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

[Kristofer Munsterhjelm]

On 04/05/2021 18.48, VoteFair wrote:
> Kristofer's example (below) helps me realize that I didn't clarify
> something important:
> 
> Here in Oregon everyone votes by mail by marking a paper ballot.  This
> means there is no way to enforce the Borda-count requirement that a
> voter use each preference level for only one candidate.

Presumably the current Plurality elections aren't really Approval
elections, so I would imagine they could enforce it the same way they'd
throw out Approval-style ballots under the current system?

>> Not really, because the scale is truncated and it's possible to both
>> equal-rank and skip ranks.
> 
> ...  the truncation issue, equal-rank issue, and skipping ranks issue
> become the same for both methods.  Correct?

Yes. However, I don't think it would be of much help, because the
"Borda" you end up with is not the Borda that's analyzed in academic
literature. So you may call it (a generalization of) Borda, but you
would have to show that results pertaining to Borda itself apply to this
generalization. (Borda is not bad because it has the name "Borda", but
because it behaves in a particular manner.)

For instance, the clone independence problem relies on the range of
points in Borda being a function of the number of candidates in the
election. Once you make the range fixed, that particular aspect of Borda
changes.

It would also alter instant runoff versions (Nanson and Baldwin) as some
of their behavior depends on candidates being given e.g. 1...5 points
when five candidates remain, then 1...4 points once someone has been
eliminated.

-km