Retrieve the Hidden Leaves in the Forest: Prevent Voting Spamming in Zhihu

Abstract

Nowadays, more and more people start posting their opinions on online social networks, such as commercial product evaluation websites, forums, and crowdsourcing $Q \& A$ websites. In practice, most majority vote schemes cannot reveal the true distribution of opinions, due to the spam problem. Many public relationship companies can recruit people or use automatic commenting machines to promote target products and ruin the reputation of their opponents. In such a sense, the opinions on these websites may not be reliable. In the literature, there are a lot of studies contributed to detect such spams, based on the characteristics of posted content, social relationship, user activity, posting time, etc. We find that most spam detection schemes rely heavily on the experience and preference of experts. This is dangerously as it can lead to bias and dictatorship. In this work, we take Zhihu - one popular Chinese $Q \& A$ website as a case study, and propose a time diversity based voting scheme to reduce the impact of voting spamming. We illustrate that, our proposed opinion tolerant system can maintain a good balance in the appearance of different opinions.

A Definition of Diversity of Visibility

In order to formally evaluate the appearance of the diversity of answers, we borrow the concept of the true diversity from [24]. Considering a set of groups G and supposing the proportion of each group $g_i \in G$ is $q_i$, the true diversity with 1-mean is

$$\begin{aligned} D=\exp \left( -\sum _{g_i \in G} q_i \ln (q_i) \right) . \end{aligned}$$

(12)

A large number of true diversity indicates that there is a good balance between the proportion of species.

In our case, the diversity is not only related with number of answers in different groups, but also their positions. Let us denote the position of an answer a under the ranking policy p as L(a, p). We consider the fact that the visibility of an answer decreases with the decreasing of its position. Therefore we define the visibility index of an answer at position L as $\lambda ^L$, where $\lambda$ is the decay factor, under the assumption that there is an exponential decrease of visibility by rankings. For a set of answers N, we denote the set of its groups as G(N), such that

$$\begin{aligned} \nonumber&\forall g \in G(N), g \in 2^{N} \\ \nonumber&\forall g_i,g_j \in G(N), g_i \cap g_j = \varnothing \\&\cup _{g \in G(N)}=N. \end{aligned}$$

(13)

The total visibility index of each group $g \in G(N)$ is

$$\begin{aligned} V(g,p)=\sum _{a \in g} \lambda ^{L(a,p)}. \end{aligned}$$

(14)

The corresponding visibility ratio of each group $g \in G(N)$ is

$$\begin{aligned} q(g,p)=\frac{V(g,p)}{\sum _{g' \in G(N)} V(g',p)}. \end{aligned}$$

(15)

Then the diversity of visibility of a set of answers N under the ranking policy p is defined as the true diversity of the visibility of groups. Formally, it is defined as

$$\begin{aligned} D_{vis}(N,p)= \exp \left( - \sum _{g \in G(N)} q(g,p) \ln \left( q(g,p) \right) \right) . \end{aligned}$$

(16)