Summability criterion: Difference between revisions

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{{Merge|Summability criterion (Wikipedia version)|date=February 2019}}

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The [[summability criterion]] is a [[voting system criterion]], used to objectively compare [[voting system]]s. The criterion states:

<em>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.</em>

==Complying methods==

[[Majority Choice Approval]], [[Schulze method]], [[Approval voting]], [[Range voting]], [[Borda count]], [[Borda count|Nanson's method]], and [[Plurality voting]] all comply. [[Instant-Runoff Voting]] does not comply.

==Commentary==

Summability is the only publicly expressed criterion that addresses implementation logistics. Election methods that comply with the summability criterion are easier to implement than those that do not. Those who support the summability criterion say that it is essential for ensuring the integrity of an election.

Under methods that do not comply with the summability criterion, usually every individual vote (rank list) or at least every unique vote and its number of occurrences, must be available at a central location to determine the winner. The votes cannot feasibly be compressed by summing, as in other election methods.

==Summability of various methods==

In [[plurality voting]], the number of ballots for each candidate may be counted, and these totals reported from each precinct.

In [[Approval voting]], [[Borda count]], and [[Range 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 method]]s, 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. <ref>''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.</ref>

==References==

== See also ==

*[[Voting system]]

*[[Monotonicity criterion]]

*[[Condorcet Criterion]]

*[[Generalized Condorcet criterion]]

*[[Favorite betrayal criterion]]

*[[Participation criterion]]

[[Category:Voting system criteria]]

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.