Variety of Voting Systems

Hi, I am new to this forum, but I’ve been sort of obsessing about alternative voting systems for the past few months and I’d like to know what others think about my ideas. I think we can all agree that FPTP and instant-runoff are poor systems that should be replaced with higher quality alternatives. I mean, this is ridiculous:


As far as I can tell there are around six feasible high-quality alternative voting systems, which include some ranked choice systems, some range systems, and some hybrids. The single winner systems I am more or less narrowed down to, in rough order of my own preferences, are:

  1. Score voting
  2. Approval voting
  3. STAR voting
  4. 3-2-1 voting
  5. Ranked Pairs voting
  6. Schulze voting

Basically I think that all of these systems have pros and cons that make them fairly difficult to compare with each other. I guess I also feel like it might be a positive thing to have a variety of different voting systems implemented in different states, and that organizations that are promoting alternative systems could band together to push an agenda of diversification among high quality systems rather than promoting a single type of system above all the others. I think that not only would it make people feel less like they may be choosing the “wrong” alternative, but would also open up a floodgate to in vivo studies of these systems, which could in turn lead to compounded improvements in the quality of our representation (at least on a federal level). Do you think that’s a reasonable assessment?

On that subject, there are 26 states that have either initiative or veto referendum power and that hence might be able to push for alternative voting systems against the resistance from state legislators and courts. Maine succeeded in making a change, but only with the tokenism of instant-runoff, and even then it was against significant push-back. I think it would be great if these six systems (or maybe some other group of high quality alternatives) could be organically and equitably distributed among some modest proportion of those states so that we could get a better idea about how these systems perform on the large scale. Anyway, that’s all, just a topic for discussion.


If complexity isn’t a problem (Ranked Pairs is very complex to write but you have included it), I recommend that you also consider:

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Yes, when I was naively trying to think up my own system, something like Distributed Voting seemed natural. I don’t know much about its performance or much about the abstract analysis of it, but it seemed to me like it might have some problems with tactical or accidental “exaggerations.” I could well be wrong, but that’s part of the reason I am on the fence between score and approval voting, I think it would be great if people could honestly indicate their relative preferences, but I don’t know if it’s feasible.

I was trying to develop a system similar to Distributed Voting where voters would have more incentive to indicate their true preferences, but it had a lot of messy unintended flaws.

I’ll look into those systems more regardless, thank you!

I think it would be great if people could honestly indicate their relative preferences, but I don’t know if it’s feasible.

DV treats the problem in this way:

  1. If you give all the points to one candidate and the one loses, the vote becomes null. This pushes to give some points also to the other candidates.
  2. If you distribute the points equally among several candidates, you increase the average probability that one of them will win, but you don’t necessarily like them all in the same way.

Honest vote [10,8,6,4,2,0]
Tactic 1) [10,0,0,0,0,0]
Tactic 2) [10,10,10,0,0,0]
Average tactic: [10,9,5,2,1,0]

Welcome to the forum!

True, but that is what this forum is for. There are lots of criteria.

For myself personally, I prefer methods that do not give a strong advantage to those who closely watch the polls and strategically adjust their vote. STAR isn’t perfect, but I think it is one of the better ones for avoiding this. Approval and Score both give strong strategic benefits to those who consider who is likely to be a front runner and vote accordingly. (various Condorcet methods seem to avoid this but they seem extremely unlikely to be adopted in real government elections)

I think “give each candidate from zero to 5 stars” is probably the best user interface for a ballot. Ranking is too much work, approving feels awkward to me because I don’t think in binary. Again, this is just my own preference.

It would be great… but of course, the challenge is that there are a lot of vested interests involved. People aren’t all just going to agree to switch to a new system if they feel like it would in any way disadvantage “their side.” And no one wants to be a guinea pig. They want a system they trust.

So… again, a good topic for this forum: how to get people to adopt such systems. One option is to encourage people to use them for non-goivernment elections, on the web.


