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Social Choice and Beyond
Sunday, September 23, 2007
Fractal Voting
Mood:  happy
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Topic: Fractal Voting

Fractal Voting (FV) is a voting method I developed. It is one of a class of utilitarian methods similar to range voting (RV) in some respects. Other utilitarian methods are approval voting (AV) and Evaluative Voting (EV). RV, AV and EV are all special cases of FV. Utilitarian voting methods involve a ranking of candidates or alternatives from most preferred to least preferred. In general there are two types of rankings: ordinal and cardinal. Ordinal ranking involves a list such as ABCD where the position of the letter, for example, indicates its preference ranking in this case A is preferred to B is preferred to C etc. Cardinal ranking also indicates how much A is preferred to B and how much B is preferred to C etc. This "how much" is also referred to as preference intensity. With utilitarian methods  numbers are usually asssigned to the candidates and the differences between the numerical rankings of two candidates indicate the preference intensity. One of the differences between FV and RV is that voters don't assign numbers to the candidates but indicate  preference intensities graphically.

Fractal Voting consists of a graphical user interface (GUI) or we could call it a graphical voter (GVI) interface (we will use the terms voter and user interchangably) and underlying software which translates the voter's preferences into numerical values which can then be used to sum up the votes for  each candidate and  determine the winner. Range Voting involves a system defined scale such as 0-99, 0-9 etc. The voter assigns a number contained in this scale to each candidate, and then the numbers are summed for each candidate to determine the winner. With Fractal the voter determines the scale and the scale can be more finely determined or less finely determined in different segments as the voter wishes. For example, if the voter wants to differentiate among candidates near the top of the scale more finely, he or she can subdivide that portion of the scale more finely in order to make these distinctions. The fineness of the scale is called the sensitivity level.  The sensitivity level, in general, will differ for each voter depending on how finely a voter can distinguish between two candidates or alternatives. This concept can be generalized to include fine distinctions between tastes or smells for example. A person might be asked to distinguish and rank several wines. Some people would be able to distinguish them very finely and others would only be able to make rough distinctions, say between good and bad.

With RV, the system defines the sensitivity level which is the same for all voters. RV with a scale 0-99 has a higher sensitivity level than RV  with a scale 0-9 and allows finer distinctions among candidates to be made. For example, candidates A and B might each be given ratings of 5 with RV (0-9) but given ratings of 51 and 57 with range (0-99). So finer distinctions can be made the more levels are available. With Fractal, the user or voter has complete control over the sensitivity which is variable over the whole scale. For instance, at the beginning of the voting process, the first thing a voter would do is to choose the number of levels he or she would like to start out with. This might be just two - good and bad. So there would be two "buckets" if you will, the good bucket and the bad bucket. All candidates in the good bucket would be indistinguishable from or indifferent to each other.

However, before choosing the number of levels or buckets, the voter would first choose their most preferred or favorite candidate or candidates and least preferred candidate or candidates. Then all others would be relative to those. So initially a screen would be presented to the voters with two buckets - one for most preferred and one for least preferred. The voter would drag appropriate candidates onto these buckets from a list arbitrarily located on the right side of the screen. Then the voter would choose how many buckets or levels to start with. Please note that, if the voter chose 100 buckets and didn't go any deeper or finer than that in terms of sensitivity level, the voting method would be the same as RV. After the initial choice of number of buckets, that number of buckets appears on the screen as well as the buckets at either end denoting most preferred and least preferred. Now the voter drags other candidates from the list onto the buckets. Then the voter has the option of clicking on any one of the buckets and further subdividing this segment of the  scale. Let's say that the voter started with 10 buckets and in all but one bucket there is only one candidate. In one bucket there are 4 candidates. Thhe voter may choose to click on that bucket and then choose to subdivide that bucket alone into, for instance, 4 finer levels. These buckets then appear on the screen along with the list of the candidates who were in the original bucket. The voter then drags candidates from this list onto one of the buckets that represent subdividions of the original bucket. This process can be repeated indefinitely leading to finer and finer distinctions. When the voter is satisfied he or she can terminate the process and submit his or her vote.

