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Printed in all capitals because it is an acronym, STAR stands for "Score, Then Automatic Runoff". Ballots for a STAR election are exactly the same as for an election using Range Voting (often called Score Voting) and there are no differences in the directions provided to voters. With the only difference being in the vote-count, the difference between STAR Voting and Range Voting may fail to even be noticed by voters. With STAR Voting, an initial round of vote counting is used to select the top two candidates, rather than the single winner in the case of Range Voting. A second, instant runoff count of the ballots is then conducted, interpreting each ballot as a vote for one or the other of the two remaining candidates according to which one the voter rated higher.

Whether using Range Voting (RV) or STAR Voting (*V), the voter is asked to assign to candidates a score within some specified range such as from 1 to 5. The choice of the range of scores is not specified either for RV or for *V but it is generally understood that the only important feature of that range is the number of different rankings available to the voter. For example, choosing 101 to 105 instead of 1 to 5 makes not a bit of difference to an election outcome even though somehow that choice may seem a bit odd.

Mathematicians often deal with equivalent representations of systems and they have a vocabulary for that topic. After writing a first draft of this article and realizing it seemed too confusing I decided that clarity demanded that I introduce a term from that mathematical vocabulary, the canonical form. Sometimes among the many equivalent forms of a system there is one particular form that stands out as somehow the natural form and mathematicians conventionally refer to that as the canonical form. Often, when one of the different equivalent forms seems most simple or it provides exceptional clarity it is the one declared to be the canonical form. The concept of canonical forms is important in the context of voting because, with clarity and understanding about the voting system, voters will more readily understand how to vote meaningfully.

RV is not just a single voting system but rather many systems and among them are both Approval Voting and Balanced Approval Voting. Approval Voting (AV) is the example of RV with a range limited to just two numbers; generally the chosen range consists of the scores 0 and 1; that is the canonical form for AV. Likewise, Balanced Approval Voting (BAV) is often characterized as RV with a range of just three possible scores and generally the range chosen consists of the three scores -1, 0 and +1; that is the canonical form for BAV. For both AV and BAV the default score to be used when a voter does not specify one is required to be 0. It will be convenient later in this article to refer to ranges of four or more scores as large ranges.

The typical description of RV specifies that the scores across all ballots are to be added together and the candidate with the largest total is declared to be the winner. Missing from that typical description is any mention of what score to apply to the sum when a voter skips over the candidate and fails to assign any score. Now a voter who skips over a candidate without providing a score probably does so either accidentally or with the intent of not influencing that candidate's prospects. In either event, it seems only appropriate to choose the default score to be zero. But in turn, making that the default means that zero should be one of the possible scores. We conclude that at a minimum, the canonical form for RV should include zero in the range. The only remaining question about the canonical form is where in the range 0 should lie.

An earlier article, in which we defined positive, negative and balanced voting systems, relates to this choice. A positive voting system allows voters only to express support of candidates and never opposition. For a positive system, the default score, 0, should surely be the smallest score in the range. In the opposite extreme, choosing the default score, 0, as the largest in the range we have a negative voting system where the voter is allowed only to cast a negative score in opposition to a candidate. Placing zero in the middle is balanced voting where the voter has a balanced choice of voting either support or opposition to any candidate. Of course only a range with an odd number of scores can have a middle score.

RV ballots tend, with large ranges to use number symbols for the voter to make selections; for the sake of clarity it is hard to see why any choice other than numbers in the canonical range should ever be used. For AV and for BAV numbers do not appear on the ballot; for AV there is just a checkbox next to each candidate's name for the voter to mark support; for BAV there are two check boxes, one for marking support and the other for marking opposition. Still, the score values tend to be used for teaching voters about AV or about BAV and especially in that situation clarity is surely at a premium. So even with AV and BAV it is best to stick to using the canonical range, -1, 0, +1.

But you no doubt wanted to read more about STAR voting. *V is built upon RV and since BAV is an instance of RV, a natural question is whether there would be any benefit from building *V on top of BAV. The answer to that question is a resounding no, the added runoff cannot contribute any advantage at all. It is a fairly easy application of high-school algebra to show that the winner in a BAV election would remain the winner in the subsequent runoff.

Does this uselessness generalize to an arbitrary *V election? I've not tried to answer that question, but that surely should be a question of interest to STAR advocates. However, it is an easy observation that if the runoff actually can make a difference for some larger choice of a range, then the value of adding the instant runoff stage with *V would at most be to correct a problem that is somehow introduced by building *V on an RV with a large range.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)

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