I have four voters: $A$, $B$, $C$, and $D$.
\begin{align*} &A\ \text{has}\ 6\ \text{votes}\\ &B\ \text{has}\ 6\ \text{votes}\\ &C\ \text{has}\ 2\ \text{votes}\\ &D\ \text{has}\ 1\ \text{vote} \end{align*}
I have to find out a quota such that $D$ in only a dummy voter, i.e. adding it to a losing coalition still makes it losing coalition. But I think there is no such quota. I tried every number from $1$ to $10$ and it makes no sense that there is quota provided that $D$ is only dummy voter.
Below I list the coalitions which do not contain $D$ and label them $K_1, K_2, \dots, K_8$. I use $|K_i|$ to denote the number of votes coalition $K_i$ has.
\begin{align*} K_1 = \{A, B, C\} &\quad |K_1| = 13\\ K_2 = \{A, B\} &\quad |K_2| = 12\\ K_3 = \{A, C\} &\quad |K_3| = 8\\ K_4 = \{B, C\} &\quad |K_4| = 8\\ K_5 = \{A\} &\quad |K_5| = 6\\ K_6 = \{B\} &\quad |K_6| = 6\\ K_7 = \{C\} & \quad |K_7| = 2\\ K_8 = \{\ \} &\quad |K_8| = 0 \end{align*}
Adding $D$ to any of these coalitions increases the total number of votes by one. So we need to find a number $Q \in \{1, \dots, 14\}$ such that if $|K_i| < Q$ (i.e. coalition $K_i$ doesn't make quota), then $|K_i| + 1 < Q$ (i.e. coalition $K_i$ together with $D$ doesn't make quota).
Example: $Q = 9$ does not work. Coalition $K_3$ is a losing coalition, but if $D$ was added to the coalition, it would become a winning coalition. Therefore, $D$ is not a dummy voter.
You should be able to find a value of $Q$ that does work (I think there are eight different possibilities).