It has been suggested that Summability criterion be merged into this article. (Discuss) Proposed since March 2024.
Compilation complexity is the smallest number of bits required to summarize a input to a function, such that the output of the function can be computed correctly. The notion was particularly studied in voting theory.[1] Often, a group has to accept a decision, but some of the voters have not arrived yet. It is desired to take the votes of the present voters and summarize them such that, when the other voters arrive, we can determine the winner. The compilation complexity of a voting-rule is the smallest number of bits required for the summary.
An important advantage of low compilation complexity is that it makes it easier to verify voting outcomes. For example, suppose an elections are held in a country of 1,000,000 people, divided into 1000 voting-stations of 1000 voters each. Low compilation complexity lets us summarize the outcome in each voting-station separately, which is relatively easy to verify by double-counting by representatives of the parties. Then, every citizen can verify the final outcome by summing the results from the 1000 voting stations. This verifiability is important so that the public trusts and accepts the voting rule.[1] Compilation complexity is also algorithmically useful for computing the backward induction winner in Stackelberg voting games.[2]
^ abChevaleyre, Yann; Lang, Jérôme; Maudet, Nicolas; Ravilly-Abadie, Guillaume (2009-07-11). "Compiling the votes of a subelectorate". Proceedings of the 21st International Joint Conference on Artificial Intelligence. IJCAI'09. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.: 97–102.
^Xia, Lirong; Conitzer, Vincent (2010-07-04). "Compilation Complexity of Common Voting Rules". Proceedings of the AAAI Conference on Artificial Intelligence. 24 (1): 915–920. doi:10.1609/aaai.v24i1.7627. ISSN 2374-3468.
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