STAR vs. Score

Jack Waugh

some people could argue that since her strength of preference is weaker it's fair that her vote carry less weight

No, of course not. Everyone deserves the same weight. But in Score, she has to vote Bad 4 or 5.

Multiround tallying systems are confusing. They produce results that belie the expectation that all balanced systems would behave identically. And for me this expectation came from the logic that if two systems behave differently, at least one of them must be cheating some voter out of some of her rightful power, which contradicts the assumption that both systems are balanced.

I guess some of your points are:

the decision between the top two may matter more than the decision between a random two. So STAR makes sure everyone has full strength in that decision even if they vote their desires without regard to any estimate of where the other voters stand.
STAR performs much better than Score when voters vote that way.
STAR makes it difficult to find a better performing strategy, even though theoretically, one exists. The signal--to-noise ratio for finding it is prohibitively low.

Let's add to the candidate field of your example, Bad II, a clone of Bad, and Worse II, a clone of Worse. Of course, all the voters are aware this has happened, so can adjust their strategies. Since the four bad and worse candidates are the front runners, unless there is a significant upset (difference between perception of where the voters stand and where they turn out to actually stand), the finalists will be Bad and Bad II or Worse and Worse II. How should Vicki vote?

SaraWolk

@Jack-Waugh
Bad1: 1 star
Bad2: 1 star
Worse1: 0 stars
Worse2: 0 stars

I disagree that the fact that score and STAR don't produce identical results means that one or the other is cheating. Neither is cheating voters. They are both good methods and the they optimize for slightly different things.

STAR optimizes for both strength of support and number of supporters.
Score optimizes for strength of support specifically.

Both are valid goals and methods, but there's a real world benefit to narrowing down the list of proposals to help lay people make a good choice. If we promote both loudly (and also list all other good methods we can think of) the considerations would be overwhelming to most and would lead most to get overwhelmed and quit researching, or worse, come to a decision after only considering a one-sided set of considerations.

Take Condorcet for example. Condorcet has largely failed to get adopted anywhere because of lack of consensus around the best version, despite that all versions are quite a bit better than most methods in use. If Condorcet advocates had come together around a good well rounded proposal and simplified their pitch a long time ago it would likely be the dominant RCV method, but no, they focused on academic debate over cohesive advocacy. We cardinal advocates should take note. Are we debating because we want better democracy in the real world, or because we find the question interesting and enjoy the debate for its own sake?

Jack Waugh

@SaraWolk, I think that if the conditions here are that 99% of the electorate considers the race as being between the Bad party and the Worse party, and they aren't even taking Obscure into consideration as a possible winner, Vicky must give Bad[a] and Bad[b] scores of at least 4 so as to exert sufficient pressure to do her part toward preventing Worse[a] and Worse[b] from being the finalists. The existence of the clones reduces STAR to Score and so the situation demands the same strategy as would be appropriate for Score.

As to why pose questions and try to answer them, it's because I need to learn what is going on with these systems, to try to prevent being pulled into error again.

I am involved with a little political group that thinks it is drafting platform planks for a national-level party. I joined it for the sole purpose of trying to prevent error in its stance on voting systems. I would be concerned for the rhetorical effect on State-level parties if a national-level party publishes a severely misleading stance in this regard. The first draft of a platform on which this group bases its work (from another group) requires a ranking voting system in all cases. I feel that allowing that stance to stand would be severely misleading, because choosing ranking eliminates rating, and there are grounds to judge that several rating systems are more democratic than even the most democratic ranking systems. And especially more so than IRV, which is in practice what people mean when they call for ranked-choice voting.

I believe that of the people involved in the group, I have by far the most knowledge on single-winner voting systems. I think most of the group either don't care, or think I am the one who has the deepest understanding. Of course, they don't think I am infallible, and I have taken care to present myself as fallible. I said, I am not God and my opinions might not be correct, but, I keep saying, I can present arguments to support them. Interest in the details of these arguments has been slight to nonexistent. But I have been asked questions about what opinions I have, going outside of those I initially stated when approaching the other members of this group on this subject. For example, I have been asked whether I think IRV is better than FPtP.

I have been telling this group that STAR is at least as democratic as Score. I don't want egg all over my face from finding out later that it is false.

