Legislators are offering up a bill to use approval voting state-wide. Approval voting allows voters to vote just like plurality in a single-winner election, but voters are open to marking more than one candidate.

Approval voting is one of very few single-winner systems (plurality and IRV are not of them) that always allow voters to mark their honest favorite. It is immune to vote splitting. This allows candidates to earn a more accurate level of support. Approval voting may offer a real challenge to the two-party system when voters start telling politicians whom they really approve of.

Description of the bill and Approval Voting is here: http://www.electology.org/hb-240

I'm not sure what the implications of this are; this may be entirely stupid. But sometimes novel stupid is still interesting!

Here's the idea: the votes are cast just like in approval voting. But the counting is different. I'll use this example: candidates A, B, and C are running. The votes are (A: 36, AB: 30, BC: 15, C: 19), giving totals (A: 66, B: 45, C: 34). So under approval voting, A wins. But not under my system. Here's how it works.

The total number of votes for each candidate is converted to a normalized vector, representing the ideal candidate. So the ideal candidate would be 45.5% like A, 31% like B, and 23% like C.

Now, each possible pairing of candidates is evaluated to see how similar they are. This is done by seeing what percentage of voters marked them the same (either both yes or both no). If you normalize that vector, you get the percentage of each candidate that is "like" each other candidate. So candidate A is (A: 67.1%, B: 32.9%, C: 0%), B is (A: 24.5%, B: 50%, C: 25.5%) and C is (A: 0%, B: 33.8%, C: 66.2%).

Now, subtract each result vector from our ideal candidate vector, and sum the magnitudes. That tells you how different each candidate is from the ideal. A: 46.9%, B: 42%, C: 91%. So B wins, because the voters thought he was most similar to the averaged, ideal candidate of the whole group.

In essence, what's happening is that the voters for AB are declaring that A and B are similar, and the voters for BC are declaring that B and C are similar, so each vote for A-only or C-only ends up contributing a little towards B anyway.

In our example, this can be translated to equivalent vote totals of (A: 74, B: 77, C: 49). Another way of looking at that is that the system saw the 55 A-only and C-only votes, and created 55 additional votes, distributed among the candidates in a convoluted way.

This means that the system is arguably more representative of the electorate as a whole, because it makes the assumption that the preferences of multi-candidate voters say something meaningful about the hidden preferences of single-candidate voters. This approach should be extensible to other systems like ranked-choice and range.

My interest is mainly on the theoretical aspects of whether reforms can even take place here in the US - they seem simply too great, and the powers that fight against them have very, very strong kung fu. It would be great if #OWS spurred reform, but I'm not counting on it, at least by itself.

Your thoughts, fellow redditors?

I have just created this collaborative map of open-source projects & resources around preferential voting. Including software, votes services, formats, and other tools / datas.

https://github.com/CondorcetVote/Condorcet-Voting-Open-Source-Ecosystem-Map

This is still incomplete, pull requests are welcome to improve it. Projects must be free (open-source), serious, not too specific to one case (custom test, specific research), and maintained.

If you don't know how to use Github, you can also contribute here.

I have a small group of people trying to elect a single “thing”. Just curious to see if anything is better than a majority vote. And then reading more about why it could be better.

I've been trying to evaluate the claim by Ranged Voting advocates such as Warren Smith that Arrow's Theorem does not apply to the Ranged Voting method. After much thought and consternation, I've finally come to agree with this argument.

The problem I had in evaluating this claim is that most formulations of Arrow's Theorem aren't precise enough. For example, after reading John Geanakoplos' Three Brief Proofs of Arrow's Theorem I was left with the interpretation that Arrow's Theorem did apply to ranged voting, but violated Independence of Irrelevant Alternatives in a rather weak and mostly irrelevant way. **

What I found extremely helpful was Freek Wiedijk's Formalizing Arrow's Theorem, which presents a fully formal, computer-checked proof based on Geanakoplos' paper, produced using the Mizar proof assistant. The proof itself wasn't as useful to me as the formal statement of Arrow's Theorem and IIA.

In Freek Wiedijk's statement of Arrow's Theorem, IIA is given a formal definition that is much more intuitive and natural than my interpretation of the informal definition given in John Geanakoplos' paper. Ranged Voting certainly satisfies this definition of IIA, as well as Pareto-optimality and non-Dictatorship. However, the formal statement lays the resolution of this apparent contradiction bare. The key is the following line on page 199:

reserve f for Function of Funcs(N, LinPreorders A), LinPreordersA;

This means that this statement of Arrow's Theorem only applies to voting systems that consider only the rank of voter's choices. (allowing for ties). Because Ranged Voting takes more information into account, it's possible to modify the results of an ranged election without modifying the relative rankings of the options by each individual voter. For example, given three voters and three ranged ballots:

A: 10   B: 5   C: 0
A: 10   C: 5   B: 0
B: 10   C: 5   A: 0

A wins the election because A has the highest average score (20/3 versus 15/3 for B and 10/3 fo C). However, if the votes had been:

A: 10   B: 9   C: 0
A: 10   C: 5   B: 4
B: 10   C: 5   A: 0

Then B wins the election (23 / 3 for B, 20/3 for A, 10/3 for C) even though the preferential orders did not change. Thus Ranged voting cannot be a function from the voter's preferential orders to society's preferential order, because a function always produces the same output given the same input.

So, in short, Freek Wiedijk's formal proof of Arrow's Theorem supports Warren Smith's thesis that Arrow's Theorem does not apply to Ranged Voting.

** Ranged voting violates my interpretation of John Geanakoplos's definition of IIA because ranged voting accounts for the voters' degree of preference for one candidate over another, not only the direction of preference. This violation is the same basic idea above, dressed up a bit differently. However, I don't think this definition captures the intuitive notion of what IIA is.

Edit: It occurs to me that the my interpretation of Geanakoplos's IIA implies that the voting system uses a ballot that, in effect, only considers the rank. So while this formulation appears to be a stronger statement and applies to more voting systems, this appearance is deceiving.