That does make sense. The only issue I have with it is that it seems to introduce a degree of arbitrariness that is too similar to non-determinism for my liking, i.e. the process could in some cases be bordering on chaotic. Probably that is almost never an issue though. At the same time, proportional re-distribution while natural seems somewhat arbitrary as well, i.e. it doesn’t take into account the voters’ actual marginal utilities of votes for each candidate when redistributing voting capital. The criticism about arbitrariness can also be made of score voting. I’ll have to think about that system more.

Hopefully this isn’t a rant, I was also trying to develop a system where voters directly indicate their marginal utility functions by writing down a string of candidate symbols rather than just distributing voting points en masse, and then voters lose voting capital as the election procedure goes on. For example, say you allow voters 12 characters. Then rather than saying, candidate A gets 8 points and candidate B gets 4 points, a voter could indicate the string


As candidates are protected from elimination, voters lose symbols in proportion to their investment in that candidate, starting from the right end of the string. There’s kind of a discrete-continuous problem here, but you could for example keep track of spill-overs. And when a candidate is eliminated, you could simply delete all instances of that character in the string and push all remaining characters to the left. For example, take a simple election between two voters, who submit the strings as follows:


Then candidate A has the most characters present, so is protected from elimination in the first round. Voter 1 invested 7/11 of those characters, and the average number of characters for the remaining candidates is (7+4)/2=5.5, so Voter 1 pays 5.5*(7/11)=3.5 characters and Voter 2 pays 5.5*(4/11)=2 characters. Say the bold characters are ignored, so then the votes are updated as

Voter 1: AAAABBBAAAB (-0.5)

Next, C is protected, since it is the highest grossing vulnerable candidate, and hence Voter 2 has to pay 3 points for the remaining B characters:

Voter 1: AAAABBBAAAB (-0.5)

Now B is eliminated (replaced with dummy character X) and all candidates are made vulnerable again:

Voter 1: AAAAXXXAAAX (-0.5)

The remaining characters slide to the left:

Voter 1: AAAAAAAXXXX (-0.5)

Clearly A will win the election, which makes sense. I think this procedure gives voters direct incentives to indicate their true preferences and their true marginal utility functions, since as they lose characters from the right, they will want to submit a string that distributes their votes as accurately as possible no matter how many remaining characters they have. I’m not sure how it performs in general though. Again, just food for though.

I totally get that. It’s just that people are paying outrageous costs for inaction, since the longer they choose to postpone switching to a new system, the longer they will have to put up with pluralism. Definitely the political status quo is a huge problem since the political elites don’t want to relinquish any power, that’s why I think it will have to be a people’s movement.

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Preachin’ to the choir! :slight_smile:

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Lol very good. I agree that encouraging the use of alternatives on a smaller scale is important. But I also think that it would be great if the organizations like FairVote (I’m not sure why they promote instant-runoff instead of ranked pairs??? Do you know what the deal is?), the Center for Range Voting, and the Center for Election Science all came to an agreement that the costs are too high to wait for a consensus about what the supreme voting system is, and experimentation is our best option for the future. Especially because almost any option is superior to FPTP, and we have an array of far better options that people seem to have been unable to agree on for a long time. It’s like a trolley problem but there’s a third track, you’re on it, and the trolley is headed your way lol.

At the same time, I’m almost certain that changing the current voting system now will only make it even easier to change it again in the future.

They are sort of locked in for a number of political reasons and do not play well with the other groups.

As for the other groups:

  • the Center for Election Science likes Approval
  • the Center for Range Voting like Score
  • The equal vote coalition is pretty neutral but have closest ties to to STAR advocacy.

I would think that any of these three groups would support an initiative of the other three. You have seen this with the Approval campaigns like Fargo and the STAR campaigns in Oregon and California.

FairVote is sort of the odd one out but they have more money and resources so they can afford to be.

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I see, I figured as much about FairVote. Who funds them is a good question, there is relatively way too much media coverage of instant-runoff and it’s a distraction from the more reasonable discussion. That definitely is good news if true that the other organizations are mutually supportive, I’ll have to find resources about them conferring with each other. Any one of the options they promote seems miles ahead of what we have in place now.

