WikiPeerMeeting 06/16/06

Preliminary Meeting Notes

A link to the pdf, which looks much better than the below. The SFI wiki does not have LaTex math enabled, as far as I can tell.

However, my wiki does. (Thanks Ross!) So here is the link to the corresponding page on my wiki. The math comes out a little strange sometimes, but at least it works. From now on, if there is work I type that includes math, I will just link to my wiki.

Here is the plaintext, just in case the math gets switched on:

Overview

Consider a system in which all of the individuals in the system are able to vote on the reputation level of each of their peers. We are looking at two different voting models: one where the weight on an individual's vote is independant of his skill level, and one where the weight depends on the individual's reputation, which is correlated with his skill level.

<Note: this paragraph sucks big time> This difference can be compared to the difference between the structure of the online encyclopedia, Wikipedia, and the online news service Slashdot. On Wikipedia, each person is equally able to contribute. On Slashdot, each member is able to vote based on how well his postings are ranked by his fellow individuals.

• N individuals (nodes)
  • Initially these individuals are placed on a fully connected graph.
  • Eventually, we would put them on social networks with different topologies.
• Each individual, i, has a real skill level, denoted $\omega _{i}\in [0,1]$. We call those with $\omega _{i}>.5$ high ability and those with $\omega _{i}<.5$ low ability.
• The skill level of i is observed noisily by his neighbors on the social network. The signal to person j about person i's ability level is $S_{ij}(\omega _{i},\omega _{j})=\omega _{i}+\epsilon (\omega _{j})$, where $\epsilon (\omega _{j})$ is the level of noise in the signal observed by j. Note that the level of noise depends on the ability level of the observer. We assume that observers of high ability have less noise in their signal, and thus are better able to assess the abilities of others. That is, ${\frac {d\epsilon }{d\omega _{j}}}<0$.
• In each period, j takes his signal from i and incorperates it into his evaluation of i's reputation. He does this using a Markov Chain: $R_{ij}(t)=\beta R_{ij}(t-1)+\beta S_{ij}(t)$ where $\beta$ is the weight that the individual puts on past experiences. This parameter could be thought of as the persistence of past experiences, or as memory.
• Based on the updated reputation value, j votes on the skill level of his neighbors on their social network. He either votes that the individual is of high ability ($V_{ij}(t)=1$) or low ability ($V_{ij}(t)=0$) according to whether $R_{ij}(t)$ is greater or less than ${\frac {1}{2}}$.
• These votes are tallied for each person. They are either unweighted (each neighbor's vote counts equally) or weighted by the individual's reputation in the previous period (vote importance correlated with ability).
  • In both systems, if the vote is greater than .5, then the individual is deemed to be of high ability. Otherwise, they are deemed to be of low ability.
  • In the weighted voting system, the talley from the previous period becomes the individual's weight in the next period. That is, $\alpha _{i}(t)=\sum {\frac {\alpha _{j}(t-1)}{d_{i}}}V_{ij}(t)$.
• We are measuring how well individuals in the system determine the ability level of their neighbors through reputation. Thus we measure the percentage of the N individuals who were correctly identified as low ability or high ability.

Pseudo Code:

Each step:

1. For each individual, j:
   1. Calculate the observed signal that individual j receives from each of his neighbors, i, according to $S_{ij}(\omega _{i},\omega _{j})=\omega _{i}+\epsilon (\omega _{j})$.
   2. Based on that signal, calculate j's beliefs about each i, according to $R_{ij}(t)=\beta R_{ij}(t-1)+(1-\beta )S_{ij}$
   3. Cast a bianary vote for each of j's neighbors based on $V_{ij}(t)=1$ if $R_{ij}(t)\geq .5andV_{ij}(t)=0ifR_{ij}(t)<.5$.
2. Calculate the wieghted vote for each individual according to $\alpha _{i}(t)=\sum _{j=1}^{d_{i}}{\frac {\alpha _{j}(t-1)}{d_{i}}}V_{ij}(t)$
3. Update everyone's weight, $\alpha (t)$

---

WikiPeer Group