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<div dir="ltr" data-setdir="false">They're not equivalent, and you even go on to explain the differences. STAR is score with run-off and Borda with run-off is, well, Borda with run-off.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Of course, by limiting it to 6 scores, if voters want to make sure that they would make a difference in a run-off between any pair of candidates, it does have the potential to make it a little bit Borda-y. However, at the other extreme, if a full continuum were allowed, it could become very approval-y.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Toby</div><div><br></div>
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On Monday, 3 May 2021, 00:33:59 BST, VoteFair <electionmethods@votefair.org> wrote:
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<div><div dir="ltr">Recently I realized that, if I'm not mistaken, STAR voting -- "Score <br></div><div dir="ltr">Then Automatic Runoff" -- is equivalent to the Borda count with a <br></div><div dir="ltr">top-two runoff. Is this belief correct?<br></div><div dir="ltr"><br></div><div dir="ltr">Both methods simply add numbers that are directly (although not <br></div><div dir="ltr">necessarily explicitly) specified on the ballot.<br></div><div dir="ltr"><br></div><div dir="ltr">On a printed ballot the column titles for STAR voting are different from <br></div><div dir="ltr">a typical ranking ballot:<br></div><div dir="ltr"><br></div><div dir="ltr">"5" instead of "First choice"<br></div><div dir="ltr">"4" instead of "Second choice"<br></div><div dir="ltr">"3" instead of "Third choice"<br></div><div dir="ltr">"2" instead of "Fourth choice"<br></div><div dir="ltr">"1" instead of "Fifth choice"<br></div><div dir="ltr">"0" instead of "Sixth/last choice"<br></div><div dir="ltr"><br></div><div dir="ltr">Yet in this six-level case the Borda count would assign 5 points to the <br></div><div dir="ltr">first choice, 4 points to the second choice, and so on down to 0 points <br></div><div dir="ltr">to the sixth/last choice. And those numbers are added, just as they are <br></div><div dir="ltr">in STAR voting.<br></div><div dir="ltr"><br></div><div dir="ltr">If a top-two runoff (a pairwise comparison between the two candidates <br></div><div dir="ltr">who have the highest number of points) is added to the Borda count, then <br></div><div dir="ltr">the two methods are counted the same.<br></div><div dir="ltr"><br></div><div dir="ltr">Of course STAR voting and the Borda count (either with or without <br></div><div dir="ltr">top-two runoff) have different ballot-marking instructions:<br></div><div dir="ltr"><br></div><div dir="ltr">Specifically, the Borda count method (either with or without the top-two <br></div><div dir="ltr">runoff) requires that a voter not use the same preference level for more <br></div><div dir="ltr">than one candidate, and requires that a voter not skip (leave unmarked) <br></div><div dir="ltr">any preference levels. Of course there is no obviously "best" way to <br></div><div dir="ltr">count a ballot that violates either of these requirements.<br></div><div dir="ltr"><br></div><div dir="ltr">In contrast, STAR voting allows multiple candidates to be marked at the <br></div><div dir="ltr">same preference level.<br></div><div dir="ltr"><br></div><div dir="ltr">In addition, voters marking a STAR ballot are encouraged to indicate the <br></div><div dir="ltr">strength of their preferences by rating their favorites much higher than <br></div><div dir="ltr">their strongly disliked choices.<br></div><div dir="ltr"><br></div><div dir="ltr">In both cases the use of the top-two runoff discourages the tactic of <br></div><div dir="ltr">marking most candidates at the highest and lowest rankings (which would <br></div><div dir="ltr">become equivalent to approval voting if everyone used this tactic).<br></div><div dir="ltr"><br></div><div dir="ltr">Otherwise, are there any other important differences?<br></div><div dir="ltr"><br></div><div dir="ltr">As a related question, are there any academic references to using the <br></div><div dir="ltr">Borda count with a top-two runoff? If so, such references would also <br></div><div dir="ltr">apply to STAR voting, right?<br></div><div dir="ltr"><br></div><div dir="ltr">For those who don't know, fans of STAR voting heavily promote their <br></div><div dir="ltr">method within the state of Oregon, and so far within Oregon it's used in <br></div><div dir="ltr">a few places (party nomination and, as I recall, a couple of local <br></div><div dir="ltr">elections). A couple of state legislators have sponsored bills for <br></div><div dir="ltr">adopting STAR voting more widely within Oregon.<br></div><div dir="ltr"><br></div><div dir="ltr">I've communicated with leaders of the organization that promotes STAR <br></div><div dir="ltr">voting. When I point out that tactical voting can undermine the <br></div><div dir="ltr">fairness of STAR voting, they basically respond with what I would <br></div><div dir="ltr">characterize as saying "I can't imagine any voting tactic that would <br></div><div dir="ltr">cause any unfair results." When I point out a specific tactic that <br></div><div dir="ltr">would produce an unfair outcome they respond either by claiming the <br></div><div dir="ltr">outcome is not unfair, or by saying something equivalent to "I can't <br></div><div dir="ltr">imagine that kind of situation happening."<br></div><div dir="ltr"><br></div><div dir="ltr">I think it would be helpful to point them in the direction of any <br></div><div dir="ltr">meaningful mathematical analysis that relates to their method. So does <br></div><div dir="ltr">anyone here know of any academic articles that apply to using the Borda <br></div><div dir="ltr">count with a top-two runoff?<br></div><div dir="ltr"><br></div><div dir="ltr">Also, to repeat my initial question, am I overlooking anything in <br></div><div dir="ltr">believing that the mathematics behind the Borda count with a top-two <br></div><div dir="ltr">runoff is equivalent to STAR voting?<br></div><div dir="ltr"><br></div><div dir="ltr">In advance, thank you for any help.<br></div><div dir="ltr"><br></div><div dir="ltr">Richard Fobes<br></div><div dir="ltr">The VoteFair guy<br></div><div dir="ltr">----<br></div><div dir="ltr">Election-Methods mailing list - see <a href="https://electorama.com/em " rel="nofollow" target="_blank">https://electorama.com/em </a>for list info<br></div></div>
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