Prior
Probability is a term associated with a complex mathematical formula devised by
the eighteenth century mathematician Thomas Bayes. You most likely will have to
look long and hard to find a simple, everyday-English definition of the term. I did a quick search of all the usual
suspects on the internet (Wikipedia, etc.), and the most lucid definition I
could find came from Dictionary.com:
“The probability assigned to a parameter
or to an event in advance of any empirical evidence, often subjectively or on
the assumption of the principle of indifference.” Here is my homespun
definition: Prior Probability is a
common-sense estimate of the probability of an event made at the outset of an
investigation.
For
example, the recent book Abraham
Lincoln’s Most Famous Case, investigates three accounts of Abraham
Lincoln’s Almanac Trial. The most popular story has Lincoln winning the case
with a brilliant cross-examination, another says he won it with a brilliant
final argument, and the final version says he won it with unethical trickery.
Before conducting any investigation to determine the truth of the matter, which
version seems most likely based on what we already know about Honest Abe, the
author of the Gettysburg Address? That’s the prior probability. At the end of
our investigation, we arrive at the posterior probability—what most likely
happened? Lincoln’s Most Famous Case
investigates these three versions of the story, and renders a verdict on which
story has the most posterior probability.
This is
a rather lengthy leadup to advancing the proposition that prior probabilities
can help us to craft an effective cross-examination. Although it does not use
the term, the 1929 book Cross-Examination of Witnesses (by Asher L. Cornelius) describes a method of using prior
probabilities in case analysis.
1.
Write
a narrative of the case stating the undisputed evidence and the contentions of
the parties in the most neutral, nonjudgmental language possible.
2.
Identify
the point(s) of contention.
3.
As
to each of the points of contention, make a common sense determination which
side of the argument seems more likely (has the greatest prior probability).
Write down these prior probabilities and the facts which support them.
4.
Draft
a cross-examination aimed at emphasizing the prior probabilities and the
undisputed facts supportive of the prior probabilities.
Here is
one of the examples used in the book:
EXAMPLE CASE ANALYSIS FROM CROSS-EXAMINATION
OF WITNESSES
Anderson purchased an apartment house from an owner Baker for
$65,000 and paid
$15,000 down, leaving a balance of $50,000 to be paid on the contract at the
rate of $600 per month. Anderson claimed that the owner Baker, from whom he purchased the
property, misrepresented the facts in this transaction, in, the following
particulars:
(a) That the rentals from this property of $700.00 per
month had been reduced so that they were at absolute bed-rock at the time the
transaction was closed and that all of the tenants were prompt' in paying same,
and that an expenditure of only about $300 per annum was required for heat.
(b) That the owner represented that all of the apartments were in good repair as
to decorations; that the building would easily carry the contract and pay for
itself out of the rentals.
Anderson purchased the property, entered into possession and
discovered the following facts: ,
1. That it cost him $250 per month for heat;
2. That the tenants were not prompt in paying rent;
3. That heating plant required $500 repairs;
4. That the property lacked approximately $300 per month of paying for itself from the rentals.
Anderson brought suit for rescissions against Baker. The defendant in his answers denied that he made any such representations as above set out. -,
What, now, are the probabilities in this case? The lawyer for the plaintiff, in planning his cross-examination of the defendant and his witnesses should reach the following conclusions respecting the same:
STATEMENT OF PROBABILITIES
(1) Anderson as a purchaser would be vitally interested in knowing what income the apartment produced. Baker, the owner, had that information. Anderson did not. The probabilities, therefore, strongly support the contention of Anderson that he asked for this information. If Baker had given him the actual facts he would have refused to purchase the property. So, here again, the probabilities support Anderson’s
claim that Baker misrepresented the income.
(2) Since heating costs of large apartment buildings vary widely, depending upon the efficiency of the heating plant as well as upon the construction of the building, the probabilities are strongly with Anderson when he stated that he asked Baker what the cost would be and Baker told him. If Baker made any representations at all about the heating costs of the apartment, it would have to be a representation consistent with the purchase of the building by Anderson. Had Baker told the real facts, Anderson would not have purchased.
(3) As to the condition of the interior decorations, the individual apartments being all rented, Anderson did not have access to them and he was compelled to depend on
Baker for information. Here again a true disclosure would,
in all probability, have blocked the deal.
(4) Since the tenants in the building were none of them prompt in
paying their rent, and since Anderson naturally would be interested in making
inquiries as to their character, the probabilities are that Anderson did
inquire and that Baker concealed and misrepresented the real facts.
Since one of the important objectives in cross-examination is to
show that the witness is not testifying truthfully, one forceful method of
doing this is to show the improbability of his story by emphasizing facts
before the jury which render such story improbable. Counsel, therefore, cross-examined
the defendant in, this case as follows:
Q. You, as the owner and operator of this property, knew the annual
cost to heat this building?
A. Yes, sir.
Q. The heating costs of apartment buildings vary widely do they not, depending upon the condition
and efficiency of the heating plant and the construction of the building?
A. Yes, sir.
Q. You had exact information as to what it cost to heat this building?
A. Yes, sir.
'Q. Mr. Anderson, your prospective purchaser, had no information as to what these
costs were 1
A. No, sir.
Q. And he, as a prospective purchaser of this building, would naturally be
very much interested in knowing what these heating costs were.
A. Yes, sir.
Q. You were ready to answer his questions in this regard?
A. Yes.
Q. And yet he asked you nothing about this important subject?
A. No, sir.
The
process described in Cross-Examination of
Witnesses is a slightly different method of conceptualizing the analytical
process we describe in Chapter 3 of Cross-Examination Handbook, but it uses a similar procedure and arrives at much the same
place you would arrive at using our method. Cross-Examination
of Witnesses describes a workable analytical mode, and If you feel more
comfortable using its analytical framework than ours, by all means do so.
Although there is more than one way to skin a cat, the cat ends up flayed no
matter how you do it. What Cross-Examination
of Witnesses says nothing about, however, is how to go about actually
drafting, constructing, and arranging the cross-examination. Chapter 4 of Cross-Examination Handbook fills this
void.
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