiff’s injury are separated by intermediate pairs
of cause and effect. The horseshoe was missing a nail,
yes, but it might have fallen off anyway, in the heat of
battle; and how likely is it that one downed rider (unless
it really was the king) made the difference between
victory and defeat? (And mightn’t he have fallen any-
way?) And in the employment case, might not other
factors have doomed the employee’s job? There is plenty
of employee turnover even when the employer is not a
victim of fraud.
   The “indirect purchaser” rule of Illinois Brick Co. v.
Illinois, 431 U.S. 720, 730-36 (1977), is a notable example
of the evidentiary concerns that lead courts to disregard
secondary causal relations. Suppose competing manu-
facturers conspire to raise the prices of their products,
in violation of federal antitrust law. The buyers—suppose
they’re retail dealers—pay the higher prices, but turn
around and raise the prices they charge their pur-
chasers, the consumers, in an effort to minimize the
impact on their profits of the manufacturers’ higher
prices. The injury caused by the price-fixing conspiracy
is likely to be shared between the direct purchasers
from the conspirators and the indirect ones (the con-
sumers in the example). But to determine the relative
hurt would require a complex inquiry, and so the
indirect purchasers, though harmed, are not allowed to
12                                    Nos. 10-3062, 10-3068

sue. This may seem a harsh result, but is mitigated by
the fact that the antitrust violators are not allowed to
offset against their liability the amount of loss that the
direct purchasers, the dealers, who are allowed to sue,
were able to pass on to their customers in the form of
higher prices. By allowing a windfall to the direct pur-
chasers—they can sue for the full markup over the com-
petitive price for the manufacturers’ product even if
they passed on much of the higher price to consumers—the
law gives them a greater incentive to sue, which should
increase deterrence, which should benefit the indirect
purchasers indirectly.
  The doctrine of proximate cause thus protects the
ability of primary victims of wrongful conduct to ob-
tain compensation; simplifies litigation; recognizes
the limitations of deterrence (unforeseeable conse-
quences of a person’s acts will not influence his decision
on how scrupulously to comply with the law); and elimi-
nates some actual or possible but probably minor causes
as grounds of legal liability. All this is true in RICO cases
just as in other tort cases whether common law or statu-
tory. Holmes v. Securities Investor Protection Corp., 503
U.S. 258 (1992); HK Systems, Inc. v. Eaton Corp., supra, 553
F.3d at 1090.
  The doctrine has no application to this case, at least on
the record compiled to date. The defendants’ aim was to
obtain a larger share of tax liens. The larger share came
from other bidders, the bidders we’re calling one-armed.
The only injury was to those bidders, who included the
two plaintiffs. The County’s rule limiting related entities
Nos. 10-3062, 10-3068                                     13

to a single bidding agent was intended for the benefit
of unrelated bidders rather than for its own benefit
(except very indirectly, insofar as the rule encouraged
bidding). It was a matter of indifference to the County
who bought the tax liens, for whoever it was would have
to pay the County the taxes on the properties subject to
the liens. The one-armed bidders were thus the only
victims of the fraud—and the plaintiffs were one-armed
bidders.
  The defendants stole a business opportunity from the
plaintiffs by flooding the auction room with raised
hands that shouldn’t have been there. The only inter-
mediate cause and effect pair was the raising of hands
(cause) and the auctioneer’s determination of the
winning bid (effect), and this pair doesn’t weaken the
inference that by having more hands in the air the de-
fendants stole tax liens from the other bidders. That
would be obvious if the auctioneers awarded tax liens
in identical-bid cases on a strictly rotational basis, as the
Supreme Court assumed when, in its opinion affirming
our previous decision, it characterized the plaintiffs’
theory of causation as “straightforward.” 553 U.S. at 647;
see also Hemi Group, LLC v. City of New York, 130 S. Ct. 983,
992 (2010). Straightforward it was and after discovery
straightforward it remains because, as we shall see,
random awards—the character of many of the awards in
identical zero-percent bidding—are similar to awards
made on a strictly rotational basis.
  The defendants argue that if there is any possible slip
‘twixt cup and lips (to continue law by proverb), the
14                                    Nos. 10-3062, 10-3068

