Concept

Logic — where it appears

The study of which conclusions follow from which assumptions, made precise enough to be checked mechanically. It supplies the notion of consistency that every aggregation problem is measured against.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

16 rules, and none that survives. A table of every systematic anonymous aggregation rule for 3 judges: one row per rule, showing the verdict it gives at each count of yes-votes, whether it decides every proposition, and whether it is consistent. No row has both.

No rule escapes the doctrinal paradox

A court whose members each hold a consistent position can reach an inconsistent verdict by majority. The anchor's first rung exhibits one such case, which invites the hope that a better rule would avoid it — and every rule that responds to the votes at all fails somewhere.

applied · Judgement aggregation

Where the two procedures part company. A table of 3 judges' verdicts on two premises and the conclusion each is committed to, with the two majorities at the foot disagreeing about the conclusion.

Deciding the premises or the conclusion

A body that cannot be both decisive and coherent has to choose which. The two live options are to vote on the reasons and let the verdict follow, or to vote on the verdict and let the reasons look after themselves — and they reach opposite answers on exactly the profiles the impossibility identifies.

applied · Judgement aggregation

Named alongside it

The objects these essays reach for when they reach for this one.

Aggregation Consistency Judgement aggregation Majority Voting rule Decided by exhaustion Deliberation Impossibility Manipulation

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