Variety of Voting Systems

Yes the tactical aspect also seems difficult to model in Yee Diagrams, and on top of that generally I don’t believe they could be a suitable indicator of quality for anything but ranked choice systems, even without tactical voting.

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Equal Vote Coalition’s mission statement is not about STAR, it’s about maximizing the five pillars of a good voting method. Most cardinal methods, hybrid methods, and some Condorcet methods meet our basic criteria for being supportable. Equal Vote has been the spearhead for initiatives for Approval Voting (before STAR was invented) and STAR Voting to date.

Approval Voting is mathematically “Equal” and is very simple, but sacrifices honesty and expressiveness, so while we support it -we hope that advocates are successful- it’s not the end all for our mission.

Where we agree with CES is that in terms of advocacy it’s important to have a single answer to the question of what voting method should we adopt. In our case we recommend a single ballot type (0-5) with variations for single-winner, multi-winner, and proportional elections.

CES’s mission statement used to promote cardinal rated methods, but they have recently moved to supporting just Approval.

On stepping stones: My personal opinion is that most people are MUCH more comfortable comparing the current system with ONE alternative at a time. Others like to get into the weeds and learn everything they can to make an educated decision. For that reason I recommend a community led process with interested individuals over time to learn about voting methods and build consensus around a reform well before launching an initiative. Once the interested folks have done that work they are trained to advocate for the system they chose.

Adopting a “stepping stone reform” which is problematic -like IRV- or which is not the ultimate goal isn’t an effective tactic in my opinion and makes people less likely to consider the final proposal. I think this has already been well demonstrated with places that have adopted Top-2. I’m sure a great campaign could overcome, but it’d be harder and more confusing then starting with a clean slate.

One of the hardest questions we get in the field is “why is STAR better than IRV?” Answering requires explaining what’s wrong with IRV and also what’s great about STAR in one paragraph or less to people without the vocabulary or foundation to follow what you are saying. It’s confusing if rushed though, but people want it fast and they want to get all the details as well. Comparing STAR to the current system is a lot easier.


For Equal Vote we use Yee’s and other simulations to measure “Accuracy” but there are still 4 other key metrics.

  • Honesty (strategic incentives can be measured but even still that’s not a complete picture of honest v strategic voting)
  • Equality (Is every vote equally weighted and does the system have implicit bias?)
  • Simplicity (For voters, to tabulate, and to secure)
  • Expressiveness (Can voters express preference order? Degree of support?)

Yes Yee diagrams are supposed to measure accuracy, but I don’t think they are capable of even that much for any system that is not ranked choice. The reason is that the shape and size of chaotic regions in the Yee diagrams will be dependent on more than just the metric of the plane–for example, the utility of the voters, which may not be expressible for the entire electorate as a function of distance in the plane–so the visualization in turn can be very misleading. There is no way to standardize the diagrams.

That assumes that the voters are using a strategy based on a threshold.

Honesty is not a thing in voting. Voting is a struggle for power.

Approval is fully expressive, via probabilistic voting.

That is not necessarily true. Voting systems can be designed so that it is computationally infeasible to devise a strategic vote that yields non-negligibly higher utility for a voter than an honest indication of their preferences (obviously in the context of the syntax of the ballot format). In that case, strategizing becomes too expensive. It depends on what we consider “honesty” in the context of the ballot format, which is always a social construct, but most people I think can come to at least a partial agreement about what it would mean.

For example, using ranked choice voting, if a voter would honestly rank some candidates as A>B>C>D in terms of how happy they would be with each candidate winning the election, I think we can all agree that if the voter indicates A>C>D>B on their ballot, then they are being “dishonest” and perhaps strategizing. If we look at voting as a struggle for power, why not just have us wage war on each other? Rather than a power struggle, you could look at voting as a substitute for social conflict resolution.

Because in a war, we would have unequal power, one individual to another (who is a better shot, etc.), but with Approval Voting, we get equal power.

Plus, war produces casualties, over and above the disadvantage someone suffers from public policy that is not to their liking.

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Assuming that is possible, the resulting voting system would give a different result than Range Voting does, wouldn’t it?