plaintiff must prove that it did not occur. Not so. The
plaintiff doesn’t have to prove a series of negatives;
he doesn’t have to “’offer evidence which positively
exclude[s] every other possible cause of the accident.’ ”
Carlson v. Chisholm-Moore Hoist Corp., 281 F.2d 766, 770
(2d Cir. 1960) (Friendly, J.), quoting Rosenberg v. Schwartz,
183 N.E. 282, 283 (N.Y. 1932). In technical legal terms
the burden of proving an “intervening cause”—something
which snaps the “causal chain” (that is, operates as a
“superseding cause,” wiping out the defendant’s lia-
bility, see Restatement (Second) of Torts § 440 (1965))
that connects the wrongful act to the defendant’s in-
jury—is on the defendant. Roberts v. Printup, 595 F.3d
1181, 1189-90 (10th Cir. 2010).
   The district judge required the plaintiffs to prove the
nonexistence of potential superseding causes rather
than requiring the defendants to present evidence to
support their conjectured superseding causes. He said
that otherwise “a jury would be forced to speculate as
to whether Defendants violating the [related-entities
rule] would [if the Treasurer, who administers the tax-
lien auctions, had learned of the violation before or
during the complaint period] have been permanently
barred from the County tax lien sales, excluded for only
a day or a year, or faced some other unknown conse-
quence.” 2010 WL 3526469, at *8. This possibility would
cancel the effect of the defendants’ fraud on the number
of liens won by the plaintiffs only if whatever sanction
the Treasurer imposed would have allowed the de-
fendants to continue violating the related-entities rule:
for example if she would have barred them from bidding
Nos. 10-3062, 10-3068                                    15

for one day but allow them to resume their collusive
activity the day after. That is beyond unlikely, and
hardly “evidence” of a superseding cause that the plain-
tiffs would have to rebut in order to withstand sum-
mary judgment. And so the plaintiffs can’t be faulted, as
the defendants argue, for having failed to depose the
Treasurer—the defendants, who had the burden of
proving that the Treasurer would have let them off scot
free, didn’t do so either. Had the Treasurer forced the
defendants to stop colluding in violation of the related-
entities rule (and in violation as well of the oath they
had sworn, when they signed up to bid in the auction,
to comply with the related-entities rule), the one-armed
bidders would have obtained more liens than they did.
   The defendants present other implausible speculations
concerning possible superseding causes, and demand
that the plaintiffs refute them. They argue that the “plain-
tiffs’ failure to obtain more liens than they actu-
ally won could have been the result of competition from
third-party bidders, the auctioneers’ subjective percep-
tions, or failures of Plaintiffs’ bidders to keep pace with
the auction and to bid on liens they may have intended
to bid on.” The defendants note that one of the plaintiffs
complained to the Treasurer’s Office that it was being
“relegated” to “seats in the back of the room where it
was difficult for the bidders to be recognized, and the
auctioneers to view them” and that a bidder for the
other plaintiff admitted that she might have been
slower at raising her hand than other bidders on some
occasions. But so far as yet appears—for of course there
has been no trial—these were isolated instances over the
16                                    Nos. 10-3062, 10-3068

