Step 1: Understand what is asked.
We must find the oxidation state of iodine in the ion $I_3^-$. This ion has three iodine atoms joined together and carries a total charge of <-1>.
Step 2: Recall the basic rule.
For any ion, the sum of the oxidation states of all atoms must equal the total charge on the ion. This is just charge bookkeeping.
Step 3: Set up a simple equation.
Let the oxidation state of one iodine atom be $x$. There are three iodine atoms, so together they give $3x$. The whole ion has charge $-1$.
\[ 3x = -1 \]
Step 4: Solve for x.
Divide both sides by 3:
\[ x = -\frac{1}{3} \]
So the average oxidation state of each iodine is $-\tfrac{1}{3}$.
Step 5: Understand why it is a fraction.
A fraction looks odd, but it is just an average. The three iodine atoms are not all the same. The value $-\tfrac{1}{3}$ is the mean spread over the three atoms, which is what this kind of question wants.
Step 6: Pick the answer.
The value $-\tfrac{1}{3}$ matches option 1.
\[ \boxed{-\tfrac{1}{3}} \]