I have $n$ tasks that I wish to delegate to $m$ independent individuals, where $m$ is a factor or divisor of $n$. Each of the tasks $T_{1} ... T_{n}$ is independent. From the following two extremes, which or what in between, is the optimal solution?
1) Highest quality, least efficient: assign $T_{1}$ to all $I_{j}$ (where $j = 1, 2, 3,..., m$) and choose the best result; move onto $T_{2}$ and do similarly; repeat for all $T_{i}$ (where $i = 1, 2, 3,..., n$).
2) Most efficient, lowest quality: assign $T_{1}$ to $I_{1}$, $T_{2}$ to $I_{2}$, and so on for $T_{m}$ to $I_{m}$. Decide which results are of sufficient quality, then assign $T_{m+1}$ to $I_{1}$, $T_{m+2}$ to $I_{2}$ and so on until $T_{n}$ is assigned to $I_{n}$
The primary objective is to get as many $T$ finished and of satisfactory quality in a given time $t$.
I hope this reformulation of your problem is close to what you meant. You have $n$ tasks $T_1,\ldots,T_n$ and $m$ workers $I_1,\ldots,I_m$. Worker $I_i$ will perform task $T_j$ in time $t_{ij}$ (which is known in advance), but the result may or may not be of sufficient quality: the probability that it is of sufficient quality is $p_{ij}$, independent of the results of other workers on this task and this worker on other tasks (and of the assignments that are made). Let $X_{ij}$ be the decision variable, $1$ if worker $I_i$ is assigned task $T_j$, $0$ otherwise. Then the probability that at least one worker completes task $T_j$ with sufficient quality is $1 - \prod_{i}(1 - p_{ij} X_{ij})$. The objective is to maximize the expected number of tasks completed with sufficient quality, which is $$ \sum_{j} \left(1 - \prod_{i} (1 - p_{ij} X_{ij})\right)$$ In order for everything to be completed by time $t$, you have the constraints $\sum_j t_{ij} X_{ij} \le t$ for every $i$.
This problem is a nonlinear integer programming problem. It may be quite difficult to find an optimal solution, but methods to get nearly-optimal solutions (e.g. simulated annealing or tabu search) may be useful.