course of six years. And as for whether the plaintiffs
were outbid by bidders who were not members of the
conspiracies, this is unlikely since the case is only about
identical zero-percent bids (so there are only low bidders,
rather than a lowest bid), and the defendants presented
no evidence to establish such a superseding cause of
the plaintiffs’ injury.
  The defendants were throwing sand in the district
judge’s eyes. The object of their conspiracies was to
obtain liens that would otherwise go to one-armed
bidders—there could be no other reason for wanting to
pack the room in violation of the County’s rule. The
plaintiffs were major bidders. They bid for many thou-
sands of liens. How likely is it that they lost no bids to
bidders who had 13 arms in the room but should have
had only three?
   Once a plaintiff presents evidence that he suffered the
sort of injury that would be the expected consequence
of the defendant’s wrongful conduct, he has done
enough to withstand summary judgment on the ground
of absence of causation. Liriano v. Hobart Corp., 170 F.3d
264, 271-72 (2d Cir. 1999); Kingston v. Chicago & N.W. Ry.,
211 N.W. 913, 915 (Wis. 1927); Martin v. Herzog, 126 N.E.
814, 816 (N.Y. 1920) (Cardozo, J.) (“evidence of a collision
occurring more than an hour after sundown between a
car and an unseen buggy, proceeding without lights, is
evidence from which a causal connection may be
inferred between the collision and the lack of signals”). The
causal relation between a defendant’s act and a plain-
tiff’s injury, like that required to establish standing under
Nos. 10-3062, 10-3068                                      17

Article III of the Constitution, need only be probable.
Clinton v. City of New York, 524 U.S. 417, 432-33 (1998);
MainStreet Organization of Realtors v. Calumet City, 505
F.3d 742, 744-45 (7th Cir. 2007); Village of Elk Grove
Village v. Evans, 997 F.2d 328, 329 (7th Cir. 1993). Other-
wise how could a person obtain a judgment for medical
malpractice based on a failure to diagnose a disease
that proved fatal but had it been diagnosed earlier might
have been cured? Matsuyama v. Birnbaum, 890 N.E.2d
819, 828-31 and n. 23 (Mass. 2008); Holton v. Memorial
Hospital, 679 N.E.2d 1202, 1213 and n. 2 (Ill. 1997); Doll
v. Brown, 75 F.3d 1200, 1205-07 (7th Cir. 1996). And how
could four equally qualified employees who were dis-
criminated against when a company made a single pro-
motion obtain any relief? Yet we’ve held that the plain-
tiff in such a discrimination case is entitled to damages
equal to 25 percent of the pay he would have received
had he gotten the promotion. Biondo v. City of Chicago, 382
F.3d 680, 688-89 (7th Cir. 2004); see also Griffin v.
Michigan Department of Corrections, 5 F.3d 186, 189 (6th
Cir. 1993). That is the nature of the relief—statistical,
probabilistic—sought by the plaintiffs in this case.
  We gave our most exotic example of probabilistic
injury in Milam v. Dominick’s Finer Foods, Inc., 588 F.3d 955,
958 (7th Cir. 2009): “Suppose you’re playing roulette on
a 37-number wheel (18 red, 18 black, and 1 green) at the
Casino de Monte-Carlo, and after you have placed
your $1,000 bet on red, which will pay you $2,000 if the
ball lands on red, the casino collapses through the negli-
gence of a building contractor, destroying not only the
roulette wheel but also your chips, and you cannot get
18                                    Nos. 10-3062, 10-3068