I supported IRV for years because it made intuitive sense to think that it gives third parties and independents a chance. After all, it tallies in rounds, and in an early round, you get a chance to support, effectively, your favorite candidate, and if that effort fails, you get a say in the final round as between the bad and the worse. It's very strongly intuitively attractive. It took discussion and argument and deeper study to see that my intuition was simply not correct. Intuition in general is not guaranteed to amount to a correct understanding of the facts in all cases, and neither is "common sense." Sometimes I think common sense is correct 80% of the time, and sometimes I think it is so only 20% of the time. Intuition and common sense are heuristics, mental shortcuts, useful for making emergency decisions when we do not have time for study in depth.

Recognizing that there are reasons for seeking deeper and more nearly rigorous understanding, I nevertheless encounter an effective obstacle in that I am neither practiced nor talented in math. I think for people who are, their intuition more closely matches the reality, quite as how people who are good at chess can assess a position. If my level of familiarity with math matched that of Turing, and Euler, and Ramanujan, and von Neumann and the uncredited females he stole ideas from, and Curry, and Amy Noether, I could probably work this out by myself. But I'm not at that level, and so tend to ask for help.

When you or I or any of the readers asserts that a single-winner voting system gives equal power to the voters, one voter to another, the correctness or incorrectness of that assertion turns on the matter of who is selected as the winner by that system.

Suppose groups of us are engaged in a literal tug of war. But rather than a single rope, there is a hub device and several ropes attached to it, leading to the groups of people who are going to pull on it. The hub device and the ropes are free to move over the ground. A circle is drawn in the grass, and the hub device placed at the center of that. Every group picks up their respective rope and pulls on it. The hub device will stay in the center if our forces balance to zero. Otherwise, it will be pulled toward some point on the circle. If our forces, person for person, are equal, surely only one outcome is possible. How can a contest go two different ways without changing the relative power of the participants? This point still confuses me.

At this point, I do not have a complete mathematical definition of voting equality. The closest thing I have to it is a pair of conditions that I argue are necessary. I give provisional credence to the idea that these conditions may also be sufficient, simply for lack, for now, of clear evidence to the contrary.

First condition: Frohnmayer balance. If one voter can move the needle, another voter must be able to move it back.
Second condition: best known freedom of expression. The best known is that shared by Score/STAR/Approval. Counterexamples that still meet the first condition include Borda count (requiring ranking all candidates), "vote for and against", and "vote for or against."

Clearly, Score and STAR meet both of these conditions.

The first condition is directly related to the final result, as it is defined in terms thereof. Being able to move the needle is defined in terms of effect on the final result under certain conditions, which can happen.

The second condition is indirectly related to the final result. The argument goes that if a system balances the power of voters whose honest stances or even strategic stances match votes that the system allows them to cast, but if there are other voters whose stances do not have corresponding votes that the system allows them to cast, they are being cheated because they are being partially muzzled. Clearly a system that allows them votes corresponding to their stances, and takes those votes fully into account in the tally, is giving them more power than a system that gives them a Sophie's Choice of votes that do not so precisely correspond to their stances as to the possible stances of other voters.

But anyway I'm still left confused about whether equality implies a unique result. Intuitively, it should.

rob

Here is an example where STAR produces a different result than Score on a Nader scenario, assuming that:

Gore and Bush are the two front runners,
it is very close between Gore and Bush
most voters that like Nader best, prefer Gore over Bush.

These are pretty reasonable assumptions based on the 2000 election. (right?)

Nader voters who attempted to best express their preferences might vote Nader: 5, Gore: 3, Bush: 0. Under Score, lots of people voting this way, rather than giving Gore a 5, could cause Gore to lose. But giving Gore a 5 disallows that voter from expressing their preference for Nader over Gore.

In STAR, they could express that preference without handing the election to Bush (their least favorite), since Gore and Bush end up being the two front runners, and 3 vs 0 counts as much as 5 vs 0 in the second round. In fact, no matter which two are the front runners, they have expressed their vote in the most effective (i.e. strategic) way.

The big problem with Score in this sort of scenario is that it can help entrench the 2 party system, since a 3rd party candidate like Nader would be discouraged from running (unless he runs under one of the major parties), since he can hurt those that like him, by causing their least liked candidate to win. That is, he has still split the vote, albeit not as strongly as under FPTP.

So yes, you could get different results under Score vs. STAR in that scenario, especially if you assume that not all voters are 100% sure who the front runners will be. (i.e. the more likely people are to wrongly guess that Nader might be a front runner, the more likely it would be for them to rate Gore lower than Nader)

In a 3 person race, I think STAR does really well. I have my doubts when it gets to be more than 3, which is why I'd prefer a method that selected the Condorcet candidate if one exists, and only hold that second round if there is no Condorcet winner.

