Summability criterion: Difference between revisions
→Examples
Dr. Edmonds (talk | contribs) (→Summable methods: MJ uses median not sum. A sum is parallelizable but a median is not. I don't have a reference for this but it is well documented that the median is not because it needs a sort.) |
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== Examples ==
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In [[plurality voting]], each vote is equivalent to a one-dimensional array with a 1 in the element for the selected candidate, and a 0 for each of the other candidates. The sum of the arrays for all the votes cast is simply a list of vote counts for each candidate. [[Approval voting]] is the same as plurality voting except that more than one candidate can get a 1 in the array for each vote. Each of the selected or "approved" candidates gets a 1, and the others get a 0. ▼
Any [[weighted positional method]] can be summed this way, but with different one-dimensional arrays depending on the method. Alternatively, precincts may sum up the number of times each candidate was ranked at each of the
For example, with [[Score voting]], a voter who votes A:10 B:6 C:3 D:1 is treated as giving a 10 to A, a 6 to B, etc. Comparisons across different score scales can be made by dividing the score by the max score (i.e. instead of a 6, treat it as a 6/10=0.6, etc.) so that a voter who scores a candidate a 3 out of 5 and a voter who scores a candidate a 6 out of 10 can have their scores treated and counted the same without any issues.▼
<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 [[Bucklin voting]].
▲=== Condorcet methods ===
==== Cardinal methods ====
▲
▲For example, with [[Score voting]], a voter who votes A:10 B:6 C:3 D:1 is treated as giving a 10 to A, a 6 to B, etc. Comparisons across different score scales can be made by dividing the score by the max score (i.e. instead of a 6, treat it as a 6/10=0.6, etc.) so that a voter who scores a candidate a 3 out of 5 and a voter who scores a candidate a 6 out of 10 can have their scores treated and counted the same without any issues.
=== Pairwise methods ===
Some voting methods, such as [[STAR voting]] can be made precinct-summable using pairwise information alongside other pieces of information.
==== Condorcet methods ====
See [[pairwise counting]].
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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.
[[: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).
=== Median methods ===
The [[Majority Judgement]] and [[Bucklin]] methods can be made summable by counting the number of voters who gave a candidate each specific grade or rank. This is in contrast to other rated 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).
=== Instant-runoff voting ===
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