Well this is a CES forum with myself and @Sara_Wolf (both directors for Equal Vote) being very active on it. The center for range voting is basically just Warren Smith. He is a CES founder but is not active much anymore. It is a small community. If you hang around for any length of time you will see the same names repeatedly. Mostly what you find is that people are pretty happy with Cardinal systems and would just take any of them. There are a few advocates for condorcet systems or sequential elimination systems but that depends on if you think Monotonicity is a deal breaker.

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I agree on this, but I’m not sure you’ll get wide agreement. I am personally thrilled to see the progress Maine is making. Others might think that failures of ranked choice might discourage people from changing from the status quo at all. (I’ve heard that regarding ranked choice in Burlington Vt, where it supposedly failed to produce the “correct” result in an election, and was repealed)

Let’s hope Oregon makes progress in getting STAR in real elections, then we’ll start to have data on all three.


The front page of Equal Vote’s site includes quotes such as

We propose a new voting system, developed in 2014 by some of the nation’s top voting reform experts. Instead of limiting the voter to supporting just one candidate, STAR Voting allows voters to rate all the candidates similar to how we rate books on Amazon, restaurants on Yelp and songs on iTunes.


The Equal Vote Coalition is the driving force behind STAR Voting, an innovative voting method for more fair and representative elections.

so I’d say they’re no more neutral than organizations like C4ES.

Equal Vote and their officers seem to go out of their way to avoid saying negative things about Approval or even IRV.

CES isn’t quite as good about this. Although they have modified this document a bit after some complaints, still:

And of course FairVote is much worse.

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In the Yee diagrams it is seen that the DV has very little chaos, which does not increase with the increase of the candidates (which instead happens with the IRV). It’s also true, however, that in the Yee diagrams totally honest votes are considered therefore it’s necessary to make other evaluations.

it doesn’t take into account the voters’ actual marginal utilities of votes for each candidate when redistributing voting capital.

I think that voters, once they understand the normalization used, tend to adapt to it. In any case, as you also imply, any voting method introduces arbitrariness in its own way.
In other contexts I pointed out that the SV is equivalent to an instant-runoff method where the candidate with the lowest sum is eliminated, without redistributing the points (never redistributing the points, it’s an arbitrary and, in my opinion, unrealistic method).

I think your system has the best representation of interests ever; if I’m not mistaken I have heard about it in the context of websites, for example:
music streaming site that tracks songs listened by a user. The sequence of songs that he listens can be represented in the way you indicate, and then algorithms are applied to that sequence to understand which new song to suggest to him.
It would be nice to have a similar sequence in the voting too but it seems too complicated for a voter to write, and then I don’t even know if the interests towards the candidates can really be represented in that way.
I believe that the range is the method that best meets the simplicity of writing, and the effectiveness in representing interests, so I focused on that.
Anyway, congratulations on the idea; if you find an easy way to represent that sequence, I could also support it.

At first glance, I would say that a voter could tend to vote like this:

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If DV is not chaotic I can definitely get behind it! Also, I guess there is a “limiting case” argument for proportional redistribution. For example, using the string voting as a crude model (supposing it is a reasonable representation of interests) you could assume that as the allowed number of characters gets arbitrarily large, voters will tend to approach a stable distribution among the candidates, i.e. far out in the string, the probability that a random character represents a particular candidate should depend only on the candidate. I think that’s a reasonable assumption, and in that case the long string method will, at first, conform to a discrete analogue of proportional redistribution in terms of costs to voters. And if the marginal costs are distributed more-or-less proportionally, then so should be any marginal gains.

I agree that the string method is more theoretical than practical. It allows voters to control their marginal utility functions for a small number of discrete votes, but for proper redistribution you would want to be able to analyze the marginal utility functions for an arbitrarily large number of discrete votes. Pushing the characters to the left achieves some level of redistribution, but the problem is illustrated in the example I gave, where Voter 1 at some point in the algorithm ends up with a string like AAAAAAAXXXX, and hence one of their available votes isn’t counted at all. If they had submitted a longer string, basically “loading up” the marginal utility function beyond the characters that are counted in the algorithm, they would have a better chance at having their votes fully redistributed according to their marginal utility.

