It has nothing to do with the plugin. There are problems with your JS on your site https://codex.ww.wp.xz.cn/Using_Your_Browser_to_Diagnose_JavaScript_Errors.
litres_plugin.js:2 Uncaught TypeError: $(...).live is not a function
You need to fix it before the plugin can work.
Also you are using a caching plugin, WP-Polls is not designed to work with caching plugin, so you will get weird behaviour.
Thank you for so prompt support. But I did nothing with the code, I have only installed the last version of WP Poll recently. The previous version of the plugin has worked correctly. Has the mistake you mentioned existed already? Thanks a lot in advance.
I just updated my reply, take a look.
Really, it has started working! I was a conflict with some other plugin.
Thank you very much for your quick support, Lester!
I like the plugin and also the note on the Java script error was useful to me. Thank you