Summability criterion: Difference between revisions

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====== Median methods ======

Alternatively, precincts may sum up the number of times each candidate was ranked at each of the <math>c</math> possible ranks. This ''positional matrix'' can then be used to compute the result for any weighted positional method after the fact, or for median-based methods like [[:Category:Graded Bucklin methods|Category:Graded Bucklin methods]]. This shows a contrast between median methods and point-scoring methods, where the grade level doesn't matter, only the strength/quality/degree of the grade (i.e. in ~~other~~ methods, two 1/5s are equivalent to one 2/5).

Alternatively, precincts may sum up the number of times each candidate was ranked at each of the <math>c</math> possible ranks (or grades). This ''positional matrix'' can then be used to compute the result for any weighted positional method after the fact, or for median-based methods like [[:Category:Graded Bucklin methods|Category:Graded Bucklin methods]]. This shows a contrast between median methods and point-scoring methods, where the grade level doesn't matter, only the strength/quality/degree of the grade (i.e. in points-scoring methods, two 1/5s are equivalent to one 2/5).

===== Cardinal methods =====

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If some other voter ranked B above A, then that would be added into this matrix by adding a 1 to the B>A cell (i.e. increasing it from 0 to 1), etc.

Rated pairwise methods

[[:Category:Condorcet-cardinal hybrid methods]] require one additional piece of information per candidate: the score for the candidate. This can be stored in the cell comparing the candidate to themselves (i.e. A>A would have candidate A's score).

=== Non-summable methods ===

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===== Instant-runoff voting =====

[[IRV]] does not comply with the summability criterion. In the IRV system, a count can be maintained of identical votes, but votes do not correspond to a summable array. The total possible number of unique votes grows factorially with the number of candidates.

== Importance of summability ==