Jack Waugh

@rob said in STAR vs. Score:

Nader voters who attempted to best express their preferences might vote Nader: 5, Gore: 3, Bush: 0.

But I'm pretty sure that's not the optimal strategy for Score. I think that many of them should vote Gore 5, and a few should vote Gore 4. They don't have to coordinate, to achieve that kind of a mix. If each individual dithers mentally between 5 and 4, the result can be random, so with everyone's random behavior, relative frequency follows probability.

Jack Waugh

As @Sass has pointed out to me, in some States of the US (I don't know about the provinces in other countries), there is a legal reason to promote STAR rather than Score. Those States have a (constitutional?) requirement that elections be decided by majority. STAR (like IRV) manufactures a fake "majority", which may pass muster in the courts, where Score would not.

rob

@Jack-Waugh said in STAR vs. Score:

But I'm pretty sure that's not the optimal strategy for Score. I think that many of them should vote Gore 5, and a few should vote Gore 4. They don't have to coordinate, to achieve that kind of a mix. If each individual dithers mentally between 5 and 4, the result can be random, so with everyone's random behavior, relative frequency follows probability.

So, even if they strongly prefer Nader to Gore, they should strategically say otherwise on their ballots, because they suspect only Bush and Gore will be front runners?

I don't see that as a positive. Score supposedly encourages voters to express their true preferences. If doing so is not good strategy, that is a failure, in my opinion. This is exactly why STAR does what it does.

What you are actually suggesting is that people vote in Score as if it is FPTP... attempt to guess who will be the front runners, and give your full vote power to your favorite of the two of them. Yuk.

Voting the way you suggest is strategic relies on voters knowing who is likely to be a front runner. This is unlikely to be true in many local elections, and even unlikely to be true in presidential elections once we have system in place that doesn't favor a two party system so strongly.

@Jack-Waugh said in STAR vs. Score:

STAR (like IRV) manufactures a fake "majority", which may pass muster in the courts, where Score would not.

Calling this a fake majority seems to miss the point of the final step of STAR. STAR isn't just to pass legal muster, it is because systems that expect voters to be strategic have all kinds of issues such as forcing a two party system.

Jack Waugh

@rob said in STAR vs. Score:

I don't see that as a positive.

The question here was of whether the systems would give different results when voters use the strategy that applies to the system they are faced with. Assuming the voters vote the same way in both systems does not necessarily provide the answer.

rob

@Jack-Waugh We can't know what strategy voters Score voters will use. Meanwhile STAR reduces (but doesn't entirely eliminate) the incentive to be strategic.

I assume you think that a strategic vote under Score will be based on the voter knowing who the front runners are. But unless you know 100% how others are going to vote, that's a bit tricky to know, isn't it? Especially if you are assuming that those other voters are using the same strategy, which means they need to know how you are going to vote. And those are obviously dependent on one another.

So the best you can get is a Nash equilibrium. It's possible that there will be multiple equilibria, which I would expect in the case of a Condorcet cycle.

Which basically means your question is unanswerable. Because Score (as you seem to acknowledge) demands strategy, it is intrinsically unpredictable. You don't just need to know what voters' preferences are, you need to know what their strategy is, and how much they know about others' preferences... and then add a bit of "hall of mirrors" style infinite recursion into the mix for good measure. (you can see my simulator of this recursive equilibrium seeking behavior at https://pianop.ly/voteSim/voteSim.html or a video -- of an earlier version that didn't yet have Score voting -- at https://www.youtube.com/watch?v=NiS2A0QLeJU )

Many of us think that you should be able to vote without concern for who the front runners are. We don't want to worry that inaccurate polling could easily throw the election. We don't want a tight three way race to turn into a game of chicken. We don't want voting methods to work significantly differently in elections for which there is (or isn't) a lot of media attention.

You say in another thread that anything that deviates from "one person one vote" is anti-democratic, and I would argue that you are violating that principle if you are giving extra voting power to those who are better able to guess how others will vote.

In any case, I'll just say this. If you are trying to sell Score to the public, while acknowledging that voters are expected to vote dishonestly (or insincerely, or strategically, or whatever you want to call it).... good luck. I can pretty much guarantee you that a system that allows such fine-grained expressiveness, but then strongly incentivizes voters to use that expressiveness to say something that misrepresents how they really feel, is not going to fly. There are a lot of people (including myself) for whom that just feels dirty.

