A new(?) STAR variant

Well yes, that is the point. STAR is a compromise with maritarian IRV people. In broad strokes STAR is “Use Utilitarianism to get to the top 2 then use majoritarianism.” These new methods are an attempt to make score more Utilitarian.

Well that is the point of Utilitarianism. It is not just your preference but the magnitude of that preference. STAR ignores all this information on the ballot about the magnitude of the preference and maximises impact for each person. This means that somebodies slight preference could cancel out a life changing preference from another.

Of course. This is why we sum the scores in the standard score system. This is why score is such a compelling system. STAR breaks that argument so you are just arguing for score over STAR.

When people score candidates the scores they give them is dependant on the other candidates. Score relies on there being enough candidates to properly get utilities. I explained this concept in a prior post

So what I am trying to do with this “New STAR” is to account for the fact that we never have the enough candidates for everybodies scores to be on the same scale. What STAR does is reduce it to how they would vote if there had only been two candidates. What I want to do is try to give everybody the same voice but also weight that voice by the utility difference between the top two they expressed on the original ballot.

I have given the Olson reweighing as well as my own to attempt to do this. I am not totally sure that either really does what I want but they both do it more than STAR. I am not saying that means it is better. I am trying to be utilitarian and STAR is intentionally being majoritarian.

If you understand what I am trying to say and have a suggestion for how to do the reweighting in a better way than either I have proposed I would appreciate it. An example I have been thinking about is the following

Suppose that with candidates A,B and C you would score them A:10, B:6, C:0. However, if there was also a candidate D you would have scored them A:3, B:2, C:0, D:10 because you love D. What if the top two turn out to not include D. How do we methodologically keep the information about the relative preference but account for the fact that A and B were suppressed by D being a candidate. Since the scale is different for each person we need this to work for everybody. A person who still likes D the best but is not a total fanatic may score A:9, B:6, C:0, D:10. For these two ballots the ratios of all candidates other than D are the same. If D were not in the race their ballot would look the same so if D is not in the top two runoff I want their ballots to be the same. Make sense?

I think so. This is basically a restatement of Vote Unitarity and an endorsement of Sequentially spent score.

Yes - ideally adding a constant to every score on every ballot would give the same result.

Edit - I think any approval method that passes IIB used with KP would pass this, so this includes Thiele/PAV.

How about on only some ballots? I.e. if only 1 ballot has its scores upped by the same constant out of all of the ballots in the election.

And are there other such properties that are related to to the stronger IIB property (a ballot with no preference between a set of candidates shouldn’t impact the relative standings of the candidates in the set)?

Ah, because with KP, adding the constant essentially counts as “changing a fraction of a ballot to now approve everyone rather than nobody”?

I think is the case with IIB passing methods with KP.

Increasing your score by 1 for all the candidates effectively just adds a ballot that approves all the candidates (or a fraction of a ballot, depending on how you look at it).

STAR is on the far edge of acceptability in terms of complexity. Voters need to be comfortable auditing the results and even understanding the system enough to use it casually.

Send people to star.vote and anyone can readily understand what’s happening. The runoff is a simple ballot-count, each ballot has to be in one box or the other.

I think anything more complex lives only in the realm of theory at least until STAR itself is the norm (and then we could discuss adapting what people know to add some tweak).

When describing STAR, I can say, “it’s like a primary and general election in one ballot” and that doesn’t work with the more complex normalizing.

This doesn’t mean the normalizing is worse in terms of abstract utility etc. I like it and dislike majoritarianism. But for pragmatic actual advocacy in the real-world, I think STAR still wins out clearly. Especially since the complexity only affects (mostly contrived) edge cases.


Agree that the places that this more complex system has any effect tend to be mostly contrived cases. (at least that’s my gut feel on it) In cases with any significant number of “middle ground” voters, the advantages seem to disappear.

I do think, however, that new variants like this have value in other contexts beyond promoting them for government elections. They might be pragmatic and real world (e.g. “let’s vote on our pizza topping”), but not necessarily government.

