Summability criterion: Difference between revisions
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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.
Since IRV does not comply with the summability criterion, it is silly to try to apply that criterion in that case.
== Importance of summability ==
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The summability criterion addresses implementation logistics. Election methods with lower summability levels are substantially easier to implement with integrity than methods with higher summability levels or methods that are non-summable.
Suppose, for example, that the number of candidates is ten. Under first-order summable methods like [[plurality voting|plurality]] or [[Approval voting]], the votes at any level (precinct, ward, county, etc.) can be compressed into a list of ten numbers. For [[Schulze method|Schulze]], a 10×10 matrix is needed. In an [[IRV]] system, however,
IRV therefore requires
To illustrate this point, consider the verification of a vote tally for a national office. In a plurality election, each precinct verifies its vote count. This can be an open process where The counts for each precinct in a county can then be added to determine the county totals, and anyone with a calculator or computer can verify that the totals are correct. The same process is then repeated at the state level and the national level. If the votes are verified at the lowest (precinct) level, the numbers are available to anyone for independent verification, and election officials could never get away with "fudging" the numbers.
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