anonymous voting using poll module invalidates cache
After hours of testing, it looks like the Advanced Poll module does the job. Here is an excerpt about it from the module's project page:

... a replacement to Drupal's poll module and provides multiple voting systems, decision-making tools, and management options.

Voting systems: Basic polls, Approval Voting, Borda Count, and Instant-Runoff Voting.
Vote management: view each user's vote, delete all votes, or restrict the poll to a list of users.
Time management: schedule when to open or close the poll, and choose when to show results.
Choice management: write-in choices, and support for HTML (or other input filter).
Usability: fast Ajax interaction and customizable default settings.
Migration: convert regular Drupal polls into Advanced Polls.