Jack Waugh

@rob said in STAR vs. Score:

Many of us think that you should be able to vote without concern for who the front runners are.

Many of us would like FTL space ships, too, but Prof. Einstein put the kibosh on that. And in voting-systems theory, our Einstein is Gibbard.

rob

This post is deleted!

rob

@Jack-Waugh It saddens me to see you taking that approach. Your argument boils down to this: “since perfection is impossible, we should just accept poor quality.”

It is most certainly possible to dramatically reduce the incentive to be strategic, compared to Score. By “being strategic” I mean, attempting to estimate how others will vote, and then, based on that information, adjusting your own vote to increase its power.

You have said you think that an advantage of Score is its simplicity. You also say that you expect voters under Score to be strategic in how they vote. That's not simple. Or maybe I should say, it is simple for the method (all it has to do is count!), but complicated for the voters.

So let’s be clear: you are advocating for a method that gives some people significantly more voting power than others.

Jack Waugh

@rob Americans seem to have mastered strategy for FPtP pretty well.

rob

@jack-waugh said in STAR vs. Score:

Americans seem to have mastered strategy for FPtP pretty well.

I don't see that as a positive.

I also see the latest strategy involves accusing the other side of cheating when things don't go their way. Another strategy once used was when the election goes the way they didn't like, a whole bunch of states seceded from the union.

So I'm not sure why you are comparing to FPtP. It is a bad system that polarizes and doesn't pick anything resembling a consensus candidate.

Score may or may not have similar issues. But it certainly won't always pick the Condorcet candidate if one exists, and I see that as a big problem.

The bigger issue, assuming you are interested in actually seeing any of this stuff in action as opposed to seeing another 20 years of debating and nitpicking, is that Score has been around a long time and made no progress. While the things that bother me about it may not bother you, they clearly bother other people.

Jack Waugh

@rob said in STAR vs. Score:

@jack-waugh said in STAR vs. Score:

Americans seem to have mastered strategy for FPtP pretty well.

I don't see that as a positive.

No doubt you have had more important things to do in your life than to remember where this discussion was. I wasn't arguing that any effect of the use of FPtP was a "positive." I was arguing that mastery of its strategy is evidence that voters eventually catch on to the strategy that works for a given voting system.

Score may or may not have similar issues. But it certainly won't always pick the Condorcet candidate if one exists, and I see that as a big problem.

Then demonstrate the problem. Show a case where STAR does better.

The bigger issue, assuming you are interested in actually seeing any of this stuff in action as opposed to seeing another 20 years of debating and nitpicking, is that Score has been around a long time and made no progress. While the things that bother me about it may not bother you, they clearly bother other people.

This is not a debate about what to try to market. It is a debate about whether a complex system works better than a simpler one. How can any of us think clearly about comparing these systems if we don't address even the simplest questions related to them?

rob

@jack-waugh said in STAR vs. Score:

I was arguing that mastery of its strategy is evidence that voters eventually catch on to the strategy that works for a given voting system.

And... I don't see the need to master strategy as a good thing. Especially for a new system. The method should do the work for the voters, and shouldn't give an advantage to those who are best at guessing who front runners will be.

My point is, yes I am aware that is how it works under FPtP. It's one of many reasons I think that system is awful.

Jack Waugh

"I don't see the need to master strategy as a good thing. Especially for a new system. The method should do the work for the voters, and shouldn't give an advantage to those who are best at guessing who front runners will be."

This is not a choice we have. Allow me to introduce you to the Gibbard Theorem.

"My point is, yes I am aware that is how it works under FPtP. It's one of many reasons I think that system is awful."

I agree. The problem with FPtP as compared to alternatives is not that it encourages strategy, and that they don't. The problem is what global consequences result from the strategy it encourages.

Dear, beloved comrade, I'm asking you to stop beating around the bush and if you know of a case where STAR outperforms plain Score, exhibit such a case.

rob

Edit: I just noticed this is a reply to something from 24 days ago. Weird. Anyway, in case you still think this...

I'm well aware of the Gibbard Theorem. Did Gibbard also provide the profound insight that even if you wear a seatbelt, you can die in a car crash?

Just because perfection isn't attainable doesn't mean everything is equal. Some systems are highly resistant to strategic voting, some far less so. I believe any Condorcet method would result in the vast majority of voters putting no effort into strategically altering their vote from what it would be if they were simply trying to honestly express their preferences. And for those few who do try to be strategic, the vast majority of them would not gain any benefit from doing so.