Imagine there were a STAR voting web-widget that people can use for things like private clubs/groups or various online “just for fun” polls. The default might be to tabulate it using standard STAR voting, but if people want to use other tabulation schemes – including plain old score voting – that’s as simple as changing a setting when you post the poll (or, you know, write your organization’s bylaws). Voters and others could also see the alternative tabulation methods’ results if they were interested, but of course whoever set up the election would have decided ahead of time which one actually counted, and that is the one that would be shown by default.

I’d love to see one that has optional tabulation methods such as:

  1. pick the Condorcet candidate first, if there is one, if not pick the highest average normalized score from the Smith set (normalize each ballot so max score out of Smith set candidates is 5, min score is zero)
  2. pick the candidate with the highest median score (using interpolated median so the likelihood of getting ties goes down as the number of voters go up, see [1] below )
  3. pick the IRV winner (converting the ballots to ranked, and of course allowing equal ranking). If only to demonstrate the downsides. :slight_smile:

One advantage to both score voting and #2 above is that it could easily show a bar chart of the results. Results for other methods (including STAR, unfortunately) can be really hard to show as a meaningful bar chart.

So I’d always suggest keeping such wider contexts in mind when discussing such things.

  1. Interpolated median is a variation of median that works will when responses are forced to be to whole numbers, and can be seen as “the calculated estimate of where the true median would have been had there been finer granularity in the scale used”: http://www.weekscomputing.com/webhelp/hs520.htmIntMedian
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Right on, I agree with all that.

Personally, I prefer plain score voting for situations with no contention and trust that all will be honest. In that case, I like to think of score as not normalized at all. So, people with stronger preferences can express them and others who want to express weaker preferences can do so and consciously choose not to have equal weight.

And for representative government, I’m learning toward qualification systems that have some blinders built in (so the qualification process cannot be biased by irrelevance like candidate’s height or whatever) and then a lottery system to select representatives from the qualified pool. Recent entertaining reference for that: http://revisionisthistory.com/episodes/44-the-powerball-revolution

But I’m on board with the desire that a variant of star.vote polling tool could be available with this sort of alternate-algorithm. I agree that the utility is better in terms of its outcome.

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There is still the scale problem which this helps at the cost of complexity. I made a page on electowiki to try to clarify now that I have had some feedback from everybody. Comments or modifications to the page itself are welcome.

For simulation purposes, it might help to try STAR where, in the runoff, the voter casts anything from an infinitesimally small scored margin in favor of their preferred candidate all the way to maximally scoring their preferred candidate higher than the other candidate.

Just to return to this:

The reason for STAR over score isn’t about a fundamental difference in philosophy about how to deal with scores or utilities. I think it’s more about strategic voting. For example, under plain normal score voting, someone might feel strategically forced to vote down a candidate they like, if they like the two frontrunners. Under STAR they can still give 5 and 4 because they will still get a maximum vote in the run-off.

This new system has a fundamentally different approach to scores than plain score voting, looking at ratios rather than differences. And I’m doubtful about this approach.

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That is fundamentally anti-utilitarian. If they give a 4 and a 5 they care 1 unit of difference. If somebody else gave a 0 and a 5 then treating that preference the same is unfair.

I do not see why. We all agree that the favoured of the two in the runnoff should be pushed up to a full 5. The question is, “What is the fair thing to do with the other”. There are three options

  1. Push them up proportionally to the amount to pushed up the other (This is STLR voting)
  2. Leave them at the original score. (This is a variant I have put on the STLR voting electowiki page)
  3. Drop them to 0 (This is STAR voting)

I would be happy with either of the first two but the third seems unfair because it treats a tiny preference the same as a huge preference. This is majoritarianism.

Superficially it looks anti-utilitarian. However, according to Jameson’s simulations, STAR has a higher VSE (utility) than score. The point is that a utilitarian does not have to be a supporter of score voting, even if it it looks like it perfectly parallels what they’re after. When you take into account how people vote in reality, another method - e.g STAR - might give a more utilitarian result.

I see pushing up the favoured candidate to a 5 and the less favoured candidate down to 0 as symmetrical, so I don’t really see the difference between the two.

I also see the 5-4 and 1-0 cases as symmetrical. In one case my favourite two candidates have made the run-off and in the other my least favourite two have made the run-off. But the 5-4 will remain unchanged, whereas the 1-0 will be converted to 5-0, which I don’t think is reasonable. Like STAR, this also treats a tiny preference as a huge preference and is majoritarianism, but only at one end of the scale. So it’s inconsistent.

