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The summability criterion is a voting system criterion, used to objectively compare electoral systems. The criterion states:
Each vote should be able to be mapped onto a summable array, such that its size at most grows polynomially with respect to the amount of candidates, the summation operation is associative and commutative and the winner could be determined from the array sum for all votes cast alone.
Summability of various methods
In plurality voting, the number of ballots for each candidate may be counted, and these totals reported from each precinct.
Some other methods that are summable:
- Approval voting
- Baldwin's method [1]
- Borda count
- Bucklin
- Majority Judgment
- Nanson [2]
- STAR voting [3]
- Schulze method
- Score voting
In approval voting, Borda count, and score voting, each ballot contains votes for more than one candidate, and, with the last two, these votes may have different values. However, the sum of all values for each candidate may be found at each precinct and reported.
With Bucklin voting, the precinct totals for each candidate at each rank may be summed and reported.
In many Condorcet methods, each ballot can be represented as a two-dimensional square array referred to as a pairwise matrix. The sum of these matrices may be reported from each precinct.
Instant-runoff voting does not comply with the summability criterion. [4]
References
- ^ Hogben, G. (1913). "Preferential Voting in Single-member Constituencies, with Special Reference to the Counting of Votes". Transactions and Proceedings of the Royal Society of New Zealand. 46: 304–308.
- ^ Nanson, E. J. (1882). "Methods of election". Transactions and Proceedings of the Royal Society of Victoria. 19: 197–240.
- ^ "Compare STAR and IRV - Equal Vote Coalition". Equal Vote Coalition. Retrieved 2018-11-12.
- ^ Gaming the Vote, Why Elections Aren't Fair (and What We Can Do About It), William Poundstone, New York: Hill and Wang, 2008, p. 170.
See also
| It has been suggested that this article be
merged into
Compilation complexity. (
Discuss) Proposed since March 2024. |
The summability criterion is a voting system criterion, used to objectively compare electoral systems. The criterion states:
Each vote should be able to be mapped onto a summable array, such that its size at most grows polynomially with respect to the amount of candidates, the summation operation is associative and commutative and the winner could be determined from the array sum for all votes cast alone.
Summability of various methods
In plurality voting, the number of ballots for each candidate may be counted, and these totals reported from each precinct.
Some other methods that are summable:
- Approval voting
- Baldwin's method [1]
- Borda count
- Bucklin
- Majority Judgment
- Nanson [2]
- STAR voting [3]
- Schulze method
- Score voting
In approval voting, Borda count, and score voting, each ballot contains votes for more than one candidate, and, with the last two, these votes may have different values. However, the sum of all values for each candidate may be found at each precinct and reported.
With Bucklin voting, the precinct totals for each candidate at each rank may be summed and reported.
In many Condorcet methods, each ballot can be represented as a two-dimensional square array referred to as a pairwise matrix. The sum of these matrices may be reported from each precinct.
Instant-runoff voting does not comply with the summability criterion. [4]
References
- ^ Hogben, G. (1913). "Preferential Voting in Single-member Constituencies, with Special Reference to the Counting of Votes". Transactions and Proceedings of the Royal Society of New Zealand. 46: 304–308.
- ^ Nanson, E. J. (1882). "Methods of election". Transactions and Proceedings of the Royal Society of Victoria. 19: 197–240.
- ^ "Compare STAR and IRV - Equal Vote Coalition". Equal Vote Coalition. Retrieved 2018-11-12.
- ^ Gaming the Vote, Why Elections Aren't Fair (and What We Can Do About It), William Poundstone, New York: Hill and Wang, 2008, p. 170.