Also, and probably more importantly, under such a system parties would have little incentive to strategically nominate, by reducing the number of candidates from their party to one.

beating around the bush and if you know of a case where STAR outperforms plain Score, exhibit such a case

I've given one, please stop saying I haven't. Nader vs Bush vs Gore is an obvious one. I feel like I already explained it pretty well, but in case you didn't get it, I'll have another go.

Under Score, Nader being on the ballot would have caused many "N>G>B voters" to lower their score for Gore, so they could express that they prefer Nader to Gore. In other words, he'd be a spoiler just as he was under FPTP. (this would further mean that candidates like Nader would have felt pressure to do like all the others on the left did, which is run as a Democrat. Same would apply to right-leaning candidates. Which would leave the two party system entrenched)

Under STAR, all people whose preferences were N>G>B would be able to a) express that they like Nader more than Gore, in case Nader became a front-runner against Gore, and b) give 100% of their voting power to Gore, if Gore and Bush were front runners.

The problem with Score would be an even bigger problem in elections where the three front runners were closer (e.g., where lots of people thought Nader could actually win), or in elections where voters were less informed as to the likely outcome, such as local elections.

In the case of Perot - Bush Sr - Clinton, STAR would likely have allowed Perot to win, I suspect it would have been a much tighter 3-way race. People such as myself would have given Perot a 5, Clinton a 2, and Bush a 0. A lot of other people would have given Perot a 5, Bush a 2, and Clinton a 0. (note that Perot was a true centrist, in that he was almost equal in his appeal to Republicans and Democrats) Under Score, voters would have probably been foolish to not give one o the major party candidates a 5, since they'd be scared that Bush and Clinton would be front runners and they'd be wasting voting power. (as happened with FPTP)

In both of those races, under STAR, there would be very little incentive to vote with anything other than honest preferences. They would not have to worry about which two of the three would be front runners, since they'd be able to give the full power of their vote to their preferred of the front runners. Not under Score.

(all that said, I think STAR doesn't do so well if there are more than 3 viable candidates, which is why I prefer Condorcet.... but still, STAR is dramatically better than Score at reducing strategic incentives)

Jack Waugh

@rob said in STAR vs. Score:

Some systems are highly resistant to strategic voting, some far less so.

I suspect that voting strategy has not only a magnitude but also a direction. The measure, however you take it, of how "highly resistant" a system is to it would only reflect the magnitude, I suppose. That would leave the possibility that system A is more highly resistant, but the strategy it does allow pits individual interests against collective interests (like the Prisoner's Dilemma), but that another system B is less resistant, so allows strategy of greater magnitude, but the direction of the strategy would align the same way with individual interests as with collective interests. It is when those directions are not aligned that the harm happens.

As for your three-candidate scenarios, yeah, intuition says I could probably come up with an example illustrating your point, given the difference in number of rounds of tallying. But systems that lead people to think (correctly or not) that strategy in nomination is no longer helpful to their cause, will likely lead to races having more than three candidates.

rob

@jack-waugh said in STAR vs. Score:

But systems that lead people to think (correctly or not) that strategy in nomination is no longer helpful to their cause, will likely lead to races having more than three candidates.

You are right that STAR isn't as good with more than three candidates.

What it comes down to, from my perspective, is that to reduce the incentive to strategically exaggerate (*), you need to minimize any reliance on "strength of preference."

STAR does this by doing a pairwise comparison as the last step. A pairwise comparison by its nature doesn't consider strength of preference (as you can see when it is a 2-candidate race in simple FPtP).

Condorcet methods try to do it all with pairwise comparisons. This reduces incentive to exaggerate even further. But since we can't guarantee there will be a Condorcet winner, we'll never get it to zero.

However, my position all along has been that getting it all the way to zero would be nice, but isn't necessary. If you get it close enough to zero, attempts to be strategic will have just as much chance of backfiring as they have of helping. A Condorcet method, including one with a very simple "tie breaking" formula, is good enough. STAR may or may not be good enough. Score is not good enough. Again, this is my opinion, but I it does come from a pretty solid game theoretical foundation.

* technically, incentive to exaggerate isn't the only thing we are trying to reduce. We also want to reduce vote splitting, which creates the incentive to strategically nominate, which in turn causes partisanship and polarization. Finally, we also want to aspire to "one person one vote", so each person has equal voting power. All of these things are accomplished by reducing the consideration of "strength of preference" in the tabulation.