So I was thinking, maybe the theoretical voters could submit significantly longer strings, and then have the algorithm only look at the beginning portions, and allow the characters beyond that to slide into place when candidates are eliminated. But I think that opens the floodgate to tactical voting of the kind you suggested. When the strings are totally truncated, I’m not sure that tactical voting in that sense would actually be a good idea, because the tactical voter runs the risk of their alternative choices being eliminated early, and then having no fall-back if their first choice gets eliminated. So it’s risky. Basically I think honest voters would have more consistent control over the entire election, while tactical voters would have disproportionate control over the beginning stages, but then their influence would die out quickly.

The other method similar to DV I was thinking of is analogous to the string method, where voters incur costs in voting capital proportional to their investments in protected candidates. So again, rather than eliminated the least-grossing candidate, candidates are protected in turn, costs are incurred for protection, and then the final remaining vulnerable candidate is eliminated and remaining capital is redistributed. I think that would tamp down on strategic voting, but again I am not sure how it fairs in practice, and I know that there are problems with it. For example, if you have two voters with distributions

Voter 1: [1,0,0,0,0]
Voter 2: [0,1/4,1/4,1/4,1/4]

I think we can agree that the most rational approach to deciding a victor is to uniform-randomly select one of the four candidates that Voter 2 supports, and then select uniform-randomly between that candidate and the candidate that Voter 1 supports. But with incurred costs and redistributions, I think Voter 1 comes out on top, basically because Voter 1 incurs costs to protect his candidate once at the beginning of the first round, but then Voter 2 incurs costs three times for the remainder of the round before one of their candidates is eliminated and the points are redistributed. So vote-splitting exists. I don’t know how it works with many voters though. Vote splitting is avoided in DV because there are no incurred costs, but then there is the (minor?) risk of tactical voting.

If tactical voting is a very minor problem in DV, I think it turns out to be superior to a protection-cost/redistribution system. But if there were a way to incur costs without vote splitting, I think that would be a great theoretical development. I was having costs incurred basically like an auction against the average of the remaining candidates, but there might be a better way. For example, maybe voters pay the cost of the difference between the highest-grossing candidate and the second-highest, so it’s kind of a grass-trimming situation. I don’t know, just spit-balling here.

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When the strings are totally truncated, I’m not sure that tactical voting in that sense would actually be a good idea

Yes, truncation should avoid those tactical votes.

Vote splitting is avoided in DV because there are no incurred costs, but then there is the (minor?) Risk of tactical voting.

In practice I don’t know, because I have yet to test it, but I have already created a site that allows you to create polls with DV (maybe you want to try it):

Regarding the “chaos”, DV for single winner is a subcategory of the IRNR method, and at this site you can compare IRV with IRNR to see the difference (select the 2 voting systems at the top right):
I also did tests on the actual DV and the results were like that.

Are you familiar with Yee Diagrams? Basically, each pixel represents an election where the average voter is located at that pixel, and voters prefer closer candidates. The voters’ X & Y coordinates are normally distributed, with sigma=75 in my code for each axis. The pixel is given the color of the winning candidate (the candidates are drawn on the diagram after the simulations; they’re the circles.) Ideally, each pixel should be the color of the nearest candidate. Here’s one I made for distributed voting.

Areas that appear “blurry” with many differently colored pixels near each other are ones where there is a lot of chaos, since it means that the winner is unclear and changes from simulation to simulation.

Here’s a picture indicating the win probability of the blue candidate (5 trials per pixel; white indicates that blue won all 5 trials; black indicates that blue lost all 5.) Gray areas are high chaos, and white areas are low chaos. Black areas may be high or low chaos.


For comparison, here’s a Yee Picture for score voting

For thoroughness, here’s the probability picture for score voting


If you are making such diagrams can you do STAR voting and STLR voting?

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