ArgMax : Variable Domain Error

I’m attempting to utilize the ArgMax function, but am receiving the error "ArgMax::vdom: Variable domain … should be either Reals or Integers."

ArgMax[{objective, cons == 1}, assign, {assign} ∈ {0, 1}]

As a quick overview, we have edges denoted $ e_{i,j}$ in $ \mathbb{R}^3$ , and we want to assign an integer value of 0 or 1 to each such that their sum is at most 1 for each set of edges. So, objective is defined as a set of sets as summations with constant coefficients $ objective = \{\{3e_{\{4, 2, -2\}, \{1, 3, 1\}\}} + 2e_{\{4, 2, -2\}, \{2, 1, 1\}\}}\}, \{7e_{\{5, 3, -1\}, \{-2, 6, -1\}\}} + 6e_{\{5, 3, -1\}, \{-1, 4, -2\}\}}\}\}$

We also have a set of sets for constraints defined as $ cons = \{\{e_{\{\{4, 2, -2\}, \{1, 3, 1\}\}} + e_{\{\{4, 2, -2\}, \{2, 1, 1\}\}}\}, \{e_{\{\{5, 3, -1\}, \{-2, 6, -1\}\}} + e_{\{\{5, 3, -1\}, \{-1, 4, -2\}\}}\}\}$ .

Lastly, we have the variables defined in $ assign = \{e_{\{\{4, 2, -2\}, \{1, 3, 1\}\}}, e_{\{\{4, 2, -2\}, \{2, 1, 1\}\}}, e_{\{\{5, 3, -1\}, \{-2, 6, -1\}\}}, e_{\{5, 3, -1\}, \{-1, 4, -2\}\}}\}$ .

I’m new to Mathematica, so this may be a trivial fix, but if anyone can point out my error, I would greatly appreciate it.