Adaptive response sampling for surveys

[annikaschmid]

Feature request

We currently allow %-based rollouts for surveys, as well as the option to set a response limit.

For some users with high volumes, that's not enough. Here is what we've heard:

• Being able to specify a response limit per time period, e.g. "250 responses per month", or "7 responses per day"
• Ideally, PostHog would adapt the rollout of surveys across the time period specified by the user, e.g. when a user wants 250 responses over a one-month period, we make sure they receive approximately 8 responses per day

One proposal how this could be achieved from @neilkakkar: "I think the naive targeting all users and adjusting the rollout % based on how many responses have been received so far would work pretty well - and better than trying to extra optimise it based on several other factors / guestimating cohort sizes who are active.. This is also reasonably straightforward to implement - we have all the pieces in place already."

More details in this Slack thread here: https://posthog.slack.com/archives/C07QD3LT8U9/p1728406374642269

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