You could, if you wanted, turn this on its head and look at dislike for candidates. In this case I would give 5 and 4 to my least favourite candidates, and 0, 1 to my favourites. If we did the transformation on these scores it would be the opposite case where I would get a full vote in the run-off.

This gives another illustration as to why I think the numerical difference between the scores is the important factor, not the ratios. So if we’re having a run-off (and not using normal score voting), I think the STAR version is the only one that really makes sense.

I can see the motivation for wanting to keep the magnitude of the preference in the run-off, but then not having a run-off does that, which is score voting. So for me it’s score or STAR (within the confines of methods relevant to this discussion anyway).

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When you say “normal score voting”, do you specifically mean that when the voter has scored A:5 B:4 in the scoring phase, that they must give A only 1 point more than B in the runoff? Or that the voter ought to be allowed to give anything between 1 point and [max score - min score] points? The latter would be best implemented using the rated pairwise ballot (or at least, by giving the voter an option of what % of voting power they’d like to use, which would be applied the same to every runoff they have a preference in).

Only for dishonest voting. For honest voting score is better. This means that the amount of honestly matters. But either way that is a good point. VSE/Bayesian regret should be the gold standard. Work done by Brian Olson gives me some confidence that STLR Voting will do well in terms of that metric. I would appreciate if anybody has the ability to check.

This is because we disagree about what the score mean. For me a positive score is a measure of the level of support. A zero represents everything from no support to hatred. What my system is doing is assuming that all the zeros are hatred not that the difference is what matters. I understand your reasoning as well. I do not think it is “wrong” I just think my interpretation is more practical .

Such a system could work but it is likely more important to distinguish between those you like than those you dislike.

I meant no run-off. When I said “So if we’re having a run-off (and not using normal score voting)”, it could say “If we’re having a run-off (as opposed to using normal score voting)”.

Just on this bit, according to Jameson’s VSE simulations, STAR is better than score even for honest voting. I think this might be because of the normalisation people make with their own votes anyway. Some people have a larger utility difference between their favourite and least favourite candidates, but they might all use the top and bottom scores, so there would be some distortion. And having a final run-off might then actually improve things.

Obviously simulations have assumptions built in and should not be taken as gospel of course. It’s also interesting to note that with these simulations, Ranked Pairs (the Condorcet method) actually comes out top of all the methods tested with honest voting.


Of course one of the things that detractors of score voting say is that it’s not clear what it means to cast an honest vote.

That seems wrong. Score is a faithful mapping of utility in the honest case so it is by definition the best. I have never looked into this deeply so I will just quote Warren from when I asked him the other day

Essentially, if voters are 100% honest, then plain range does excellently and outperforms STAR.

This is why I like STLR. It restricts the options so that at least honesty is defined.

I’m not sure “faithful mapping of utility” is a valid concept, especially not if you have finite limits on maximum or minimum. Also, is it on a linear scale or logarithmic, or what? Etc. I would rather think of them as “how many points do you want to give each candidate?” And I also generally assume that any rational person would want to give their least favorite candidate a zero and their favorite a maximum.

But even if it were true that utility can be measured in this way, I particularly don’t like hearing that maximizing total utility is “best by definition.” I consider game theoretically stable to be “better” than maximizing utility. It better maps to my idea of fairness, and fairness is a goal here… for me, anyway.

A simple example of the flaw with the “maximize utility” idea is dividing a bag of candy between two people, each of whom would like to have as much as they can get.

What if one person is hungrier than the other? What if one just likes candy more than the other?

To me, fairness is the idea that both people get the same amount, regardless of how much the candy makes each one of them happy. Dividing it equally (such as by using the “you split I pick” approach) also tends to be game theoretically stable, assuming that this interaction is the only two between the two people.

On a practical level, I think that game theoretically stable is perfectly possible to achieve when you make the typical assumptions that election theory, classical economic theory and game theory all have in common. (i.e. that people “rationally and independently seek to advance their own self interest”) I don’t think this will ever be true if you aim for maximizing utility… the more you try to optimize for that, the more likely you are that you leave it open to strategic manipulation.