Summability criterion: Difference between revisions
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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 ==
Informally speaking, the amount of data that has to be transmitted from the precincts should be less than the amount of data on the ballots themselves i.e. it must be more efficient to count the votes in precincts than to bring the votes to a centralized location.
Note: The word "mark/marking" is sometimes used instead of the word "bit (of information)".
=== Mathematical requirements ===
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== Notes ==
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.
=== Amount of vote-counting work ===
Summability focuses on the amount of data that has to be captured, but not necessarily the amount of work required to capture it. For example, when doing [[pairwise counting]], an election featuring a ballot that ranks a candidate last requires as many marks to count as if the same ballot had been cast without the last-ranked candidate. Yet in practice, the vote-counters must still take some time to check that that candidate is indeed last-ranked, meaning some work is done even while no data was produced.
=== Number of data value types versus number of data values ===
Summability focuses to a large extent on the number of data value types, not just the amount of data overall that has to be captured. This can make a difference in certain cases; for example, the regular [[pairwise counting]] approach only requires (n^2-n)data value types to be captured for all ballots, whereas the [[Negative vote-counting approach for pairwise counting]] requires (n^2) value types. This is because the latter not only records preferences in each pairwise matchup, but also the number of ballots ranking each candidate. Yet, depending on implementation, the negative counting approach actually has the same upper bound on number of data values to capture as the regular approach, and in practice could require fewer.
=== Counting first choices ===
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