- Benjamin Franklin's Prudential Algebra
- On September 19, 1772, Benjamin Franklin wrote a letter to
Joseph Priestly, a noted chemist best remembered for his discovery
of oxygen. The letter was in response to a request
by Priestly for some advice.
- In the letter, Ben Franklin states that he can not advise Priestly
because of insufficient knowledge. However, he goes on to state
that his Prudential Algebra may be of help.
- Steps of Prudential Algebra
- Form a two column list of Pros and Cons
- Estimate the respective
weights of each Pro and Con
- Strike out equal
weighted groups of Pros and Cons
- The column with remaining factors is the appropriate decision.
- See text
of letter below.
- Letter to Joseph Priestly
- Book - "Letter to Joseph Priestly", Benjamin Franklin Sampler, Fawcett, NY, 1956.
- Online - HistoryCarper
- London, September 19, 1772
In the affair of so much importance to you, wherein you ask my advice, I
cannot, for want of sufficient premises, advise you what to determine,
but if you please I will tell you how. When those difficult cases occur,
they are difficult, chiefly because while we have them under
consideration, all the reasons pro and con are not present to the mind
at the same time: but sometimes one set present themselves, and at other
times another, the first being out of sight. Hence the various purposes
or inclinations that alternatively prevail, and the uncertainty that
To get over this, my way is to divide half a sheet of paper by a line
into two columns; writing over the one Pro, and over the other Con.
Then, during the three or four days consideration, I put down under the
different heads short hints of the different motives, that at different
times occur to me, for or against the measure. When I have thus got them
all together in one view, I endeavor to estimate their respective
weights; and where I find two, one on each side, that seem equal, I
strike them both out. If I find a reason pro equal to some two reasons
con, I strike out the three. If I judge some two reasons con, equal to
three reasons pro, I strike out the five; and thus proceeding I find at
length where the balance lies; and if, after a day or two of further
consideration, nothing new that is of importance occurs on either side,
I come to a determination accordingly.
And, though the weight of reasons cannot be taken with the precision of
algebraic quantities, yet when each is thus considered, separately and
comparatively, and the whole lies before me, I think I can judge better,
and am less liable to make a rash step, and in fact I have found great
advantage from this kind of equation, in what may be called moral or
Wishing sincerely that you may determine for the best, I am ever, my
dear friend, yours affectionately,
- Factor Rating Method with Ben Franklin's Prudential Algebra
- Assign a weight, wi , to each factor to reflect its importance.
- Assign a score, si j , for each location and each factor.
- Sum wi si j for each location.
- Select the site with the highest sum as the best candidate.
- Form a comparison matrix by subtracting each sites wi si j
from the best candidates wi si j .
- Qualitatively compare each site with the best candidate using the least
number of positive factors to outweigh all negative factors.
- Conclude that best candidate is best or revise weights and scores.
- Application of Factor Rating Method to the location of a manufacturing plant.
This is from Example S5.1, page 202 of Operations Management:
Multimedia Version, fourth Edition, Roberta S. Russell and Bernard W.
Taylor, Prentice Hall, 2002 (ISBN 0-13-034834-1).
||a. Weighted scores
Site 3's (best candidate) favorable
Proximity to customers, and
outweigh Site 1's favorable
Proximity to suppliers, and
Site 3's favorable
Labor pool, and
outweigh Site 2's favorable
Proximity to suppliers,
Wage rates, and
Therefore, Site 3 is the best.
- Please note that Steps 5, 6, and 7 in Section III.A above do not appear
in Russell nor Heizer and Render, but represent my extension of the Factor Rating Method to
include Ben Franklin's Prudential Algebra. This pairwise qualitative comparison
allows me to probably use both sides of my brain to come to a harmonious
resolution of important decisions.
- Prostate Cancer Example
- For many prostate cancer patients, the selection of the best treatment
is a difficult decision because of the many trade-offs. Below is a
link to an Excel worksheet showing a typical solution.
- Prostate Cancer Treatment Selection -
(This page was last edited on
May 31, 2009