I decline to participate in anonymous employee surveys, unless I am forced to.
My reasoning is as follows.
Anonymous surveys are meant to be a way to provide feedback of one's direct manager and the department of a company as a whole, but the anonymous survey situation places employees in a game-theoretic conflict between one another and their manager, in which the survey feedback is always useless.
Organizations have an understandable desire to keep managers accountable and make sure employees feel their concerns are heard by upper management. The purpose of the anonymous survey is to solve this problem by allowing employees to discretely signal discontent with their direct manager in a way that does not risk retaliation.
However, because of the way these surveys are used, they completely fail in this function. Although it is anonymized, survey data is agreggated and presented to managers in a way that makes it obvious if a minority viewpoint is expressed. Since most teams are small, a single dissenter will be obvious from the data. Aggregate scores are then used to evaluate managers. If a manager recieves a non-positive score, they will naturally want to know which employee is skewing their score results, and will have little difficulty determining who wrote what "anonymous" feedback.
Thus, from an employee's point of view, giving anything but positive feedback will result in risk to their income and health insurance, since their manager will attempt to to find the uncooperative employee. Employees are aware of this risk and respond in a self-protective way by giving only overwhelmingly positive scores, even if they are discontent.
I have personally filled out "anonymous" surveys with positive feedback about my manager, only to resign weeks later when I received another job offer. In this case I was not actually content with my manager and the team direction but the survey gave me no way of expressing that without risk of retalliation.
Employees are coerced into giving positive feedback. Coerced feedback is no feedback at all, since the whole point of the survey is to allow for employees to discretely communicate feedback about their direct manager. This is not possible when the employee has reason to suspect the manager will read their comments and begin a witch hunt against them.
This is not a theoretical concern. I have personally sat in meeting rooms while managers went through survey feedback trying to determine which employee wrote it, so they could "address" (i.e. punish) the discontent person.
Even if I am happy with my manager and team and give a high rating, this is meaningless because I could not do otherwise. The survey is not worth filling out whether I am content or discontent with my manager.
In conclusion, I choose not not fill out employee surveys because they are not useful for anyone, ever, in any circumstances. I am not sure why these surveys are used. My only feedback on such surveys is I would prefer that we discontinue their use entirely.