[EM] STAR voting equals Borda count with top two runoff?

[Toby Pereira]

 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.
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.
Toby
    On Monday, 3 May 2021, 00:33:59 BST, VoteFair <electionmethods at votefair.org> wrote:  
 
 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.

Richard Fobes
The VoteFair guy
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