Section 07 · 3 entries
Paradoxes
Where the arithmetic misbehaves.
Reasonable-looking rules can misbehave in ways that are proved, not alleged. These entries cover majorities that run in a circle, the short list of conditions no ranked method can satisfy at once, and the discovery that ended a whole family of apportionment methods.
Every entry in Paradoxes
Each one is a single rule and what it demonstrably does, with the country and the period named.
- 7.1The Condorcet cycleMajorities that go round in a circle, so that no option beats all others and the agenda order decides the winner.
- 7.2Arrow's resultA short list of reasonable-looking conditions that no ranked method can satisfy at once, and what it does and does not prove.
- 7.3The Alabama paradoxAdding a seat to the total and watching a place lose one — the discovery that ended a whole family of apportionment methods.
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