I like to think about it this way. By not explicitly imposing a prior, you are implicitly imposing a prior that each item will receive no votes. This is totally non sensical because of course these items will get votes.
Just because we don't know what the true value of p will be doesn't mean we don't have some expectation. If I asked you what you expect the popularity of a given item will be, you won't say 0, you'll say something like the average. So why assume all items will have 0 votes in our model?
Just because we don't know what the true value of p will be doesn't mean we don't have some expectation. If I asked you what you expect the popularity of a given item will be, you won't say 0, you'll say something like the average. So why assume all items will have 0 votes in our model?