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impredicative/voting_systems.md

Last active July 3, 2025 16:57
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Maximum information content of voting systems
Raw
voting_systems.md
System Unique Ballots (Equation) Example (N = 5) Info Content (bits)
FPTP $N$ 5 $\log_2(N)$ = 2.32
Approval Voting $2^N$ 32 $N$ = 5
Ranked Choice $N!$ 120 $\log_2(N!)$ = 6.91
Borda Count $N!$ 120 $\log_2(N!)$ = 6.91
Range Voting $(S+1)^N$ 7,776* $N \cdot \log_2(S+1)$ = 12.93

Where:

  • $N$ = number of candidates
  • $S$ = maximum score for range voting (e.g., 0–5 means $S = 5$)
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impredicative commented Jul 3, 2025 •
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It would seem that an information content of $$\geq \log_2 (N!)$$ bits is advisable for a sufficiently democratic voting system.

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