the money you paid for them back because all the
casino’s records were destroyed when it collapsed. You’ve
suffered a loss equal to a 48.6 percent chance of winning
$2,000. So $972.73 would be your damages.” That is
the type of probabilistic loss that the plaintiffs claim to
have suffered in this case.
   If a trier of fact finds causation according to the
standard just explained, which requires merely a prob-
ability of a harm attributable to the defendant’s wrong-
ful act, the only remaining issue is the amount of
damages to be awarded to the plaintiff. On that phase
of the case the plaintiff has a more relaxed burden of
proof than on the issue of causation, especially if as in
this case the defendants’ conduct has made it difficult
for the plaintiff to prove the precise extent of his damages.
J. Truitt Payne Co. v. Chrysler Motors Corp., 451 U.S. 557,
566-67 (1981); Bigelow v. RKO Radio Pictures, Inc., 327
U.S. 251, 264-65 (1946); Story Parchment Co. v. Paterson
Parchment Paper Co., 282 U.S. 555, 562-66 (1931); Haslund
v. Simon Property Group, Inc., 378 F.3d 653, 657-59 (7th
Cir. 2004); BE&K Construction Co. v. Will & Grundy
Counties Building Trades Council, 156 F.3d 756, 769-70 (7th
Cir. 1998); Computer Systems Engineering, Inc. v. Qantel
Corp., 740 F.2d 59, 67 (1st Cir. 1984). “Once the plaintiff
proves injury, broad latitude is allowed in quantifying
damages, especially when the defendant’s own conduct
impedes quantification. But the injury itself must be
proved in the usual way, without speculation or burden
shifting.” Haslund v. Simon Property Group, Inc., supra,
378 F.3d at 658. (The distinction between proof of cause
and proof of damages is also well explained in Justice
Nos. 10-3062, 10-3068                                     19

Thomas’s separate opinion in Anza v. Ideal Steel Supply
Co., 547 U.S. 451, 465-67 (2001).) Even “speculation has
its place in estimating damages, and doubts should be
resolved against the wrongdoer.” Mid-America Tablewares,
Inc. v. Mogi Trading Co., 100 F.3d 1353, 1365 (7th Cir.
1996), quoting Olympia Equipment Leasing Co. v. Western
Union Telegraph Co., 797 F.2d 370, 383 (7th Cir. 1986).
Otherwise “the more grievous the wrong done, the less
likelihood there would be of a recovery.” Bigelow v. RKO
Radio Pictures, Inc., supra, 327 U.S. at 265.
  In this case, for example, the plaintiffs do not have
good records of which tax liens they bid for unsuccess-
fully. The only reason they would have needed such
records was to prove damages in a lawsuit. Since they
didn’t know they were victims of fraud, they had no
reason to think they needed good records of their unsuc-
cessful bids—for of what use would such records have
been had there been no fraud? The judge missed this
point because he confused proof of causation with proof
of amount of damages and so denied the plaintiffs
the benefit of the easier burden of proving damages than
of causation.
  The defendants must know they’re skating on thin ice.
For (to mix our metaphors) they have not put all their
eggs in the basket labeled “proximate cause” but instead
have also argued that the plaintiffs cannot prove
damages and we can therefore affirm on that alterna-
tive ground. Given the lightened burden of proof in the
damages phase of a tort case, the argument fails. It’s true
as we just noted that the plaintiffs’ records of their unsuc-
cessful bids are poor. The defendants ask us to infer
20                                    Nos. 10-3062, 10-3068

that maybe the plaintiffs didn’t bid on any of the tax liens
that the defendants bid on. (Another possibility, but the
defendants don’t argue it, is that with fewer arms in
the air, more buyers would be attracted to the auction
because their chances of being awarded a tax lien by the
auctioneer would have been greater, and perhaps in the
end the total number of arms in the air at each auction
would have been the same even if there had been no
violation of the related-entities rule.) Yet it’s undisputed
that the two plaintiffs submitted many thousands of zero-
percent bids—they presented evidence that they bid on
between 72 and 92 percent of the tax liens that were won
by the defendants during the complaint period—and
ended up with only 7 percent of the 96,000 zero-per-
cent awards during the six years in which the alleged
conspiracy was in force, while the defendants, who
often had more than four times as many arms in the air
as they should have had (13 versus three), won a total of
41 percent of the zero-percent liens. It seems highly
likely that at least part of this dramatic difference in
success was attributable simply to more hands in the
air. To the extent that awards of zero-percent bids are
distributed randomly among the bidders—and many
undoubtedly are—the three defendant groups would be
expected to win 50 percent more awards than the two
plaintiffs if everyone was playing by the rules, and this
would be 10.5 percent of the awards (7 percent plus
3.5 percent)—not 41 percent.
  The defendants argued and the district judge appears
to have been persuaded that unless the liens had been
awarded on a strictly rotational basis when identical
bids were submitted, there could be no confidence that
Nos. 10-3062, 10-3068                                       21

