Why is a single element getting better results than the sum?

I need an intuition how this is possible - Imagine I have a DAG(directed acyclic graph), so a graph without cycles and only directed edges;

Now for every DAG with $$d$$ nodes there is (at least) one topological order $$\pi:1,...,d$$ such that for every $$j$$ being an ancestor of $$i$$ it also holds that $$j, so that $$j$$ is before $$i$$ in the topological order; (follows directly from the fact that edges are directed and there are no loops)

Now I have a model defined on the graph, namely $$X_1,...,X_d$$ is such that:

$$X_i=\sum\limits_{j \in \text{an}(i)}c_{ji}X_j+\varepsilon_i,$$

where $$\varepsilon_i$$ is some positive and continous innovation, $$c_{ji}>0$$ and an$$(i)$$ are the ancestors of node $$i$$ - now given some data sample $$X^1,...,X^n \in \mathbb R^d$$ I want to estimate the topological order;

Since $$X_i/X_j \geq c_{ji}$$ if $$j$$ is an ancestor of $$i$$ and $$0 \leq X_i/X_j \leq 1/c_{ij}$$ if $$i$$ is an ancestor of $$j$$ it might be resasonable to define a matrix $$A$$ with entries $$a_{ji}=\bigwedge_{k=1}^nX_i/X_j$$ and try to find the topological order $$\pi$$ such that:

$$\max_{\pi \in \Pi}\sum\limits_{\pi(j)<\pi(i)}a_{ji}$$

Also we could based on the same idea minimize the value which is NOT in our topological sort, namely:

$$\min\max_{\pi(j)>\pi(i)}a_{ji}$$

Both have the same approach but the sum should be more robust - however when I test it, the sum leads to worse results which I dont really understand;

Anyone an idea?