How to choose negative examples for recommendation system?
Yes, we should include negative samples, more so to correct selection or sampling bias. 

The user would have seen only a subset that is selected by another algorithm or rules which decided that the subset is most relevant to the user. Of that, position bias kicks in and the user may not see everything. So the choices within a query or the documents within a query are likely to be very similar to one another (perhaps small differences). This makes it diff for the algorithm to learn the parameters. 

Whereas while scoring in production, almost all choices/documents have to be scored for each query. UNLESS the old model is used first to select a subset of hotels and if learning-to-rank model reranks among the subset. 

In my experience adding negative samples (that we can safely tell that user would not have picked/clicked the item even if he/she saw the item) helps. But it is difficult to define such base for all use-cases. 

We are still experimenting with this.