Summability criterion

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Summable Methods[edit | edit source]

Methods and their summability levels.
k=1 k=2 k=3 non-summable

Examples[edit | edit source]




Since IRV does not comply with the summability criterion, it is silly to try to apply that criterion in that case.

Importance of summability[edit | edit source]


Suppose, for example, that the number of candidates is ten. Under first-order summable methods like plurality or Approval voting, the votes at any level (precinct, ward, county, etc.) can be compressed into a list of ten numbers. For Schulze, a 10×10 matrix is needed. In an IRV system, however, each precinct would need to send a list of ten numbers, the number of first-place votes for each candidate. The central system would then return to each precinct a candidate to eliminate. Each precinct would then return the first-place votes for each of the nine remaining candidates, and receive another candidate to eliminate. This would be repeated at most 9 times. This is more than the others.

IRV therefore requires more data transfer and storage than the other methods. The biggest challenge in using computers for public elections will always be security and integrity. If N-1 times more data needs to be transferred and stored, verification becomes more difficult and the potential for fraudulent tampering becomes slightly greater.


Recounts[edit | edit source]


Some parts of this article are derived with permission from text at

This page was migrated from the "Summability_criterion" page on To view the authors prior to the migration, view the "Summability_criterion" page edit history prior to 2018-10-01

References[edit | edit source]

  1. "Compare STAR and IRV - Equal Vote Coalition". Equal Vote Coalition. Retrieved 2018-11-12.