Is there a name for this method? (STAR but with a series of normalized runoffs)

I seem to remember seeng this described, but can’t find its name or any references to it:

It’s got scored ballot, a la STAR voting (0-5 stars).

To tabulate:

First, normalize all ballots, so that there is one candidate with 0 stars and one with 5 stars. (if impossible because all candidates have the same number of stars, just leave them alone) This means ballots can have fractional stars.

Then eliminate the candidate with the lowest average.

Now continuously loop, normalizing and eliminating, until one candidate remains. Normalizing is needed on each loop to account for eliminated candidates.

When I invented (or likely reinvented) this I called it “Cardinal Baldwin’s Method”. It is essentially Baldwin’s method but instead of starting with a rank and doing a borda count you start with score. Other than that I do not know of a name for this system.

It is worth noting that others have argued for a different way to normalize. You can use the cumulative voting style so that it sums to a constant. This is done in Distributed Voting and some verions of Instant Runoff Normalized Ratings.

Also, please note that all these sequential elimination systems are non-monotonic. I made a post about them in general a while back.


Cool thanks, that’s what I was looking for.

When I (likely re-) invented it twenty years ago, I didn’t think it was any more related to obscure Baldwin than well-known IRV, and I still don’t. Baldwin is to Borda as IRV is to single-choice as “Cardinal Baldwin” is to score.

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I do not see any relation to IRV other than it being a sequential elimination method. The ballots and tabulation are different. Taking one change at a time in a 6 degrees of separation style. Starting with IRV, if you convert to Cardinal then sum you get Borda. If you then normalize ballots and sequentially eliminate you get Baldwin. If you then start with cardinal instead of ordinal ballots you get this method. There might be at more methods you could put in between but the point is that the number of changes to go from IRV vs from Baldwin is greater.

I’ve been backing “Instant Runoff Normalized Ratings” (IRNR, link above) as my pet method.
Like IRV it does have some non-monotonicity, but if you look at it on a KPY voting space diagram it has smaller non-monotonic regions, so, that’s something.


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What code did you use to get the charts?
Is it possible to modify the code to get the DV graphics (another method)?

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DV should be the same. The only difference is how the data is collected, ie with cumulative or score ballots. I do not think this matters.

I would however like to see this done for Cardial baldwin since I prefer that normalization.

I don’t think it’s a “number of changes” issue so much. To me this method seems extremely similar to IRV in how it works overall.

In any way other than it being a sequential elimination method?

More than anything else, I have seen those graphs in other contexts too but I don’t understand why there is only 1 for each method. It seems to me that these graphs are obtained assuming that the voters are perfectly honest and what I would like to do is to modify the code in order to also obtain results based on different types of tactical votes.

I think being a sequential elimination method is kind of a big deal, and is far more significant than all the other differences combined.

The main difference between this and IRV is that a score type ballot is more expressive than a ranked one. Actually, its expressiveness is just different, not necessarily “more.” If you have 0-5 stars that is arguably less expressive than being able to provide a full ranking, once the number of candidates gets to be much greater than 6.

Still, to me, this is just a variation on IRV. In theory, you can do IRV but with Score ballots (ignoring anything other than the order), but this approach tries to take into account the actual scores a bit more effectively.

Baldwin’s method is also a sequential elimination method. There are many, IRV may just be the most well known.

Nope, thats baldwin’s. IRV has at least two other differences. The aggregation is really important.

If you did this it would result in a very different method than what we are discussing.

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Sure, there may be. And there are even more election methods that are not sequential.

IRV is not only well known, but in use in real elections including where I live. So yeah, if I’m saying that this method is an interesting twist on IRV, there’s a reason I’m not choosing to compare it to some obscure method that very few know about or talk about.

I’m not trying to say that this and IRV are the only ones in their category.

This one is, though, the only variation on IRV that comes to my mind, that makes much sense. If you normalized it a different way, or if you didn’t normalize it at all, you’d simply be doing it wrong, in my opinion.

It’s both this and Baldwin’s, and I’m sure some other ones. It doesn’t have to be so black and white.

Of course, it would then just be straight IRV, but with a different ballot interface. (and I’d argue, an easier to use one, even though it essentially throws away data as soon as it is submitted)

IRV and Baldwin ballots are the same, so let’s move on to tabulation.

So Borda is cardinal? Then Baldwin is Cardinal. Then “Cardinal Baldwin” is redundant. If we’re going to be replacing the ranked ballots with cardinal ballots anyway, why go the circuitous route of first converting the rankings to a Borda count? And even if we did, that would give us Baldwin, not Borda. Getting to Borda would require the additional step of stripping IRV of its own “normalization” (as much a stretch for Baldwin as IRV) and sequential elimination, only to immediately restore them to get back on track to “Cardinal Baldwin”.

My election simulator code is here

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