The final vote can be printed out as a paper ballot showing an overall scale subdivided as the voter has indicated and all candidates listed in order of preference, preference intensity and fineness of distinction or sensitivity. The underlying software can be implemented in terms of a push down stack where the first word in the stack contains the number of words in the stack. Initially, this would be 2 for most preferred and least preferred. These words might contain the numbers 1 and 0, respectively. As the voter adds levels or buckets, words are added to the stack.  The stack would be popped up to the level where the voter indicates that he or she wishes to add levels, and then the number of levels added that the voter has indicated. For instance, if the voter initially wants to order candidates just in terms of good and bad (a binary decision), two words would be added to the stack between the words corresponding to least preferred and most preferred. One might contain the number 1/4 (corresponding to the mid-point of the "bad" bucket) and one might contain 3/4 (corresponding to the mid-point of the "good" bucket). Continuing on in this way, the buckets are each defined in terms of a numerical value in a process that is totally transparent to the voter who just has to deal with a simple GUI and repeat the same process over and over to as many levels as he or she wishes. Then each candidate is associated with a pointer that points to the appropriate numerical value in the stack.

Since the process is the same for the voter no matter how deeply he wishes to proceed in terms of sensitivity level, we call this method Fractal Voting. Think of it as branches on a tree some of which are subdivided into smaller branches which are further subdivided and so on. At each stage the voter performs the same steps so the process is simple and intuitive for the voter.  This is the essence of the fractal process: no matter what the depth, the procedure is the same. At completion each candidate will be asssociated with a pointer which represents his numerical rank. The pointer will point to a word in the stack which will contain a value between 0 and 1 which represents the intensity  of that rank. Note that, unlike RV, the voter never has to assign numerical values to candidates making the provess simpler and more intuitive akin to punching a hole on a ballot or putting a check mark next to a candidate. When all voters have submitted their ballots, the numerical values associated with each candidate are summed and the one(s) with the highest value win(s).

The advantages of Fractal over Range are the following:

1) There are no "partial strength" votes. A partial strength vote is submitted in Range when a voter does not pin his most (least) preferred candidates to the limits of the range.

2) The voter has a simpler and more intuitive while at the same time more sophisticated interface which allows him or her more options in the voting procedure.

3) The voter can choose his or her own sensitivity level and can continue to refine this as the voting process continues.

4) The voter can go into detail selectively in those parts of the overall ranking that concern him or her while doing a rough ranking in other parts of the overall scale.

5) The voter need not be concerned with numbers at all, but only with a visual on-screen representation of the preference rankings and intensities.

Fractal Voting lends itself to delegable proxies since various parts of the tree could be designated and filled in by trusted parties who have pre-voted and whose results are only a mouse click away. For instance, the voter could select certain candidates, indicate he wished to make a proxy vote and then select Ted Kennedy from a list of proxies. Then these candidates would be added to the screen in exactly the way that Ted Kennedy had previously indicated he would vote. This method would lend itself either to touch screen or computer screen voting. Security of the vote could be guaranteed by different methods, but this is really a separate issue. Issuance of a paper ballot and receipt would be a start.

In summary Fractal Voting is a generalization of AV, EV and RV and a voter could choose to vote in any of these styles if so desired. It is a utilitarian voting method since the placing of each candidate on a line in order of preference ranking and intensity reveals the voter's utility for each candidate in some sense. Social utility could be measured for each candidate by simply adding up the numerical values asssociated with that candidate in the stack over all voters. This would not represent a social utility in an absolute sense but in a relative sense. The voter is allowed to make either fine or rough distinctions among the candidates according to his or her sensitivity levels and/or knowledge of the candidates, and also to rely on the advice of trusted experts who have studied the issues and/or candidates more closely. Both the GUI and the underlying software are easily implemented.

Posted by jclawrence at 11:08 AM PDT

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