Franklin's Moral Algebra, Written Out on Half a Sheet

In the autumn of 1772, a man in London sat down to answer a friend's request for advice and, with some tact, declined to give any. What he sent instead was a way of working. It needed a half sheet of paper, a pen, and about a week of patience.

The letter and the dilemma behind it

On September 19, 1772, Benjamin Franklin wrote from London to Joseph Priestley, who faced a real choice. Priestley had been offered a well-paid post as librarian and companion to the Earl of Shelburne. Accepting meant giving up his congregation in Leeds and moving his family. The letter survives, and it is notable first for what it withholds.

Franklin said he lacked sufficient premises to judge the matter himself. That is an honest answer, and a slightly wry one, since a friend's opinion is usually cheaper than a method. He offered the method anyway. He called it moral or prudential algebra. Priestley, for the record, took the job.

How the method works

The layout is plain. Divide half a sheet into two columns, one headed Pro and one headed Con. Over three or four days, jot short hints for each motive as it occurs to you, on either side. If nothing important turns up, give it a day or two more.

Only then does the arithmetic begin. With the reasons in one view, you estimate their relative weights and look for cancellations. One reason for that seems equal to one against is struck out on both sides. A reason for that equals two against is struck out along with the two, so three disappear. Two against that equal three for remove five. What remains shows where the balance lies.

Here is a small invented example, a job offer in another city. Pro: a higher salary. Pro: work that is more interesting. Con: a long move away from family. Suppose you judge the move to be about as heavy as the salary and the interesting work together. All three come off the page. If nothing else is left, the choice is a wash, and you know to look harder for what you missed. If a single reason remains, the balance is plain.

Note how modest the operation is. Nothing is calculated. You are crossing out items you have judged to be equivalent, and the judging is yours.

Why Franklin thought the method was needed

His diagnosis is the more interesting part. All the reasons, he observed, are never present to the mind at the same time. Some considerations surface on Tuesday and others on Thursday, so inclination swings. A person can feel certain at breakfast and doubtful by supper, and both feelings are sincere.

The page fixes this by holding everything at once. Franklin claimed only that weighing each reason separately and then comparatively helped him judge better and made a rash step less likely. That is a claim about the quality of deliberation, not about the correctness of the outcome, and it is easier to defend for that reason. The sources here do not show that the method produces better outcomes than other methods, and Priestley's later experience is not documented in them.

Two questions follow naturally from the diagnosis. Have any reasons been left out because they only came to mind on a different day? And are the weights you gave reasonable, given that Franklin said reasons cannot be weighed with algebraic precision?

Limits, and how modern multi-criteria analysis compares

Franklin was candid that the weight of reasons cannot be measured with the precision of algebraic quantities. The word algebra is a courtesy. A critic can fairly say that assigning weights by feel lets in the same biases the list was meant to filter out, and nothing on the page prevents it.

Later operations research took a more formal route. Multi-criteria analysis, or MCA, explicitly considers several assessment aspects and interests that need not all carry equal weight. Supporters read it as a disciplined extension of Franklin's instinct. Skeptics note that formal weights can look more precise than the judgments beneath them.

A common modern cousin is the decision matrix. Options are rows, criteria are columns, and each criterion gets a weight, often on a scale of 1 to 5. You score each option on each criterion, multiply by the weight, and add up each row. The highest total wins on paper.

• Use Franklin's columns for a single personal choice where the reasons are mostly qualitative and you want days to surface them.
• Use a matrix when you compare several options on clear, shared criteria, or when a group needs a visible record of the decision.
• If one factor plainly dominates, such as lowest price or shortest distance, a simple single-criterion rule may be enough.

Either tool can give false precision. A tidy total is still built from judgments. Ask whether the criteria were explicit before the options were scored, and treat a close result as a prompt to look again, not as a verdict.

Franklin's sheet will not make a decision for anyone. It does something smaller. It keeps Tuesday's reasons from being forgotten by Thursday, and for a week's work with a pen, that is a fair return.

Sources

• Operations Research: Multi Criteria Analysis (MCA) - Museum Waalsdorp
• Moral Algebra — Benjamin Franklin’s Pros and Cons Letter to Joseph Priestley (1772)
• Decision Matrix vs AI: Which Helps You Decide? | Kai
• The Priority Heuristic: Making Choices Without Trade-Offs - PMC
• Why Bright People Need "BS Detection Training" | Psychology Today