The relationship between a Rating and a Scorecard

[PrettyGoodFreedomTech]

The relationship between a Scorecard and a Rating is of vital importance to the proper functioning and ultimate power of the grapevine. Any individual Scorecard is calculated from a list of Ratings as a weighted average, using the GrapeRank algorithm. A Scorecard (calculated by Alice) can then be "interpreted" (by Bob) as a Rating as discussed below and then utilized in another round of graperank processing. The ability to string results together in this fashion, to put them in series, is at the heart of the grapevine protocol. For this thread, I will call this property the composability of the grapevine. Maybe I'll think of a better name later. (The length of the longest chain in a worldview also needs to have a name. The worldview depth perhaps? Also, the presence or absence of any closed loops is going to be a topic of great interest.)

I wish to make the case that the dimension of a Scorecard and the dimension of a Raring, dim(Scorecard) and dim(Rating), are each 5. These are defined as the smallest number of fields that we must keep track of for the grapevine algorithm to work. Any attempt to keep track of less than 5 dimensions will destroy its composability and will greatly diminish the utility of the grapevine algorithm.

Definitions

The grapeRankRatings and grapeRankScorecards tables, as created in sql here, consist of the following columns of central significance, once we strip away extraneous columns like id, timestamp, etc:

Rating:

• rater
• ratee
• score
• confidence
• context

Scorecard:

• observer
• observee
• confidence
• influence
• average
• confidence
• input

Note that a Rating has 5 fields, each of which is a number or a string. We will say that a rating has a dimension of 5.

A Scorecard has 7 fields. At first glance, one might say it has 7 dimensions. However, it turns out that the Scorecard also has a dimension of 5, when one considers that confidence can be calculated from input (assuming rigor is a given), and influence can be calculated from confidence and average. Thus, it really only takes 2 values, average and input (or average and confidence), to communicate influence, average, confidence, and input. The reasons all 4 are stored are that each of these 4 numbers may have its own interpretation and utility, which means we will want all 4 of them, and it may turn out that different grapeRank protocols may calculate those numbers in slightly differing ways. If storage space is limiting, in principle it is sufficient to store only two of those four numbers for each Scorecard, but this must presume that the standard grapeRank algorithm is used universally and that rigor is the same for each Scorecard and is communicated separately.

The atom of a rating and the atom of a scorecare are the three elements that are used to address the score card uniquely:

atom of a rating:

• rater
• ratee
• context

atom of a scorecard:

• observer
• observee
• context

Equivalence

First of all, a Scorecard and a Rating are not the same thing. Not the same thing at all.

And yet ... there is an equivalence between them, in the sense that a Scorecard has a natural interpretation as a Rating, as follows:

• observer -> rater
• observee -> ratee
• context: unchanged
• rating -> score
• confidence: unchanged

Utility

Equivalence will turn out to have very important application as a mechamism of privacy protection.

Discussion

Think of a Scorecard as being what you get when you take some set of Ratings, and you squish them together into just one Rating. In the process, you may lose a lot of information. It is worth asking: what is the maximal amount of information that we can throw away without the algorithm becoming unusable? Asked another way: what is the minimal amount of information that must be kept?

The answer is that a maximally squished Scorecard will contain exactly the same amount of information as a Rating. Five fields, each of which is a string or a number. Any more than that is nice to have, but unnecessary. Any less than that, and the entire algorithm falls apart, in the sense that it becomes impossible to string them together in a series.