## Thursday, March 1, 2012

### Voting Variants - Harmonic Range Voting

Although Ethosphere could implement many different voting procedures and allow a teamspace to choose from among them, there is a method which is a combination of IRV and RV that seems well-suited to the online venue. We will call the method Harmonic Range Voting (HRV). The word "harmonic" is borrowed from mathematics -- it is the name of the arithmetic series 1 + 1/2 + 1/3 + 1/4 +... whose connection with the algorithm will become apparent. First, let's see how the procedure works.

The HRV ballot closely resembles the IRV ballot. It is a list of candidates in rank order, with the first choice candidate at the top. The list is divided by a dotted line. Any candidates listed below the line are considered to be either not suitable or of unknown merit. Candidates above the line are all deemed suitable, and their position on the list reveals their relative desirability in the opinion of the voter. This sort of ballot ranking is easy to implement as a drag-and-drop interface, and it transitions nicely from single-choice to multi-choice elections, and more generally, handles additional alternate props well. For a single-choice election, a yea vote is equivalent to placing the prop above the line while a nay is like placing it below the line. New alternate props are initially placed below the line, allowing the voter to consider them and, if desired, drag them above the line into their proper ranking.

Although this is essentially a ranked voting method, like IRV, the method of calculating a winner is more like RV. We assign the first place candidate a score of 100. Second place votes are only 1/2 as potent as first place votes, so they are given a score of 50. Third place votes are 1/3 as potent as first place votes, they get a score of 33.333.., and so on. Thus the harmonic series. From a mathematical and theoretical point of view, this is just RV with discrete ranges based on rank. But it does eliminate, or at least reduce, two of the drawbacks of RV mentioned above. First, it is not necessary to choose a subjective merit score for candidates. You just need to decide which one you like best, which one second best, etc. Also, the paradox of electing a candidate that receives no first place votes is avoided, even in degenerate cases like the one outlined in the previous post. The harmonic series ensures no candidate can win unless it has at least a few (>2) first place votes. Similarly, no candidate can be elected strictly on the basis of third place votes unless there are at least a few first or second place votes for that candidate.

### Protection of Minorities

The goal of Ethosphere is to encourage larger, more vibrant teamspaces over smaller, fragmented, stagnant ones. An effective, but undesirable, way to reach consensus is to eject all members who don't agree with the majority, or make them unhappy enough so they leave on their own, perhaps to start smaller, more cohesive teamspaces. Such balkanization of teamspaces works against the overall utility of the Ethosphere and, in the limit, results in single-member teamspaces that are pointless and completely without influence. Therefore, we wish to select voting and consensus mechanisms that do not needlessly alienate the losing supporters of a contentious vote or series of votes. Rather, we want the procedure itself to help lead the team toward a kernel of consensus that maximizes the "happiness" of all the members while still allowing props that have significant majority support to be ratified.

The HRV procedure is one way in which this may be accomplished. By blending together IRV, which favors extremist candidates, and RV, which strongly favors centrist props, we have a voting algorithm that admits compromise solutions, but only when they are needed, like when the leading choices are strongly polarized and balanced.

#### 1 comment:

1. What you describe sounds like a weighted positional system, making it more similar to a Borda method than either IRV or RV. I'm not sure how great of change this would be over traditional Borda, although as ranked methods go, Borda is pretty good.

http://rangevoting.org/BayRegsFig.html

But it does run in to tactical problems with larger number of candidates.

http://rangevoting.org/rangeVborda.html

Although, again, I'm not sure how much of that analysis changes with these non-linearly-decreasing point values. This page has some theorems applicable to all weighted-positional systems:

http://rangevoting.org/WtPositnl.html