Computational complexity theory makes it at least theoretically possible. In fact it has been proven that constructing various kinds of strategic ballots in Ranked Pairs voting is an NP-complete problem. Not that I am a pro-ranked choice guy. I would recommend the book “Economics and Computation.”

As for whether the results are different, they might be or they might not. It depends on too many other factors to say for sure.

I edited my question after you replied to the original version. Now it’s a different question.

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If the results are the same as those from Range, the extra complexity cannot be justified and we might as well use Range.

If the results differ from Range, someone was cheated out of part of their rightful political power, since Range gives everyone the same power, and only one outcome could reflect that.

I’m sorry I disagree. Many voting systems give every voter the same amount of potential influence over the election, but the outcomes are still variable depending on ballot format and the actual algorithm that it used to decide a winner. The result of the election is a compression of the political influence of each voter that depends on the voting system used, and different compression methods of the same data can yield different results.

I think it’s pretty straightforward to disprove that. Suppose voting system A accords the voters equal power and elects candidate ‘a’, but voting system B elects candidate ‘b’ instead. I am assuming the single-winner context here. Since system A by assumption accords the voters equal power, the choice of ‘a’ reflects that, and a choice of ‘b’ cheats some of the voters who preferred ‘a’ to ‘b’ out of some of their rightful power. Therefore, it is not possible that B accords the voters equal power.

Alright, but there is no way to determine which voting system is the standard against which to measure every other system. It’s arbitrary. You can find a paradigm through which whatever voting system you are considering is the standard, which again puts all of them on equal footing in that regard.

What better standard can be arrived at than a combination of (1) Frohnmayer balance, and (2) full cubic expression? By the latter, I mean that the voter can rate each candidate independently of how she rates the other candidates (and obviously the tally takes these into full account). The former is laid out at

I can see that Frohnmayer balance is a contested property. I don’t disagree that they are nice properties, but I still think they constitute an arbitrary standard. I’ll look into them more, but I think almost surely they both have pros and cons like every other property I’ve read about, and I’m sure there are very reasonable arguments both for and against them.

They would be different. If people are voting honestly in Score (a.k.a. Range), the differences might be subtle, but they are there. But we shouldn’t expect people to vote honestly in Score, since the system rewards people who exaggerate their preferences for those likely to be front runners.

I would not agree that Score gives everyone equal power, even if everyone is voting honestly. It gives voters on the extremes more power than moderates. If you give a candidate a 5, your vote has more “upward pull” than the vote of someone who gives the same candidate a 4.

I’ve tried to express this difference in a simplified scenario using my “voting for a number” example. (people can vote for a budget, by simply submitting their preferred numerical value) Score is like using average when voting for a number, better systems (such as Condorcet methods) are more like using median. When voting for a number, median does not give voters on the extremes more power than voters closer to center, while average does. (this does not mean I advocate using median when using human candidates, a la Majority Judgement)

I also demonstrated this difference here, with an example with human candidates. Score does not pick the Condorcet winner in this example, which means that people on the left have an incentive to exaggerate their preference for candidate D (who is likely to be a front runner, but is more centrist than other candidates).

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Thanks for your input. @waugh after reading about it more, I do think that Frohnmayer balance is a nice property, but it may not be as important as it seems. Perhaps it would be more important in games with perfect information, but in general–as far as I can tell–it’s more of a theoretical property than a practical one, which to me makes it relatively unimportant. I think the only real test that matters for a voting system is how it fairs repeatedly over time and over a stable electorate body, i.e. as voters/groups learn how to use or manipulate the system to their greatest advantage. In my opinion, abstract properties are usually secondary bonuses or else just a small part of a more wholistic evaluation.

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The thing I see beneficial about the Frohnmayer balance is that it minimizes the “Duverger’s Law effect” of vote splitting.

Compare plurality against “For and Against”, where you vote for one candidate and against one candidate. In plurality, parties try to eliminate similar candidates so they don’t split the vote. With For and Against, both the “for” votes and the “against” votes are split, so there is no real incentive to minimize similar candidates.

For and Against is far from perfect (it’s barely more expressive than plurality, especially if their are ots of candidates), but it does solve the worst (in my opinion) issue of plurality.

If you don’t like the way voting systems force us into two opposing parties, I’d say adopting such a balanced system is a plus.

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