What is "Summability"?
In an election, if you can tally any subset of the ballots separately and then add those sub-totals together to get the correct winner, the voting method is considered "summable." This is a key criteria that is required in order to allow ballots to be tallied (and audited) at the local or precinct level without having to be centralized in one location first. It's also key to ensuring that election officials can begin reporting preliminary results as ballots come in, without having to wait until all ballots are in hand.
In most elections, ballots are tallied at the county level in batches, and results are reported by precinct. For this reason, summability is often referred to as "batch summability" or "precinct summability."
For voting methods which are not summable, like Instant Runoff Voting (often referred to as Ranked Choice Voting or RCV), all ballots, or all ballot data must be centralized and then tallied together. Tallying and reporting meaningful results of any subset of ballots is impossible, as breaking the ballots into sets could distort the results by changing the order of candidate elimination or selection.
Is STAR Voting Batch Summable?
Yes. STAR voting is tallied in two rounds so it is a bit more involved than Choose-One Plurality election, but there is no need to wait until all ballots are in hand or until the Scoring Round tally is complete before tabulating the runoff votes. For STAR Voting, a batch sum includes the total score for each candidate and also the number of voters who preferred each candidate over each other candidate. These preliminary results are recorded on a preference matrix.
Why is Batch Summability so important?
On election day, batch summability is important because it means that preliminary results can be shared as soon as they are available during the tally, in real time, just like they are with Choose-One Plurality voting. To see how STAR Voting results can update in real-time, click the "show results" button on any live poll on the star.vote website. The ability to display preliminary election results in real time is a key component of a transparent election in which voters understand how their voting method works and how their votes are counted.
Batch summability is also a key component of secure elections and election integrity, whether an election is using paper or electronic ballots. When paper ballots can be scanned and tallied at the local level, a good chain of custody of those ballots is easy to maintain and easy to verify with security cameras, independent observers, and all the best practices for election integrity. For electronic ballots, the ballot data can be tallied and recorded at the local level as well, and ballot data doesn't need to be sent over the internet or transported from one elections site to another manually.
For elections which span multiple jurisdictions, like city elections that span county lines, or federal elections which span state lines, voting methods must be summable to comply with election laws that generally specify that ballots are counted at the county level.
Batch summability is a key component of election auditability.
Election recounts are best conducted at the local level. Local results by precinct are the first line of defense for finding any discrepancies or errors that may occur. Recounts are generally called for by a candidate who feels that the election results do not match the outcomes that their campaign was expecting. A precinct level result that is unexpected is often the catalyst for a recount or an audit. While election tabulation errors are rare, they can happen, as we saw recently in the 2021 New York City mayoral race using Ranked Choice Voting (RCV), where candidate Eric Adams sounded the alarm that reported vote numbers seemed off. His suspicions were later confirmed and it was discovered that 130 thousand test ballots had been added to the count.
Due to the huge costs, full election recounts are extremely rare and generally considered cost prohibitive. For this reason, Risk-Limiting Audits are now the gold standard for cost effective and accurate auditing protocols. A Risk-Limiting Audit is a technique that allows an accurate partial recount to be conducted. Depending on how close the election was, a specific percentage of ballots will be recounted to corroborate the election results. If the sample results don't match the official results then more ballots are recounted. This process can be repeated until the election results are confirmed within a reasonable doubt, or until a full recount has been conducted if needed.
What voting methods are not Batch Summable and which are?
Most single-winner and multi-winner bloc voting methods are batch summable, including Choose-One Plurality voting, STAR Voting, Score Voting, Condorcet voting, and Approval voting.
Summability for Proportional Representation methods is generally more complex, and in some cases may be impossible.
Proportional STAR Voting, and most other methods which have summable single-winner versions are not considered "summable" in general, but summing ballots may still technically be possible if the number of seats up for election is low enough. Summability for Proportional Approval Voting is likely a viable option. Summability for Proportional STAR Voting is more complex but may be logistically viable for races with only two or three winners. Summability for proportional methods is highly technical, but you can learn more about it here.
Ranked Choice Voting (specifically the Instant Runoff version that's in use widely and is the focus of most advocacy) is not summable no matter how many winners an election has. In RCV, ballots or ballot data needs to be centralized in one location, and all ballots need to be in hand before the elimination rounds can proceed. This often results in very long delays from voting day until election results can be reported, especially if absentee ballots will be accepted if they are mailed by election day.
In Ranked Choice Voting, it's not enough to know how many voters ranked each candidate at one level. This is because not all rankings will ultimately counted, and the election needs to track which specific ballot a ranking came from in order to know who that vote should transfer to as the ballots are processed through the candidate elimination rounds.
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