[EM] STAR voting equals Borda count with top two runoff?
electionmethods at votefair.org
Sun May 2 16:33:52 PDT 2021
Recently I realized that, if I'm not mistaken, STAR voting -- "Score
Then Automatic Runoff" -- is equivalent to the Borda count with a
top-two runoff. Is this belief correct?
Both methods simply add numbers that are directly (although not
necessarily explicitly) specified on the ballot.
On a printed ballot the column titles for STAR voting are different from
a typical ranking ballot:
"5" instead of "First choice"
"4" instead of "Second choice"
"3" instead of "Third choice"
"2" instead of "Fourth choice"
"1" instead of "Fifth choice"
"0" instead of "Sixth/last choice"
Yet in this six-level case the Borda count would assign 5 points to the
first choice, 4 points to the second choice, and so on down to 0 points
to the sixth/last choice. And those numbers are added, just as they are
in STAR voting.
If a top-two runoff (a pairwise comparison between the two candidates
who have the highest number of points) is added to the Borda count, then
the two methods are counted the same.
Of course STAR voting and the Borda count (either with or without
top-two runoff) have different ballot-marking instructions:
Specifically, the Borda count method (either with or without the top-two
runoff) requires that a voter not use the same preference level for more
than one candidate, and requires that a voter not skip (leave unmarked)
any preference levels. Of course there is no obviously "best" way to
count a ballot that violates either of these requirements.
In contrast, STAR voting allows multiple candidates to be marked at the
same preference level.
In addition, voters marking a STAR ballot are encouraged to indicate the
strength of their preferences by rating their favorites much higher than
their strongly disliked choices.
In both cases the use of the top-two runoff discourages the tactic of
marking most candidates at the highest and lowest rankings (which would
become equivalent to approval voting if everyone used this tactic).
Otherwise, are there any other important differences?
As a related question, are there any academic references to using the
Borda count with a top-two runoff? If so, such references would also
apply to STAR voting, right?
For those who don't know, fans of STAR voting heavily promote their
method within the state of Oregon, and so far within Oregon it's used in
a few places (party nomination and, as I recall, a couple of local
elections). A couple of state legislators have sponsored bills for
adopting STAR voting more widely within Oregon.
I've communicated with leaders of the organization that promotes STAR
voting. When I point out that tactical voting can undermine the
fairness of STAR voting, they basically respond with what I would
characterize as saying "I can't imagine any voting tactic that would
cause any unfair results." When I point out a specific tactic that
would produce an unfair outcome they respond either by claiming the
outcome is not unfair, or by saying something equivalent to "I can't
imagine that kind of situation happening."
I think it would be helpful to point them in the direction of any
meaningful mathematical analysis that relates to their method. So does
anyone here know of any academic articles that apply to using the Borda
count with a top-two runoff?
Also, to repeat my initial question, am I overlooking anything in
believing that the mathematics behind the Borda count with a top-two
runoff is equivalent to STAR voting?
In advance, thank you for any help.
The VoteFair guy
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