# Reputation-Based Blockchain for Spatial Crowdsourcing in Vehicular Networks
## 3 Reputation-Based Honest Blockchain Pool Mining
### Local Reputation  
After \(n\)-th times pool mining, the local reputation \(R_{j}(n)\in[0,1]\) of miner \(j\) can form a set of local reputation, which is \(R_{j}=\left[R_{j}(1),R_{j}(2),\cdots,R_{j}(n)\right]^{T}\). The reputation stems mainly from an evaluation of the historical behaviors and interactions. Consider that the local reputation evaluation consists of two parts: objective reputation \(R_{j}^{O}(n)\) (see in Section 4.2) obtained via successful pool mining and subjective reputation \(R_{j}^{S}(n)\) comes from the subjective reputation evaluation among all miners, which is collected from the interaction during the calculation/verification process when the blockchain crowdsourcing task is executed [25]. Accordingly, historical interaction records in recent \(n\) times are utilized to develop individual evaluation of subjective reputation \(R_{j}^{S}(n)\), which is a process of information fusion based on subjective beliefs. Note that for a rational miner \(j\), positive and honest evaluations can increase the positive effects. Since miners can also post crowdsourcing tasks as customers, such subjective reputation evaluation is of considerable significance as reference. There exist various forms of interactions among miners, such as information exchange and data sharing. Assuming that the subjective reputation evaluation of miner \(j\) to the other members is \(W_{j\rightarrow-j}=\{b_{j\rightarrow-j},d_{j\rightarrow-j},\gamma_{j \rightarrow-j}\}\), where \(b_{j\rightarrow-j},d_{j\rightarrow-j},\gamma_{j\rightarrow-j}\in[0,1]\) are honest, dishonest and stochastic coefficients, respectively. Since \(b_{j\rightarrow-j}+d_{j\rightarrow-j}+\gamma_{j\rightarrow-j}=1\), then we have  
\[\left\{ \begin{array}{l}b_{j\rightarrow-j}=\gamma_{j\rightarrow-j}\frac{ \theta_{j}}{\theta_{j}+\theta_{j}}\\ d_{j\rightarrow-j}=\gamma_{j\rightarrow-j}\frac{\theta_{j}}{\theta_{j}+ \theta_{j}}\\ \gamma_{j\rightarrow-j}=s_{j\rightarrow-j}\end{array} \right. \tag{1}\]  
where \(\theta_{j}\) and \(\theta_{j}\) are the positive/honest and negative/dishonest evaluations, respectively. Then, \(s_{j\rightarrow-j}=s(\alpha_{j},n)\) is the uncertainty, which is positively correlated with the computational capability proportion \(\alpha_{j}\). Subjective logic introduces the notion of uncertainty, the belief that individual miners may be in super- or partially overlapping states, to study the effect of parameters on the model. According to the subjective logic model [34], the stronger computational capability would lead to higher reputation, then the miners are less affected by subjective reputation evaluation, so the malicious evaluation of selfish miners will have less negative impacts on them. Furthermore, \(j\rightarrow-j\) is the objective evaluation of \(j\) from all nodes except miner \(j\). \(\alpha_{j}\) is the computational capability proportion upon the whole blockchain. Moreover, \(\alpha_{j}=\frac{s_{j}}{\sum\limits_{j\in\mathcal{M}}\frac{s_{j}}{s_{j \rightarrow}}}\) is mainly determined by the CPU capability and hardware basics, where \(s_{j}\) is the computational resource of miner \(j\). We denote the computational resource proportion of miner \(j\) as \(\alpha_{j}\) and \(\alpha^{(i)}\) depicts the computational capability proportion of pool \(i\) among the whole blockchain network. To simplify computation, we usually utilize local reputation to characterize reputation for most tasks. This is mainly because local reputation is more informative for simple tasks, and comprehensive reputation can be easily calculated from local reputation. Furthermore, the miner \(j\) means the miner labeled \(j\) in the blockchain network, and pool \((i)\) is the \((i)\)-th pool, where the superscript \((i)\) and subscript \(j\) represents the pool \(i\) and the miner \(j\).