Summability criterion: Difference between revisions
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{{Merge|Summability criterion (Wikipedia version)|date=February 2019}}
The '''summability criterion''' is a criterion about the vote-counting process of voting systems, which describes how precinct-summable a voting method is (i.e. whether there is a way for two areas, known as precincts, to transmit their vote totals and add this up to find the combined vote total, and if so, how easy it is, or if all the votes need to be taken to a centralized counting location to find the combined result). Unlike most other voting system criteria, it does not relate to the end result, only to the process.
'''Vote-counting''' refers to the process of collecting enough information from voters' [[ballot]]<nowiki/>s to find the result of a [[voting method]], as well as how the information is transmitted and processed.
== Requirements ==
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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
===== 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).
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Many voting methods that are summable to some degree can be manually summed in a harder way. For example, [[Score voting]] can be counted using a form of [[Pairwise counting]] that takes degree of preference into account.
=== Counting first choices ===
Some voting methods can be counted like [[Approval voting]] when counting:
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reducing the amount of work otherwise necessary to count them. For example, [[Condorcet methods]] can have this done using a certain implementation of the [[Negative vote-counting approach for pairwise counting]], or simply by using [[Pairwise counting#Counting first choices separately]].
=== Two-way communication ===
Some non-summable methods can be counted using two-way communication, which is when the precincts both transmit and receive information to and from the central vote-counting authorities during the counting process.
Most sequential [[Cardinal PR]] require less two-way communication and/or centralized counting work than most other [[PR]] methods.
== See also ==
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