Expressiveness of different kinds of ballots

Let N be the number of candidates.

Ballot type# of legal votes N=3N=5N=10N=20
Plurality (pick one)N 351020
Vote for or against one2N 6102040
Approval2N 83210241048576
Rank-order top K onlyN!/(N-K)! 6 (if K=3)607206840
Full rank-orderingN! 612036288002.43×1018
Full rank-ordering with arbitrary truncation allowed⌊N!(e-1)⌋-1 920562353004.18×1018
Rank-ordering with equalities allowed k≥0kN/2k+1 135411022475632.68×1021
Score (L levels)LN 1000 (if L=10)100000100000000001020

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