Rawls asks which society people would pick if they did not know who they would be in it. Laid out as a decision matrix, with the chooser's position as the unknown state, the question becomes a choice of rule: maximin picks one society and equal-probability expected utility picks another from the very same table. The wrong model is that maximin is a taste for safety with money.
Core ideas
The original position is a thought experiment, and a decision matrix is the form in which its argument can be checked. Three ideas carry the lesson.
Each society is an act. What the chooser does not know is which place in it will fall to them, so each place is a state, and the cell holds how well that place does in that society. The table is the one from Decision and Rationality with the unknown moved from the weather to oneself.
Maximin scores a society by the lowest entry in its row and takes the society whose lowest entry is highest. It never adds, averages or weighs, so the probabilities of the places play no part in it.
Laplace's rule treats every place as equally likely and scores a society by its average. Harsanyi argued that this, and not maximin, is what a rational chooser behind the veil would do. The two rules are the two sides of the dispute.
The material
A table with societies down the side and places across the top, and two rules applied to it.
Suppose you must pick the arrangement of a society, and you must do it before learning which place in it you will occupy. You might be among the worst off, in the middle, or among the best off. Rawls called the situation of such a chooser the original position, and the ignorance of one's own place the veil. What he claimed is that principles chosen under the veil are fair, because no one can tailor them to their own advantage.
The argument is only worth testing if it can be written down, and it can. Take two societies, one in which everyone has 5 units of welfare and one in which the worst place has 2, the middle 8 and the best 20. The unknown is your place, so the table has three states.
Maximin reads off each society's worst entry: 5 for the equal society and 2 for the unequal one. The larger worst case is 5, so maximin chooses the equal society. Nothing about the 8 or the 20 entered the calculation.
Now give each place the same chance, as Laplace's rule does. The equal society averages 5, and the unequal one averages (2 + 8 + 20) / 3, which is 10. The larger average is 10, so this rule chooses the unequal society. Same table, same chooser, opposite verdicts, and the difference lies wholly in what the rule is willing to ignore.
Maximin scores each act by its worst payoff across the states and chooses the act whose worst payoff is largest.
Rawls's case for maximin is not that people dislike risk. It is that the choice has three features: the chooser has no trustworthy basis for assigning probabilities to the places, the chooser cares little for what is gained above the guaranteed minimum, and the worst outcome of a rejected society would be one hardly bearable. Where those hold, looking only at the floor is a reasonable policy. Where they do not, for instance when the stakes are small and the odds are known, it is a poor one.
Harsanyi's reply denies the first feature. A chooser who knows nothing about their place has, he argued, no reason to favour any place over another, and equal weights are what that ignorance amounts to. Each side states a valid argument from its premises; the lab computes both and cannot say whether the veil should leave you with no probabilities or with equal ones. That is the question the lesson leaves with you.
The lab's second table carries one more figure. With each place at probability 1/3 the value-of-information tile prints 1, and here that quantity has a name: it is the value of lifting the veil. A chooser who learned their place before choosing would take the equal society in the bottom place, where it pays 5 against 2, and the unequal society anywhere else, for an expectation of (5 + 8 + 20) / 3, which is 11; the best a chooser can do without that knowledge is 10. The difference, 1, is what knowing one's own place would be worth to the chooser. The veil withholds exactly that, and withholds it from everyone, which is what makes a choice made behind it fair on Rawls's account.
In the lab's third table the unequal society pays 5, 6 and 7 against 5, 5 and 5. Maximin finds the same worst case, 5, in both rows and cannot separate them, while the average separates them at once, 6 against 5. A tie under maximin is a signal that the rule has run out of information, which is where the next lesson begins.
One limit belongs here. The numbers are welfare levels the table's author chose, and the societies are two among the many that could have been offered. The lab computes what each rule picks from the table as stated; it does not tell you that the table describes any real society.
Interactive
the same payoffs, eight ways of choosing, each computed exactly
Method
Five moves, and the second one is where the philosophy sits.
Each society on offer is a row. Keep the list short and make sure each row really is a complete arrangement.
A place is something you might turn out to occupy. Whether the places should carry probabilities, equal or otherwise, is the contested premise, so leave it open for now.
Use one scale throughout. The verdicts are verdicts about these numbers, and a different scale is a different table.
Underline the lowest entry in each row and choose the row whose underlined entry is highest. A tie means the rule has no verdict between those rows.
Average each row. If the two rules choose differently, the dispute between them is the dispute about the veil, and neither the table nor the lab settles it.
The table has equal at 5, 5, 5 and unequal at 2, 8, 20. Score each row twice.
The rules differ about one thing: whether a gain of 15 at the top can make up for a loss of 3 at the bottom. Maximin says it never can. Laplace says it can, here by a wide margin. Nothing in the arithmetic says which of them is describing fairness.
Given two societies and three places, build the matrix, compute the worst entry and the average of each row, name the society each rule chooses, and say which premise about the veil the disagreement turns on.
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