What is degree of dissociation for polyprotic acids?
I think this resembles the question Confused about strong/weak dibasic and tribasic acids?
Saying that the degree of dissociation $(\alpha)$ of citric acid is greater because its triprotic is not correct. The degree of dissociation should be calculated for each dissociation separately. The degree of dissociation of citric acid's first dissociation $\ce{C6H8O7 &lt;=&gt; C6H7O7- + H+}$ is greater than that of acetic acid, because its $\mathrm{p}K_\mathrm{a}$ is smaller (3.13 vs 4.76)$^1$, meaning it's a stronger acid.
The second value of $\alpha$ for citric acid, however, will be very to close to acetic acid's, because the second dissociation has approximately the same $\mathrm{p}K_\mathrm{a}$ (4.76)$^1$. The third $\alpha$ will be smaller, since the $\mathrm{p}K_\mathrm{a}$ of the third dissociation is greater (6.40)$^1$.
This can be seen in the common polyprotic acids dissociation graphs, like this one (source):

Note that $\alpha$ is represented on the $y$-axis in a 0-1 scale. For each of the four states of the molecule, there is a different $\alpha$, and different values of $\alpha$ happen simultaneously.
$^1$ $\mathrm{p}K_\mathrm{a}$ values taken from Wikipedia.