1
Model a choice behind the veil
Lay the original position out as a decision matrix with the chooser's place as the unknown state, and show that maximin and equal chances choose different societies from the same table.
Course · Philosophy
Justice and Collective Choice
Choose a society from behind a veil and watch two rules disagree, rank distributions by their worst-off member, measure what a free exchange does to equality, and tell a gap in treatment from a gap in outcome. Then count the ballots: find the profile where the majority goes in a circle, the one where three rules elect three candidates, the voters who gain by lying, the court whose majorities contradict themselves, and the electorate that gets wiser as it grows only when its voters are better than chance.
maximin: take the best worst case
leximin: the worst off first, then the next
Gini = 0 for equal shares, up with the gaps
A beats B, B beats C, C beats A a cycle
no rule meets Arrow's three on every profile
premises can pass while their conclusion fails
p above 1/2: a majority beats one voter
What this course is about
- Subject
- Philosophy
- Lessons
- 10
- Format
- Interactive
Overview
What you will be able to do
By the end you can state a theory of justice or a voting rule as a computation, run it on a case, and say which premise a disagreement turns on.
2
Rank distributions and measure inequality
Order two distributions by leximin, compute a Gini coefficient before and after a round of voluntary transfers, and state what an unequal distribution must do for the worst off to be allowed.
3
Separate unequal treatment from unequal outcome
Compute acceptance rates within groups and pooled, standardise them, and say which notion of fairness each comparison tests.
4
Tabulate a vote under several rules
Count pairwise majorities, find a Condorcet winner or a cycle, and run plurality, runoff, instant runoff and Borda on one profile to show that they can elect different candidates.
5
State and test the impossibility results
Check unanimity, independence and non-dictatorship on a profile, find a group that gains by misreporting its ranking, and say what Arrow's and Gibbard and Satterthwaite's theorems do and do not claim.
6
Aggregate judgments and compute a jury
Show a court whose majorities on the premises contradict its majority on the conclusion, and compute the probability that a majority of independent voters is right and that one vote decides.
Lessons
10 lessons
Distributive justice comes first, because it asks what a fair arrangement is. The second half asks how a group could reach any arrangement at all, and the answers are less comfortable than the question.
The Original Position and MaximinChoose a society without knowing which place in it will be yours, and the rule you choose with decides the society.Not marked
The Difference Principle and LeximinAn inequality is allowed only if it raises the position of the worst off, and ties at the bottom are settled one place up.Not marked
Entitlement, Patterns and the Gini CoefficientA distribution can be judged by its shape or by how it arose, and a free exchange can change the first while respecting the second.Not marked
Fairness, Statistics and Disparate RatesEqual treatment within every department can coexist with unequal overall rates, and the two ideas of fairness then give different answers.Not marked
Majority Rule and the Condorcet ParadoxEvery voter can rank the candidates consistently and the majority still go in a circle.Not marked
Plurality, Runoff and BordaOne set of ballots, four counting rules, and more than one winner.Not marked
Independence and Arrow's TheoremStrike a losing candidate from every ballot and the winner can change, though no voter's view of the others did.Not marked
Strategic Voting and ManipulationA voter can sometimes do better by reporting a ranking they do not hold.Not marked
The Discursive DilemmaA court can accept each premise by majority and reject, by majority, the conclusion they imply.Not marked
The Condorcet Jury TheoremA majority of voters who are each right more than half the time is right more often than any of them.Not marked
Recommended background
Ethics and the Arithmetic of Welfare, for the aggregation rules and the argument about priority and levelling down, and the courses it builds on for decision tables, the n-player dilemma and probability.
Practice suggestions
Work forward. The later lessons on voting assume you can read the table of pairwise counts that “Majority Rule and the Condorcet Paradox” introduces, and the lessons on distribution assume the aggregation rules of Ethics and the Arithmetic of Welfare.
Change the profile and the table. Each lab is a small instance you can edit, and each lesson turns on a figure, a winner or a rate that moves when the input does. Edit a number, predict the verdict, and then read it off; the prediction is where the learning is.
Hold the positions loosely. Each argument is stated at its strongest and its premises are marked. Whether to accept Rawls's veil, Nozick's history or Harsanyi's equal chances is left to you on purpose, and so is the choice between equal treatment and equal outcome.
What it does not cover
The proofs of the impossibility theorems. Arrow's theorem and the Gibbard–Satterthwaite theorem are stated, and their conditions are checked on profiles you can edit, but the arguments that no rule satisfies them all are not reproduced.
Sen's liberal paradox. It needs a machinery of rights and rankings that the lab does not build, and a version that omitted the machinery would misstate it.
Statistics as inference. The fairness lesson computes rates from counts; nothing is estimated, no test of significance is run, and nothing here says how large a disparity must be before it is real.
Political philosophy beyond these arguments. Legitimacy, authority, rights, the justice of war and of global distribution have no computation attached, and the course does not pretend otherwise. Rawls and Nozick appear as arguments with premises, not as authors with systems.