Given a set of numbers $Q = \{q_1,q_2,\cdots,q_n\} \subseteq (0,1]$.
The product $\prod\limits_{q_i\in Q}{q_i}$ gets smaller and smaller when the cardinally $|Q|$ increases.
That is, $\prod\limits_{q_i\in Q}{q_i} \geq \prod\limits_{q_i\in Q^*}{q_i}$ where $Q \subseteq Q^*$, where $Q$ and $Q^*$ are defined like above.
Is there a name for this mathematical property?
You can see this as a special case of monotonicity, or order-reversing:
Let $\mathscr{P}$ be the set of finite sequences $(q_1,\ldots,q_n)$, with $0<q_i\leq 1$. It comes with a natural order, given by initial subsequences, i.e., $(q_1,\ldots,q_n)\leq(q_1,\ldots,q_n,q_{n+1},\ldots,q_m)$.
We have a function $\pi:\mathscr{P}\to[0,1]$, given by $\pi(q_1,\ldots,q_n)=\prod_{i=1}^nq_i$. The property you stated means that $$Q_1\leq Q_2\implies \pi(Q_1)\geq\pi(Q_2)$$ which means that the function $\pi$ is order-reversing.
See Wiki for more details on order structures.
Remark: I chose to consider sequences instead of subsets of $\mathbb{R}$ so that we can have repeated numbers among the $q_i$'s. You could do similar analysis with finite subsets of $(0,1]$ and again obtain an order-reversing function $\pi:\{\text{finite subsets of }(0,1]\}\to(0,1]$.