each of the plaintiffs would have obtained a proportion-
ately equal share of the zero-percent liens had the defen-
dants not packed the auction room. This reasoning
reflects a misunderstanding of statistical theory. In a
large sample, random selection produces with a high
degree of confidence (certainly a high enough degree for
a damages award in a fraud case) the same proportions
as strict rotation would. Suppose an urn contains 1,000
white balls and 1,000 black ones. The urn’s owner
wants each of two visitors to have 500 of each type of
ball. He patiently removes the balls one by one, being
careful to give exactly the same number of white and
black balls to each visitor. That is strict rotation. But by
the time he is halfway through, and each visitor has 250
white balls and 250 black balls, he becomes bored and
impatient. So he blindfolds the visitors and tells each
to draw the same number of balls from the urn, of course
without being able to determine which are white and
which black. Hence the remaining 500 white and black
balls are distributed randomly between the two visitors,
rather than in strict rotation as the first 500 balls were. Yet
on average each visitor will end up with the same number
of white and black balls, just as when there was strict
rotation between white and black. That’s just on
average; in any actual drawing there is likely to be some
deviation from equality. Such a deviation would matter
in this case if the victim of a fraud had to prove his
loss with mathematical exactitude. He does not.
  The statistical evidence in this case would be enough,
when combined with evidence also presented by the
plaintiffs of the average profit they made on the zero-
percent liens that they won, to carry their burden of
22                                     Nos. 10-3062, 10-3068

proving an amount of damages with sufficient (which
is not to say with great) precision to justify an award
of that amount. The evidence was summarized in two
expert-witness reports that the defendants take a
number of potshots at. The criticisms may be sub-
stantial, but they are premature because the district
judge never ruled on the admissibility of the expert
evidence previewed in the reports. On the record as
it stands the plaintiffs made a prima facie case of
damages in the amount ($5 million before trebling) that
they seek, and so the defendants cannot prevail on
their alternative, zero-damages defense of the district
court’s decision without a trial.
  So much for the RICO claim. The plaintiffs have a
supplemental claim as well, which the district judge
also dismissed on summary judgment. The claim is for
intentional interference with a business opportunity, in
violation of Illinois common law. The judge rejected it
on the ground that the plaintiffs “cannot prove that they
had an actual expectancy of winning a specific lien.”
2010 WL 3526469, at *14. (In rejecting “proximate causa-
tion” in regard to the RICO claim, the judge, mistaking
the significance of statistical evidence, also fastened on
the inability, as he thought, of the plaintiffs to identify
“specific liens” that they had failed to win.) It is true
that the plaintiff must prove an interference with “a
business expectancy with a specific third party.” Schuler v.
Abbott Laboratories, 639 N.E.2d 144, 147 (Ill. App. 1993); see
also O’Brien v. State Street Bank & Trust Co., 401 N.E.2d
1356, 1358 (Ill. App. 1980); Crinkley v. Dow Jones & Co., 385
N.E.2d 714, 720-22 (Ill. App. 1978); Parkway Bank & Trust
Nos. 10-3062, 10-3068                                       23

Co. v. City of Darien, 357 N.E.2d 211, 214-15 (Ill. App. 1976).
But that requirement is satisfied. The plaintiffs’ busi-
ness expectancy was the expectancy of receiving liens
from their owner, the County, at auctions uncon-
taminated by fraud by competing bidders. The County
was the third party to the competition for tax liens
between the plaintiffs (and the other one-armed bidders)
and the defendants.
  The judgment is reversed and the case remanded
for further proceedings consistent with this opinion. As
this is the second reversal of the district judge in the
same case, we think it best to spread the pain and invoke
our Rule 36, so that the trial will be before a different
judge.
                                  R EVERSED AND R EMANDED.




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